Richard Feynman was a serious physicist who loved to answer unserious questions. Can math tell you how to order the optimal lunch? Can a human track scents like a bloodhound can by smelling his own footprints? Now, researchers have picked up one of Feynman's most curious unanswered questions by looking at the physics of "silly" sprinklers.

A typical lawn sprinkler with an S-shaped nozzle spins in a given direction as it spews water from its two openings. But if you throw that sprinkler into a swimming pool and hook it up to a vacuum so it sucks water in instead of spraying it out, which way will it spin — the same direction as before, or the opposite?

Feynman posed that question as a Princeton graduate student in the 1940s. According to Feynman's telling, he rigged a glass sprinkler in his university's lab. It gave a brief "tremor," then barely moved even as he raised the pressure. He repeated the process until the glass shattered, leaving the answer ambiguous. Since then, decades of follow-up experiments have turned up every possible answer — the sprinkler spinning one way, spinning the other way, jittering back and forth, or not moving at all — depending on how carefully the tests were built.

In 2024, a team at New York University led by applied mathematician and experimental physicist Leif Ristroph took a first crack at the question, finding that the reverse sprinkler rotates opposite to a forward sprinkler. But that explanation was tested only on ordinary S-shaped sprinklers, and it hadn't yet been pitted directly against two other leading theories.

One, which traces back to Austrian physicist Ernst Mach, holds that the total angular momentum of the swirling water inside the sprinkler's arms must be balanced by an opposite spin of the sprinkler itself. The other, associated with Feynman himself, focuses on pressure and suction effects right at the outer nozzles.

So Ristroph's team asked, what if the sprinkler weren't shaped like a sprinkler at all? What if its arms spiraled, bent the wrong way or curled back on themselves?

In a new study published July 13 in the journal PNASs, the researchers built seven deliberately "silly" sprinklers with unusual arm geometries to pit the leading theories against each other. That includes one sprinkler with arms that spiraled several times to maximize the water's angular momentum, and another with a counter-bend at the nozzle.

In the process, they tore down both ideas. If Mach were right, the spiral design should have spun dramatically differently. If Feynman were right, reversing the nozzle bend should have flipped the sprinkler's direction. Neither happened.

"We were forced to say, 'Feynman and followers, you guys are off,'" Ristroph told Live Science.

The spiral-armed sprinkler, meant to test Mach's theory, was just as unyielding. Even though the fluid inside carried substantially more angular momentum, "the solid barely cared," Ristroph said.

All three measurements across the seven designs pointed instead to the sprinkler's central hub, where the arms meet. There, incoming water collides and swirls, generating a flux of angular momentum inside the device that the solid structure pushes back against. The finding suggests that the reverse sprinkler is not much more than an inside-out version of a forward sprinkler governed by the same physics playing out at the opposite ends of the arms.

Ristroph emphasized that this result was made possible because of Jesse Smith, who just completed his physics doctorate at NYU while working on the project, along with a small team of Ristroph’s own students, and Ristroph's longtime collaborator Brennan Sprinkle, a computational fluid dynamics expert at the Colorado School of Mines whose surname is a coincidence.

Now, the team is building computer simulations to test whether the momentum-flux model holds up beyond the flow conditions already studied, and they hope to eventually derive it from fundamental fluid dynamics equations.

Ristroph said this "silly" problem does have real-world applications: Understanding how curved channels convert fluid flow into rotational force could inform the design of turbines and other devices that harvest energy from wind and water currents.

"If we can do something that would help with engineers designing devices to better make use of all the huge amounts of wind and water energy we have all around us," he said, "that would be, of course, a fantastic thing."

Beyond familiar particles such as electrons and protons, scientists have discovered a zoo of "quasiparticles" with exotic names, such as magnons, angulons, dropletons and polaritons. But what are quasiparticles, exactly? And given the "quasi" in their name, are they considered real particles?

One way to understand quasiparticles is to explore what a particle is. The standard mental picture of a particle "is of a discrete object, like a ball," Douglas Natelson, a condensed matter physicist at Rice University in Houston, told Live Science. However, this classic image of particles changed with the advent of quantum physics, which revealed that the universe becomes fuzzy at its smallest levels. For example, in 1924, French physicist Louis de Broglie showed that particles such as electrons could also behave as waves ‪—‬ a discovery that earned him a Nobel Prize.

Modern physics suggests that particles are excitations in fields that permeate the entire universe, a bit like a ripple in a pond, Ross McKenzie, a theoretical condensed matter physicist and professor emeritus at the University of Queensland in Australia, told Live Science. Each type of particle has its own corresponding field. For instance, photons of light are ripples of the electromagnetic field, McKenzie noted.

The quantum nature of particles means they can not only fly through an empty vacuum but also ripple through matter. For instance, photons can zip through transparent and translucent materials, and electrons can flow inside wires.

If you can picture a standard particle, such as an electron, as a ripple traveling within a material, you can also envision other kinds of excitations within matter. These other types of ripples are quasiparticles.

For example, think of "the wave" done at a sporting event. "You can watch it propagate around a football stadium; it has a location and a speed," Natelson said. "It only exists within the stadium, though, and it's made up of the collective response of all the interacting fans."

In much the same way, "quasiparticles can only exist within some medium or material, because they are built up from the response of that material's constituents or building blocks," Natelson said; in contrast, particles such as electrons and protons "can exist in free space."

In other words, quasiparticles can't exist in a vacuum and they can't exist on their own. They're reliant on particles acting together and being in a material where they can emerge, just as a wave carried out in a stadium can only exist when there is a group of people there who can perform it.

A philosophical question concerning quasiparticles is whether they are real, McKenzie noted. After all, "quasi" in Latin means "almost."

"Fundamental particles can exist in isolation in a vacuum, and quasiparticles need many interacting particles to exist," McKenzie said. "Still, I would say quasiparticles are, for all intents and purposes, just as real as particles, in how you can detect them and manipulate them."

A zoo of quasiparticles

The concept of quasiparticles originated with theoretical physicist Lev Landau in the 1950s, McKenzie said, and the idea ultimately helped Landau win the Nobel Prize in physics in 1962. Scientists have now proposed the existence of dozens of quasiparticle types, including the following:

• The phonon, which is a quasiparticle of sound — it is the smallest packet of vibrational energy that makes up sound in matter, McKenzie said.
• The electron hole, often simply called a hole, is the positively charged vacancy left behind once an electron has left its original place, McKenzie noted.
• The electron quasiparticle, which essentially consists of an electron and its interactions with its surrounding environment. This combined package means the electron quasiparticle requires more force to move, so it effectively has more mass than a regular electron, McKenzie explained.
• The exciton, a quasiparticle made of an electron and a hole orbiting each other.
• The anyon, a kind of quasiparticle so far only seen in two-dimensional systems, which may carry only a fraction of an electric charge.

"How many kinds of quasiparticles are there?" McKenzie said. "Just like there are an infinite number of possible states of matter, I would say that, in principle, there are an infinite number of types of quasiparticles."

Scientists describe activity in material as quasiparticles "because it simplifies everything dramatically," McKenzie said. In the same vein, Natelson said that "very often the math behind physical phenomena in solids is described well by quasiparticles."

Quasiparticles are not simply useful for bookkeeping. For instance, researchers typically describe the behavior of electricity in electronic devices in forms of quasiparticles such as holes and excitons, Natelson said.

All in all, the answer to the question of whether quasiparticles are real is a matter of interpretation. If the question is whether or not a quasiparticle is an elementary particle such as an electron, the answer is no — they cannot exist on their own, and they depend on the materials in which they manifest.

However, if the question is whether or not quasiparticles are real phenomena, the answer is yes — they are things that scientists can measure that can behave like particles and effectively have many of the same properties that other particles do.

The 2026 Fields Medal, one of the world’s most prestigious mathematics prizes, has just been awarded to four pioneering young researchers — including mathematician Hong Wang, the third woman ever to win the prize in the 90 years since the award was established.

The Fields Medal is an award presented every four years to mathematicians under the age of 40 for their outstanding discoveries. The International Mathematical Union announced Thursday (July 23) that Wang, a professor at New York University, is among the four recipients of the 2026 medal for her work on a decades-old conjecture about how needles move in 3D spaces. .

The 2026 Fields Medal winners also include Yu Deng of the University of Chicago, who was recognized for connecting microscopic and macroscopic descriptions of gases; John Pardon of Stony Brook University, whose work solved major problems in topology and geometry; and Jacob Tsimerman of the University of Toronto, who developed powerful new techniques in algebraic geometry that have advanced progress on longstanding mathematical puzzles.

Wang joins an exceptionally small group of women to receive the Fields Medal. Iranian mathematician Maryam Mirzakhani was the first, in 2014, followed by Ukrainian mathematician Maryna Viazovska in 2022. No woman received the award at all in the nearly 80 years before Mirzakhani's win.

Wang was recognized for her work on the Kakeya conjecture, a problem that asks how little space is needed to rotate a needle so that it points in every possible direction in three dimensions. Mathematicians had chased a solution for roughly 50 years.

Working with collaborator Joshua Zahl, Wang showed that if you track every direction the needle could point as a bundle of thin tubes, there's a precise trade-off between how thin those tubes are and how much total space they must occupy. Solving the puzzle required tools from harmonic analysis, a field that studies how complex shapes and signals can be broken down into simpler pieces.

The proof wasn't a triumphant moment for Wang, at least not right away. She and Zahl spent months checking their 127-page proof before making it public — and even then, Wang worried that their argument might be unclear. The paper nonetheless earned comparisons to a "once-in-a-century" result and set off a string of honors culminating in the Fields Medal, according to Quanta Magazine.

The 2026 Fields Medals were presented during the International Congress of Mathematicians in Philadelphia. The first Fields Medal was awarded in 1936. So far, 65 men have received the award.

Science word of the day: Cryptology

Pronunciation: Krip-TAH'-leh-jee

What it means: Cryptology is the study of secret codes ‪—‬ both making them (cryptography) and breaking them (cryptanalysis). Once associated with spy networks' secret codes and ciphers, cryptology now often refers to the computer algorithms used to encrypt data to protect passwords and personal information from prying eyes.

How to use it in a sentence: Native American soldiers known as "code talkers" harnessed cryptology in World War II by developing codes and ciphers based on their Indigenous languages.

Can you crack our science word of the day puzzle, Chain Word?

Two physicists have used generative artificial intelligence (AI) to solve a stubborn mathematical problem in physics that had vexed researchers for more than a decade.

Their solution, described July 1 in the Journal of Statistical Mechanics: Theory and Experiment, came about when the physicists chose to revisit a problem they thought they had attempted to solve exhaustively within a topic they knew intimately. This concept, known as jamming, refers to the sudden transition from a fluid system to a rigid-but-disordered one.

The simplest way to understand this idea is to imagine a pool table covered with billiard balls. If you keep adding balls, eventually the table becomes so congested that there is no space for any more and each ball on the table is securely held in place by its neighbors. This is a disordered, completely frozen situation known as a jammed state.

The study authors —‬ ‪Giorgio Parisi, winner of the 2021 Nobel Prize in physics, and Francesco Zamponi, ‪both physicists at the Sapienza University of Rome ‪—‬ and collaborators had mathematically described jamming and offered numerical solutions in a 2014 paper. In the process, they noticed that two parameters — $a$ and $b$ — would mysteriously always add up to 1.

"The parameters $a$ and $b$ dictate exactly how the distribution of contact forces and small gaps [between balls] scales as the physical system hits that critical jamming point," Zamponi told Live Science in an email. "We were quite bothered by the fact that we had never been able to mathematically prove the relation $a+b=1$."

Moreover, separate work by Matthieu Wyart, a physicist at the Swiss Federal Technology Institute (EPFL), took a completely different approach but yielded the same relation. For Zamponi and colleagues, this suggested "entirely new physical concepts" were needed to link their and Wyart's work and simultaneously explain why $a+b=1$.

Fast-forward a decade, and no progress had been made in finding these new concepts nor a reason for why $a+b=1$. Stuck in a rut, Parisi had a thought: perhaps generative AI could offer a fresh perspective. For this, he turned to Anthropic's Claude. After Claude successfully reproduced the 2014 numerical result, Parisi prompted the AI to prove why $a+b=1$.

"Giorgio initially sent me Claude's output while I was traveling, so I ended up reviewing it on an airplane," Zamponi recalled. "As I read through the LaTeX file Claude generated, it became immediately clear that the core idea was correct … That moment significantly shifted my perspective on what these models can achieve in theoretical physics."

Though the initial output contained some errors that required revision, the fundamental idea was correct. And in a total of just 40 prompts, the researchers had a verified publishable analytical solution. To their surprise, this solution was hidden directly within the equations themselves; they didn't need any external physical assumptions or deep connections between functions.

"It is entirely possible that a pure mathematician who works full time on such kind[s] of equations might have spotted the solution," Zamponi told Live Science. "But this is a particularly interesting point for us, as it highlights how Claude gave us instant access to a vast repository of mathematical training and formal skills that lay just outside our usual domain."

Whether Claude simply trawled the vast mathematical literature and used pattern matching to find a way to solve their problem or if it applied something akin to creativity is, for Zamponi, moot because they "could not see the path forward, and Claude did," he said. And although he admitted that interacting with AI forces him to reconsider his definitions of reasoning, intuition, and creativity, Zamponi will continue to collaborate with the technology to speed up mundane tasks and provide fresh perspectives on challenging problems.

Now, Zamponi is applying this collaborative approach to a problem involving the “random sequential addition of hard hyperspheres," he said. “It is another excellent case study because, while the AI drastically accelerates writing and optimizing code, I have had to provide the vast majority of the conceptual ideas, which suggests that human guidance remains indispensable, at least in this case."

Physicists have coaxed a black hole's most famous glow out of a strand of optical fiber and, for the first time, watched that light react back on the simulated black hole that produced it.

The result gives researchers a rare, hands-on look at Hawking radiation ‪—‬ the faint thermal emission that Stephen Hawking predicted should leak out of black holes ‪—‬ and offers a first clue about the tiny push that could, in principle, make a real black hole slowly evaporate, the research team said in a new study.

Working with a tabletop experiment in optical fibers, the international team detected both the radiation and its long-sought "back reaction" — the way the radiation feeds energy back and reshapes the object that created it.

According to the new study, published July 1 in the journal Nature, the light behaved exactly as Hawking predicted it should: like the glow of a warm object, with a definite temperature and a spectrum that fades away steadily toward higher frequencies. It did so even in a regime where the usual textbook description of a black hole should break down.

Where three great theories collide

Hawking radiation is famous because it sits at the crossroads of physics' biggest ideas.

"Jacob Bekenstein predicted that black holes have an entropy and a temperature, and Hawking calculated the thermal radiation of the black hole," study co-author Ulf Leonhardt, a physicist at the Weizmann Institute of Science in Israel, told Live Science via email. "In Hawking-Bekenstein radiation, quantum physics, general relativity and thermodynamics come together — subjects that are normally in conflict with each other."

The conflict runs deep: General relativity pictures space and time as smooth and continuous, while quantum mechanics describes a world of discrete, unpredictable jumps ‪—‬ and no one has managed to fully reconcile the two.

That combination is exactly what makes Hawking radiation so hard to study. Astronomers have never seen Hawking radiation from a real black hole and probably never will; the glow is far too faint to pick out across the cosmos. So physicists have turned to laboratory stand-ins that obey the same equations, building black hole analogues out of flowing water, ultracold atoms and, as in this study, light.

Building a black hole from light

The trick behind every black hole analogue is a moving medium. "Imagine a swimmer in the sea with a current faster than he can swim," Leonhardt explained. "He is swept away. This is what happens beyond the [event] horizon, and this is why normally nothing can escape the black hole."

A black hole's event horizon is the boundary where that current — space itself, in real life — starts moving faster than anything can travel. To recreate it, the team needed a material that appears to rush along at the speed of light. Their solution was elegant: use light to make the "material."

"In optics we need a material that appears to move at the speed of light," Leonhardt said. "For this we use light itself — in nonlinear optics, light acts like a material."

In practice, the researchers fired an intense, ultrashort "pump" pulse into a thin photonic-crystal fiber — a strand of glass threaded with a pattern of tiny air channels running along its length, which lets researchers fine-tune how light moves through it. As it traveled, the pulse slightly changed how the glass bent light, creating a moving speed bump that raced along with it. A second, much weaker "probe" pulse then ran into this moving front. Where the probe could no longer keep up, an artificial horizon formed — and the black hole analogue was born.

Catching the glow and its pushback

The payoff came in the ultraviolet. According to theory, Hawking radiation is created in pairs: One partner escapes, while the other, carrying "negative" energy, is the mirror image that would fall into a real black hole. In the fiber, that partner showed up as ultraviolet light.

"We counted photons in the ultraviolet that correspond to the Hawking partners beyond the horizon," Leonhardt explained. "They have a wavelength around 233 nanometers. This was our signal."

Just as important as seeing the glow was understanding how it was made. For years, researchers assumed the fiber built up its Hawking radiation through a cascade — a chain of separate steps in which the light is converted first into one intermediate form, and then another, each feeding the next before the radiation finally emerges. The team found that, instead, a single, direct interaction does the job, with the pump and probe light producing the Hawking pair in one clean step. It is a much simpler picture that the researchers said may carry over to other analogues and perhaps even to real black holes.

Because energy has to come from somewhere, making Hawking radiation should nudge the source that created it. For a real black hole, that nudge is how it loses mass and, over unimaginable timescales, evaporates entirely — the process Hawking described in his landmark 1974 paper. No experiment had ever captured that recoil.

Here, the team saw it. Producing the radiation shifted a small fraction of the pump pulse's own light to a slightly different color, leaving a telltale lopsided pattern in the spectrum. That asymmetry, absent in earlier experiments, is the fingerprint of the back reaction, or recoil — the black hole analogue quietly paying the energetic price for its own glow.

The road to a quantum experiment

The result also speaks to one of the thorniest puzzles in black hole physics: the trans-Planckian problem. Trace Hawking's radiation back to where it was born and the calculation runs into territory no physicist can vouch for — the Planck scale, the vanishingly small size at which space and time are thought to lose their familiar meaning and all known physics gives out. Hawking's prediction, in other words, appears to rest on a foundation that may not exist.

"Any light getting away from the horizon is stretched out enormously," Leonhardt said. "So it must come from waves smaller than the tiniest scale in nature, where the physics is unknown. Would that still give Hawking radiation? That was the question, and we have answered it in our experiment." Remarkably, the glow stayed perfectly thermal even in this extreme regime.

The team's next step is concrete. So far, they have used ordinary laser light, which reproduces the spectrum of Hawking radiation but not its deepest quantum weirdness. Next, the team plans to "go quantum," Leonhardt said. "We will explore how to get into the quantum regime and observe quantum features such as entanglement" — the ghostly link that should tie each escaping Hawking particle to its lost partner.

See how much you know about black holes with our black hole quiz!

Albert Einstein gave us the theory of relativity, explained the photoelectric effect and predicted the existence of gravitational waves. He revolutionized our understanding of space, time and gravity.

In fact, he is so famous for his brilliance that "Einstein" is synonymous with "genius." But being a genius doesn't mean you're infallible. So was Einstein wrong about anything?

"For sure, he was wrong about tons of things," Nicolás Yunes, a theoretical physicist at the University of Illinois Urbana-Champaign, told Live Science. "We remember him for the things he was right about, for the most part, because the things he was right about shocked the scientific world and eventually those ripples affected everyone on Earth."

For example, one of his most famous predictions was marred by a mathematical mistake. In 1916, Einstein correctly realized that the acceleration of matter could produce ripples in space-time that we now call gravitational waves. But when he and the physicist Nathan Rosen described these waves using mathematics, they ran into a problem: Any solution to the equations of general relativity that would allow for gravitational waves "blew up," Yunes said. "They had these singularities … these divergences. And solutions that diverge and explode like that, they can't be physical representations of reality."

As a result, Einstein changed his mind and decided that gravitational waves couldn't exist. He wrote up his results and submitted them to the journal Physical Review, which had recently begun sending papers to outside experts for peer review. An anonymous reviewer caught an error in Einstein's math, and when Einstein learned about it, he was so furious that he withdrew the paper and submitted it to a different journal.

But the reviewer had spotted a real error: Einstein's mathematical infinities were a coordinate artifact. Much like Earth's lines of longitude seem to converge to a "singularity" at the North Pole even though nothing unusual is happening there on the ground, Einstein's math could have been fixed by using a different set of coordinates.

Without Einstein's knowledge, the reviewer befriended and demonstrated the error to Einstein's assistant, who explained it to Einstein. Einstein corrected the error and republished the paper with the opposite conclusion, showing that gravitational waves do, in fact, exist.

Calculating "impossible infinities"

Remarkably, Einstein stumbled on the same error twice — at least, it seemed that way. When examining the mathematics around black holes, he once again calculated impossible infinities ‪—‬ this time, at the edge of a black hole. And once again, he concluded that this must mean the object couldn't exist.

"Einstein remained skeptical of the existence of black holes," John D. Norton, a professor in the Department of History and Philosophy of Science at the University of Pittsburgh, told Live Science in an email. "He was resolute in his judgment that there would be a singularity in space-time already at the event horizon of a black hole, which is now merely regarded as marking the point of no return for those falling into a black hole."

But this time, Einstein was not convinced that he made a mistake. Norton argues this wasn't just stubbornness; it reflected a philosophical belief in how Einstein thought mathematics and physics should relate to each other.

"He was unmoved by alternative analyses that found his mathematical infinities to be merely artifacts of the particular mathematical methods he preferred," Norton said.

Einstein and quantum mechanics

Einstein's resistance to quantum mechanics is probably his most famous wrong turn. His central objection was to a phenomenon called quantum entanglement: the idea that two particles can be linked in such a way that measuring one instantly affects the other, no matter the distance between them. In a 1947 letter to his colleague Max Born, he wrote, "I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance."

Einstein thought this instantaneous phenomenon seemed to violate special relativity, which says that nothing can travel faster than light. As a result, he believed quantum mechanics must be incomplete and that there was some deeper, unknown description of reality that would restore order.

"He died not liking quantum mechanics," Yunes said. It wasn't until 1964, almost a decade after Einstein's death, that John Bell proved entanglement was real.

"Today, a lot of the technology that we have relies on quantum mechanics, and so we know it's correct," Yunes said. "But it's still incompatible with general relativity, with [Einstein's] classical theory."

"It's possible that general relativity is wrong," Yunes said. "It's also possible that quantum mechanics is not the right description when you're talking about systems that are very strongly gravitating and you're looking at Planck-scale-type dynamics," which are incredibly small scales at which quantum effects dominate. For instance, the center of a black hole, which is both compressed to the quantum scale but also sits inside the most intense gravitational field in the universe, is a place where general relativity predicts a singularity that quantum mechanics has no way to describe.

But many of Einstein's mistakes still moved science forward. "General relativity is a good example," Norton said. "Einstein based it on the idea that he was generalizing the principle of relativity to acceleration and on what he soon called Mach's principle. Neither proved compatible with his final general theory of relativity."

Einstein's mistakes might come as a surprise to others, but they didn't to him. Once, when writing a book with his collaborator Leopold Infeld, Infeld told him he was taking special care with it because Einstein's name would appear on it. Einstein laughed and said, "There are incorrect papers under my name, too."

See how much you know about Albert Einstein with our Einstein quiz!

This week's science news was filled with big discoveries from the world of the small, led by a physicist's creation of a mini-universe, which was designed so we can watch time emerge from within an isolated quantum system.

The experiment was performed using a Bose-Einstein condensate — a strange state of matter that consists of thousands of atoms blended into a single quantum object at near absolute zero (minus 273.15 degrees Celsius, or minus 459.67 degrees Fahrenheit). The system showed time speeding up, slowing down and even stopping, depending on what the system was doing.

Those weren't the only highbrow high jinks using a Bose-Einstein condensate we reported on this week. We also covered NASA's upgrade to its mini-fridge-sized laboratory on the International Space Station that will use the bizarre state of matter to probe the quantum world. Back on Earth, physicists also found that complex numbers aren't necessary for quantum mechanics to work and used quantum computers to create a rare material critical to nuclear fusion. And to stick with news from the small (and weird) things of the world, we also reported that scientists have created little diving suits to transform cockroaches into search-and-rescue cyborgs.

Arctic ice thickening shows promise

First experiment to thicken Arctic ice with seawater shows promise — but there's a big catch

The Arctic is the world's fastest-warming region, where sea ice is rapidly disappearing at a rate of 12.2% per decade.

The ice is crucial for maintaining stable sea levels and marine nutrient flows, and for reflecting solar radiation away from our planet, so its precipitous decline is deeply concerning. That's why one team of researchers turned to a surprisingly simple method to stem the ice loss: flooding ice sheets with seawater to thicken them.

The results, despite some major caveats, showed a lot of promise.

Discover more planet Earth news

—Extreme heat waves are making our cities buckle. Investing in urban nature is no longer optional.

—Colorful 'painting-like' ripples cover an ancient seafloor structure in the Bahamas — Earth from space

—'Uncharted territory': Record-high ocean temperatures confirmed for June as El Niño strengthens its grip

Life's Little Mysteries

Does fast charging damage your battery more than regular charging?

If you're as shamefully attached to your devices as I am, you may have wondered about the wildly differing times it can take for them to charge. So what's the science behind fast charging, and does it damage a device's battery more than regular charging does?

—If you enjoyed this, sign up for our Life's Little Mysteries newsletter

One of the oldest gravestones of a free Black person in the U.S. found

'One of the oldest gravestones of a free Black person in America' discovered in Boston

It was found amid photos of headstones during a restoration project at Boston's Granary Burying Ground — a gravestone with only one name, "Boston."

That's how a team of conservationists chanced upon the tombstone of Sebastian, a formerly enslaved man who died free in 1729 and chose the city's name as his own.

A search through the historical archives has produced a wealth of information about Boston's past, including his reputation as a hardworking handyman throughout the city, and his emancipation following the death of the man who held him in slavery.

"It's been there all along. We just had to go look and share the story," Michelle Wu, the mayor of Boston, said in a July 4 speech.

Discover more archaeology news

—100,000 years ago, one of the earliest Homo sapiens outside Africa was stabbed in the face, analysis finds

—6,000-year-old broken ribs discovered in Syria may be one of the oldest known cases of child abuse in the world

—Neanderthals and modern humans may have shared culture 59,000 years ago in Turkey, study finds

Also in science news this week

—New sodium metal battery design charges in just 4 minutes and retains its capacity for years

—Dirty 'button' unearthed by metal detectorist turns out to be a rare 900-year-old coin from Norway's last Viking king, Magnus Barefoot

—'Astronomers have to revise estimates': The Milky Way may be larger, heavier and more lopsided than we realized

—2,500-year-old tomb of a 'warrior prince' with chariot and helmet discovered on Italy's Adriatic coast

—Malaria had nearly been eliminated around a giant dam in the Amazon — but then it came roaring back. Experts just discovered why.

Science interview

'800 seconds for a sick visit': Some factors driving antibiotic resistance have nothing to do with biology, says medical sociologist Julia Szymczak

Antibiotic resistance continues to pose a growing danger across the U.S., with more than 2.8 million antimicrobial-resistant infections occurring in the country each year. Last week, we brought you a report from Live Science health editor Nicoletta Lanese, who visited Japan to investigate how that country is curbing its overuse of antibiotics.

Now, in the second part of a feature series into the fight against this "silent pandemic," Nicoletta interviewed medical sociologist Julia Szymczak to dig into the social and emotional drivers of antibiotic overprescription.

Something for the weekend

If you're looking for things to keep you busy over the weekend, here's a selection from our best opinion pieces, interviews, diagnostic dilemmas and crosswords that we published this week.

—Superintelligent AI in space could explain the Fermi paradox [Opinion]

—'It's more than a hope; it's a guarantee': The Vera C. Rubin Observatory's 10-year movie of the universe is about to 'blow our minds,' chief scientist Tony Tyson says [Interview]

—Diagnostic dilemma: A woman heard voices for years — but not because of psychosis [Diagnostic Dilemma]

—Live Science crossword puzzle #51: Largest rodent on Earth — 4 down [Crossword]

Science photo of the week

Secretive Chinese probe snaps first photo of Earth's mysterious 'quasi-moon' — and it may pose a big problem

It doesn't look like much, but this blurry, gray image is the first-ever close-up photo of one of Earth's temporary "quasi-moons" — a fast-spinning asteroid temporarily orbiting the sun in sync with our planet.

Of equal intrigue is the spacecraft that took the image: a secretive Chinese probe that is likely gearing up to land on the space rock and snag a sample ‪—‬ although an unexpected hiccup will make that more difficult.

Follow Live Science on social media

Want more science news? Follow our Live Science WhatsApp Channel for the latest discoveries as they happen. It's the best way to get our expert reporting on the go, but if you don't use WhatsApp we're also on Facebook, X (formerly Twitter), Flipboard, Instagram, TikTok, Bluesky and LinkedIn.

A new upgrade to the International Space Station's (ISS) quantum laboratory is enabling NASA to probe the behavior of atoms further than ever before, the space agency has announced.

Combining the ISS's newly upgraded "Cold Atom Laboratory" with the near zero-gravity of low Earth orbit, scientists are attempting to understand the properties of so-called "ultracold" atoms in an environment impossible to replicate on Earth. The aim of the mission is to study how clouds of atoms behave at temperatures close to absolute zero (minus 459.67 degrees Fahrenheit or minus 273.15 degrees Celsius) — the coldest possible temperature in the universe, where atoms lose all their energy of motion.

"At the coldest temperatures, matter behaves drastically different from anything we have experienced," Jason Williams, project scientist for the Cold Atom Lab at NASA’s Jet Propulsion Laboratory in Southern California, which built the facility, said in a statement. "The wavelike nature of matter dominates, and ultracold matter can behave in ways that are not only unexpected, but that also enable extremely precise measurements of time, gravity, and motion. The lab has lots of tools — especially with this latest upgrade — to let us probe the nature of the universe."

Rule-breaking particles

Atoms and their subatomic particles are quantum mechanical objects whose behavior is fundamentally different from that of the large-scale world. For example, the laws of quantum mechanics predict that particles can be in more than one place at the same time (quantum superposition); can be mysteriously linked with each other over great distances (quantum entanglement); and move through spacetime as waves as well as moving like fixed, solid objects.

But observing these behaviors is notoriously difficult. Firstly, atoms are so tiny that if an atom were the size of a golf ball, then a human teeing one off would stand roughly as tall as the distance from Earth to the moon. Secondly, it’s impossible to isolate measurements of these behaviors for atoms in "normal" environments (like on Earth), as the desired quantum behavior is disturbed by energy from heat and gravity.

To overcome these challenges, the ISS's Cold Atom Laboratory — which is the size of a mini-fridge — uses lasers to cool gases of rubidium and potassium to just above absolute zero. At these temperatures, atoms form a state of matter known as a Bose-Einstein condensate, in which many atoms behave like a single wave of quantum matter.

Not only does this setup allow scientists to observe quantum behaviors on a much larger scale than that of single atoms, but the reduced gravity enables the condensate matter waves to expand and evolve undisturbed for much longer periods than would be possible on Earth.

This is the fourth major upgrade to NASA’s Cold Atom Laboratory since it arrived aboard the ISS in 2018. According to NASA, the significant improvements in this most recent upgrade include a redesigned magnetic trap to contain the cloud of atoms, improved atom sources, and better measurement capabilities.

Scientists launched these upgrades to the ISS in April 2026, and they have since been installed, switched on, and started making state-of-the-art measurements. As well as enabling novel tests of fundamental physics, measurements of these effects are critical in demonstrating future, space-based, highly precise quantum technologies related to positioning, navigation, timing, and gravity sensing. These technologies could one day enable astronauts to navigate on the moon without GPS and produce high-precision maps of Earth’s gravity.

"In the previous century, there was a quantum revolution that led to lasers, cellphones, and MRIs for medical imaging," Ethan Elliott, deputy project scientist at NASA’s Jet Propulsion Laboratory in California said in the statement. "We’re performing Quantum 2.0 – direct manipulation of large quantum states – and we hope for similar gains in quantum technology by advancing this science in orbit."

For the first time, physicists have built a working version of quantum mechanics without complex numbers — numbers that have been considered essential to the theory for nearly a century.

Complex numbers combine a regular "real" number with an "imaginary" one — a multiple of the square root of -1, represented by the symbol i — into a single value, like 3 + 4i. The square root of -1 doesn't correspond to any quantity you could count or measure directly (you can't have negative one apple, for instance), which is why mathematicians call it imaginary.

Still, complex numbers have many useful applications. Engineers use them to describe alternating electrical current. Physicists use them to describe waves. And ever since quantum mechanics was first documented in the 1920s, complex numbers have been built directly into its equations. Quantum mechanics describes particles using something called a wave function, and that description relies on complex numbers.

In 2021, a team of physicists predicted that a version of quantum mechanics built with only real numbers would make incorrect predictions in certain experiments involving multiple particles. The following year, other researchers ran those experiments, and the results matched standard quantum mechanics, not the real-number version. Complex numbers seemed unavoidable.

But that 2021 result rested on one specific assumption: a particular mathematical rule for combining particles. That led physicists to ask a question: Are complex numbers actually necessary to describe reality at the quantum level, or are they just a convenience?

Now, in a new study published June 18 in the journal Physical Review Letters, researchers have found a way around the 2021 result.

"Complex numbers are not needed for quantum mechanics," study first author Pedro Barrios Hita, a theoretical physicist and doctoral student at the German Aerospace Center and Heinrich Heine University Düsseldorf, told Live Science.

A different rule

The 2021 result relied on a specific mathematical rule called the tensor product, which combines two separate quantum systems into one. If you have two particles and you want to combine them into a single mathematical description, you can use the tensor product. It's a rule taught in every quantum mechanics textbook.

It works well for ordinary complex-number quantum mechanics, but past attempts to build a real-number version around that same rule ran into trouble. They couldn't reproduce the correlations seen in experiments involving three or more entangled particles.

In their new study, Barrios Hita and his colleagues found that the tensor product isn't the only option. They built quantum mechanics around a different rule based on an idea: An action taken on one part of a system shouldn't have any effect on a separate part of it.

In ordinary quantum mechanics, multiplying a particle's state by i is undetectable on its own. But when two particles combine, that i can shuffle over and effectively attach itself to the other particle instead. Physicists call this phase kickback, and it's built automatically into the tensor product.

Barrios Hita's team had to recreate that shuffling using only real numbers. They attached a small "flag" to each particle to keep track of what the imaginary part used to store. Then, they treated certain flag combinations as physically identical, even though they looked different on paper. That grouping step allowed their real-number version to match every prediction of standard quantum mechanics, including the multiparticle cases that had tripped up earlier attempts.

At its core, the trick is simple. A complex number, like 3 + 4i, is really just a pair of ordinary real numbers (3 and 4) — the i is only a label marking which one is the imaginary part. "A complex number is nothing but two real numbers," Barrios Hita said. His team essentially built a bookkeeping system that tracks those two real numbers separately, instead of combining them into one complex number. It took a long time to figure out how to make that work consistently across multiple combined particles. But once they did, Barrios Hita said, the underlying structure turned out to be elegant.

The result puts quantum mechanics in the same boat as other physics theories that are often written using complex numbers purely for convenience, Barrios Hita said.

"There are many other theories, like, for example, electromagnetism," Barrios Hita added, "which has complex numbers at its core. So, these theories are formulated using complex numbers, but [they] are not fundamental. They're just helpful tools to help express equations."

The work doesn't change any experimental predictions or point to new quantum technology. It's also currently limited to systems with a finite number of quantum states. Extending it to infinite-dimensional systems, which show up in many real physics problems, is a natural next step, and other researchers are already looking into it. Barrios Hita is moving on to different research, on how quantum properties like entanglement can be used as a resource.

Still, the study settles a decades-long debate. Complex numbers make quantum mechanics easier to write down, but they aren't required to make it work.

For the first time, a physicist has experimentally watched time emerge from within an isolated quantum system — by creating a “mini-universe.” This bizarre experiment raises an intriguing question: If the universe has nothing outside it, where does time come from?

In a new study published June 11 in the journal Physical Review Research, Giovanni Barontini, an experimental physicist at the University of Birmingham in the U.K., used a cloud of ultracold atoms to build his mini-universe. The system was so well isolated from its surroundings that, like the universe itself, it had nothing external to use as a clock. He split that system in two and ignored one half — what he called the "dark sector" — to show that time could arise entirely from within the system.

The result offers the first experimental look on why the universe has time at all. "When you put everything together, things really start to make sense," Barontini told Live Science. "How time inside the system was speeding up or slowing down, or even stopping — this was quite surprising, how well everything came together. Very neatly, in a way. Which is something that doesn't happen that often in experiments."

The work is an experimental verification of ideas that have been floating around in quantum cosmology and thermodynamics for decades. This is not a bombshell claim that time is an illusion, but it is the first time anyone has put those ideas to a direct, quantitative test in the lab.

A universe with nothing outside

Barontini set out to look at a problem that physicists have puzzled over for nearly 60 years. The Wheeler-DeWitt equation — a central equation in quantum gravity, the field that seeks to unify Einstein’s theory of gravity with quantum mechanics — describes the universe as a whole system with no external time parameter. There is no cosmic clock ticking away outside the universe. So where does our experience of time come from?

One influential idea, called relational time, says that time doesn't exist as a fundamental ingredient of reality. Instead, it emerges from relationships inside the universe, with one part of the system acting as a clock for another. But this idea had never been tested directly in the lab.

Barontini's inspiration came from watching his son play with building toys. "I thought that it's something very similar to what we do in our labs," he told Live Science. "We play with very expensive toys. We create our own small samples of reality."

In his lab, that sample is a Bose-Einstein condensate — a state of matter that forms only at near absolute zero. In a Bose-Einstein condensate, thousands of atoms slow to a near standstill and blur together into a single quantum object, behaving as one.

The dark side of time

To mimic a universe with nothing outside it, Barontini placed the condensate in a trap and divided it down the middle with a thin sheet of laser light. He watched one half, the "bright sector," closely and deliberately ignored the other half, which he called the "dark sector."

The atoms in the bright sector sloshed back and forth in the trap, periodically spilling over the barrier and back again. Barontini called the moments when atoms flooded into the bright sector the "Big Bang" and the times when they drained out the "Big Crunch" (the nickname for one theory of how the universe will end, with the universe collapsing in on itself). Then, he tracked how entropy — a measure of disorder, or how spread out energy is within a system — was exchanged between the two halves as atoms crossed the barrier.

Instead of using laboratory time to order events, he built an "entropic time" — a clock defined entirely by how much entropy was flowing between the two halves of the system. If entropy was flowing, time was ticking. If no entropy was exchanged, time stopped. "The entropy exchange between the two systems could be transformed into an internal time variable," Barontini said.

Time speeds up, slows down and stops

What surprised Barontini most was how cleanly everything fit together. The internal, entropic time reliably ordered events in the bright sector. It matched the sequence seen in laboratory time, but it flowed at a different rate.

When entropy was flooding between the sectors, entropic time ran fast. When the exchange slowed, so did the clock. And when the two halves reached equilibrium (no more entropy flowing), the internal clock stopped altogether.

"Time was speeding up or slowing down, or even stopping, depending on what the system was doing," Barontini said.

He then went a step further: Using this internal time, he derived a version of the Schrödinger equation and showed it accurately reproduced what he saw in the experiment. "This was quite surprising, how well everything came together," he said — "very neatly, in a way, which is something that doesn't happen that often in experiments."

Both time itself and the arrow of time — why time flows in one direction rather than the other — may arise from the same source: an observer giving up information. When Barontini chose not to look at the dark sector, he gave up knowledge of that half of the system. That act of ignorance, encoded in entropy, is what gave rise to time in the other half.

"Both time and the arrow of time — maybe they just are born from ignorance," Barontini said. "To have time and to observe, you have to give up some degrees of freedom."

Barontini sees this as just the beginning. The same cold-atom tool kit that generated a miniature Big Bang and Big Crunch in his trap could, in principle, be engineered to simulate far more exotic phenomena, such as black hole analogues, the conditions of the early universe, and what will happen at the moment of the Big Crunch itself.

"These are things we can do very simply, using the tools we already have to engineer our systems," he said.

The study is a proof of concept ‪—‬ a first demonstration that controlled quantum systems can serve as a test bed for some unanswered questions in physics. For now, those questions remain open.

The Large Hadron Collider (LHC), the world's largest and most powerful atom smasher, has entered a planned four-year shutdown that will upgrade it to its most capable form yet.

The particle accelerator was switched off Monday (June 29) and is scheduled to come back online in 2030 as the High-Luminosity Large Hadron Collider (HiLumi LHC), with improvements that will allow it to smash together roughly 10 times more particles than its original design. That data could help spark new discoveries in fundamental physics and shed light on the nature of dark matter, antimatter and the early universe.

"This is a very important moment," HiLumi LHC project chief Markus Zerlauth told Agence France-Presse. "From Monday, we will be entering a new phase."

Since its first successful proton collision in 2009, the LHC has allowed physicists to test theories about particle physics and the Standard Model of the subatomic world. It was essential to the discovery of the Higgs boson in 2012, which helped explain how tiny fundamental particles acquire mass. The collider covers a 17-mile (27 kilometers) loop at the border between France and Switzerland near Geneva.

The current shutdown is the third long-term, planned pause in the collider's operations. The first, a two-year shutdown beginning in 2013, consolidated connections between superconducting magnets and boosted the energy of the colliding proton beams. A second pause, from 2018 to 2022, involved a series of upgrades, replacements and preventive maintenance.

In the current period of dormancy, dubbed Long Shutdown 3 (LS3), specialists will install upgrades to boost the collider's luminosity by a factor of 10. That will increase the number of particle collisions, roughly tripling the number of times particles will smack into each other compared with the existing setup. Once the final version of the particle accelerator is online, it will run until the end of its operational lifespan in the 2040s and will be earmarked for replacement by a new, higher-energy particle accelerator in the years that follow.

"It really is an opportunity to explore the universe in a way we haven't done before," Mark Thomson, director general of CERN (the European Organization for Nuclear Research), where the LHC is housed, told New Scientist.

That jump means that experiments will produce much more data, which will allow scientists to study known phenomena, such as the Higgs boson, in more detail and increase the odds of observing rare events. For example, the HiLumi LHC is expected to produce about 380 million Higgs bosons over its lifetime of a decade or so, compared with the 55 million it's made to date. The data could help scientists solve problems with the Standard Model, which currently doesn't incorporate dark matter or dark energy, the primary forms of mass and energy in the universe.

"The LS3 represents a huge and complex logistical and engineering undertaking," Jean-Philippe Tock, head of the LS3 coordination team, said in a statement. "In the LHC alone, 1.2 km [0.75 miles] of magnets and components will be removed and replaced with new equipment, and across the whole complex, dozens of projects are planned, involving thousands of engineers, physicists, technicians and support personnel."

While the LHC won't be smashing any particles together during the shutdown period, researchers will continue to analyze data already collected during experiments during the prior operational window.

Though the LHC's primary purpose is fundamental physics research, technologies used to upgrade the collider could find their way into everyday life. For example, some instruments and techniques originally developed at CERN are now being used in medical imaging, sensors and art restoration.

For years, scientists have suspected that, at the molecular level, water is two different liquids ‪—‬ a denser one and a less-dense one ‪—‬ that are constantly switching places. Catching real molecular evidence of this microscopic transformation has been hard. But now, with help from artificial intelligence, researchers say they've finally found it.

"It's hard to imagine — here is just one water, right?" said Xiao Cheng Zeng, a physical chemist at the City University of Hong Kong and co-author of the new study, told Live Science while holding a water bottle in the air. That puzzle sent him digging through scientific literature, where he found the possible explanation: the two-state hypothesis. "That got my attention. We have literature to talk about it but no evidence."

The findings, published June 4 in the journal Nature Physics, could not only prove this long-sought molecular change is real, but also help to explain dozens of water's weird behaviors.

Most liquids become denser as they cool, but water behaves differently; it becomes denser until about 4 degrees Celsius, then starts to expand, which is why ice floats. Water also resists temperature changes better than similar liquids and has a viscosity that decreases under certain pressures. Scientists have documented various anomalies related to water and suspect they may be interconnected.

The two-state model is an attempt to be that unifying explanation.

A 30-year hunch

Zeng has been studying water since his postdoc days in the late 1990s, when he worked on liquid freezing. The two-state hypothesis itself came onto his radar later — around 2006, when he first encountered it at scientific conferences. But for years, he set it aside as too difficult to tackle directly. That changed roughly around 2016, as researchers began reporting experimental evidence that supercooled water could split into distinct high-density and low-density forms.

Around two and a half years ago, Zeng handed the problem to Liwen Li, a postdoctoral researcher in his lab. Rather than repeating the conventional approaches other groups had already struggled with, Li suggested the use of "unsupervised deep learning" — AI trained to spot patterns in data without being told what to look for.

"So AI [is] forced to learn — to use [its] knowledge to create, to explore," Zeng told Live Science.

The team ran massive molecular dynamics simulations, using the GROMACS simulation package. They tracked how hundreds of thousands of water molecules moved and interacted and generated tens of millions of data points.

"Traditionally, you may need a lot of students to figure that out. ... With computers and AI, it took [Li] maybe a year and a half," Zeng said. Without AI, he estimated, the same analysis might have taken closer to a decade.

The AI came back with "reaction coordinates" — a small number of variables, distilled out of all that molecular motion, that describe exactly how a water molecule's local arrangement shifts from the denser structure to the looser one and back. They plotted the system's behavior along those coordinates to see the shape of the conversion. That included the number and location of energy barriers, or saddle points, that molecules have to cross to make the switch.

Two paths up the mountain

The team found that the path the two structures take to convert into each other changes depending on certain conditions. Most of the time, the switch happens along what the researchers call a "semi-loop" pathway, with a single energy barrier to cross.

But near the boundary between high-density and low-density water — the same kind of threshold where ice and liquid water coexist at 32 degrees Fahrenheit (zero degrees Celsius) — the molecules can take a more roundabout "full-loop" path, with three separate barriers instead of one.

Zeng compared it to hiking a mountain that's been sliced in half, with a gentle slope on one side and a sheer cliff on the other. Most hikers stick to the slope; that's the semi-loop. But near the boundary where the two halves meet, it's as if the mountain were becoming whole again, letting hikers circle the entire peak. That's the full loop.

Zeng and his team are now building a more rigorous machine-learning model to confirm the result. They hope to eventually connect it to properties like density, viscosity and temperature.

Confirming the structure in real water won't be simple. Zeng said it will likely require new and sensitive experimental techniques — the kind developed by labs like Pacific Northwest National Laboratory, which previously found indirect spectroscopic evidence for water's two-state behavior.

"Once we have this ... confirmed by experiment," he said, "this model can be used to [understand] how water interacts with nature."

Since most biological and pharmaceutical processes happen in water, a better understanding of water's molecular structure could shed light on how dissolved salts, proteins, and drug molecules interact in solution. "These interactions are vital for injectable drugs and cell function," he noted, but applying this knowledge to practical uses is still a long way off.

Physicists recently wondered what would happen if you tried to split a photon ‪—‬ and they found some unexpected behavior that may transform the way we think about particles.

The experiment, in which researchers simulated a photon being sliced by a shutter under various conditions, showed that a severed photon can lead to a complex mixture of zero to infinitely-many photons — raising some big questions about the nature of particle interactions.

Photons are elementary packets of light, which means they are not made up of anything else. So what does it even mean to try splitting a photon? It may be possible thanks to wave-particle duality — a core principle of quantum mechanics, the bizarre physics of the very small.

According to wave-particle duality, a photon is not only a particle but also a wave. Using theoretical calculations, the researchers investigated what would happen if you sent this photon through a shutter and closed it while the photon was passing through, effectively cutting off the tail end of the photon wave.

"I think that most physicists would expect there to be a certain probability that you have zero photons and a certain probability that you have a single photon left after you have done this," Johannes Skaar, co-author of the new study and a professor of theoretical physics at the University of Oslo, told Live Science. "And that is approximately true, but it is not exactly true."

What are the chances?

This brings up another strange aspect of quantum mechanics: its probabilistic nature. Particles exist as a cloud of probabilities stretching to infinity. Until a particle is observed, its properties, such as its position or energy, are in a superposition of possible values; all we can know are the chances of finding it in a certain state.

Through their calculations, Skaar and his colleagues determined how cutting a photon affects these probabilities. In their study, recently accepted in the journal Physical Review Letters, they found that it would create a complex mixture of photon states, including one with an infinite number of photons.

Each of these states has a probability that depends on how quickly the shutter cuts the photon. The expected number of photons becomes infinite only if the shutter is closed infinitely quickly. For realistic shutter speeds, even a thousand photons would be extremely unlikely.

This may sound very strange, but the quantum physicists were unfazed. In fact, what surprised Skaar and his colleagues was what happens if you make measurements of the cut photon from different perspectives.

"When you measure from one side of the shutter, then it will look like a single photon state," Skaar said. "Then, on the other side, it will look like a vacuum state — that means no photons. And that is very strange because the actual state globally is this mixture from zero to infinity."

Changing how we think about particles

The fact that these complex mixtures can be treated locally as very simple states raises fundamental questions about the nature of particles. Skaar said they are still reckoning with the full extent of these implications and they are now considering how this process could play out for other quantum particles, such as electrons.

They hope that by following this theoretical thread through, they may be able to develop a neater way of describing particle interactions. Currently, particles' infinite stretching means they have been interacting for an infinite amount of time. This then poses a problem for causality ‪—‬ the order of cause and effect ‪—‬ in particle interactions, the team said.

These new theoretical photons with a cutoff tail would not have this problem, meaning the causal link in an interaction would be clear, Skaar said. He admitted that there is much more work to be done to develop the theoretical description of this interaction. However, the new result is an important step toward describing particle interactions with a clear causal relationship, which Skaar described as the team's "ultimate goal."

For decades, physicists have pursued a goal that sounds nearly impossible: to build a clock that keeps time using an atom's nucleus rather than the electrons orbiting it.

Now, researchers have demonstrated the first functioning nuclear clock ‪—‬ an advancement that could eventually lead to more robust timekeeping devices and new ways to search for dark matter and physics beyond the Standard Model.

"Having worked in this field for more than 15 years, it is just beautiful, how a very 'wild' idea such as manipulating an atomic nucleus with a laser has turned into reality," Thorsten Schumm, a professor of quantum metrology at the Vienna University of Technology and a member of the research team, told Live Science via email.

How is a nuclear clock different from an atomic clock?

Today's most accurate clocks are optical atomic clocks, which measure the frequency of electrons jumping between different energy levels inside atoms. These clocks are so precise that they would lose less than a second over a 100 million years.

A nuclear clock works similarly, but it uses a transition within the nucleus itself, where the nucleus jumps between energy levels. Because the nucleus sits deep inside the atom, it's far less affected by external disturbances from things like electric or magnetic fields. According to Schumm, the nuclear transition can be 1,000 to 10,000 times less sensitive to environmental noise than atomic transitions are.

"This means that it would be easier to stabilize a nuclear clock over long periods of time," Jacob Higgins, a postdoctoral researcher at Northwestern University who previously worked on thorium clock experiments at JILA in Colorado but was not affiliated with the study, told Live Science in an email. "The transition used for the nuclear clock experiment has a higher quality factor than optical atomic clock transitions, which means that in principle, it can be measured more precisely given the same amount of measurement time."

Together, those advantages could allow nuclear clocks to outperform even today's best atomic clocks according to Higgins.

Why thorium-229 is special

The nuclear clock relies on a rare isotope called thorium-229, whose nucleus contains an unusually low-energy excited state that can be manipulated with ultraviolet laser light.

For decades, scientists had suspected thorium had a low transition, but identifying and controlling it proved extremely challenging. Researchers spent years testing different thorium-containing materials, laser systems and detection methods before finally pinning down the transition.

"It was a long road," Higgins said.

One key advancement was the development of continuous-wave lasers that operate at the precise wavelength needed to excite the thorium nucleus. Before those lasers existed, researchers had to excite the nucleus and then wait several minutes for it to decay and emit a detectable signal. That process was too slow to build a practical clock.

"With the continuous lasers, we can measure the nucleus in absorption and get an immediate response, whether the laser is still at the right frequency (and if not, correct it back)," Schumm said. "Once we had that, it was 'just' implementing some electronics and atomization to have the clock stabilize itself to the nucleus."

Thanks to this set-up, the researchers kept the nuclear clock running continuously for 24 hours.

Unlike many optical atomic clocks, which require ultracold atoms to be suspended in a vacuum chamber, the thorium nuclei are embedded inside a crystal at room temperature.

Because the thorium transition remains stable inside a solid material, researchers may eventually be able to build compact clocks that are useful for navigation systems, telecommunication networks and data synchronization.

A tool for studying the universe

Some physicists are more excited about what nuclear clocks could reveal about fundamental physics, rather than the clocks' timekeeping abilities.

Atomic clocks primarily probe electromagnetic interactions involving electrons. Nuclear clocks, by contrast, are sensitive to the strong nuclear force, weak nuclear force and electromagnetism — three of the four fundamental forces of the universe, along with gravity. This can make them useful detectors of new physics, in a way.

"The nuclear clock is foremost a different clock, ticking on different fundamental physics mechanisms," Schumm said. "Essentially all modern theories beyond the standard model predict additional particles or 5th forces … which can be probed with the nuclear clock in some parameter regime."

Thorium-229 is particularly intriguing because the energy difference between its two nuclear states results from a delicate balance between electromagnetic and nuclear forces. Because those large contributions nearly cancel each other out, even tiny changes in the underlying forces could shift the clock's frequency.

"So small shifts in these forces — like if the nucleus were to couple to certain forms of dark matter or if there were an oscillation of a fundamental constant — will be amplified in our measurement," Higgins said.

Researchers, including Higgins, have already used early versions of the clock to place constraints on some dark matter models, and they expect its sensitivity to improve as the technology itself gets better.

Although the first functioning nuclear clock is a major achievement, these timekeepers remain in their infancy. Scientists still need to gain a better understanding of how the thorium transition responds to factors like temperature and magnetic fields while developing more powerful and stable laser systems.

"I think it will be many years before the thorium clock can compete with today's best optical atomic clocks," Higgins said, "but we will learn a lot of new science on the pathway to getting there."

It started with a plate of ginger chicken. In the late 1970s, physicist Richard Feynman — best known for his earlier work on the Manhattan Project — sat down for lunch with his friend Ralph Leighton at a restaurant in Glendale, California. Leighton was agonizing over ordering his usual favorite, or risking something new.

Feynman turned the choice into a math problem, and solved it on a piece of notebook paper. His equation showed exactly when Leighton — or any indecisive diner, for that matter — should stop taking risks and stick with what one knows is good.

For decades, Feynman’s notes on the "restaurant problem” were unreadable. But now, researchers reconstructed a decision-making problem from Richard Feynman's previously undeciphered notes and proved him to be right. The findings were published on June 1 in the journal Proceedings of the National Academy of Sciences.

The problem with picking lunch

Imagine you're visiting a new city for a week. Each night, you can either try an unknown restaurant or return to the best one you've already found. You want to maximize your total dining experience over the whole trip.

That kind of problem has a name in mathematics: an "optimal stopping problem." The same logic shows up in apartment hunting and job searching. But Feynman argued you can always go back to a previous restaurant. The goal is to maximize your cumulative enjoyment, not just find the single best spot.

Feynman's notes showed that the optimal strategy involves a quality threshold — a minimum score you require before committing — that starts high and drops as your trip runs out.

Brian Christian, a computer scientist and cognitive scientist at University of Oxford, began working on the problem about 13 years ago alongside his collaborator Tom Griffiths. They tracked down Feynman's original notes through the Feynman Lectures website.

The team proved that Feynman's solution was indeed optimal, then extended it to other versions of the problem: do people actually solve the problem this way?

They recruited 2,520 participants online and presented them with a digital version of the scenario: a grid of restaurants in a virtual city, each with a hidden quality score revealed only on the first visit. Participants aimed to maximize their total score over a fixed number of nights. Each person played just once.

"We wanted to really capture people's gut intuitions," Christian told Live Science. "When you just get thrown into this situation, what do you do?"

The answer: People don't follow Feynman's optimal curve in reality. Instead of the precise mathematical threshold, participants used a much simpler rule. Their quality bar started high and dropped by the same fixed amount each night regardless of how long the trip was or what the restaurant landscape looked like.

The simple strategy captured about 90% of the value that the optimal approach would yield.

"People are not doing the optimal thing. They're doing something radically simpler," Christian said. "And still the simple strategy is being tailored in a way that feels very situationally appropriate."

The slope of people's declining threshold was identical across every condition — a week-long trip or a month-long one, restaurants distributed evenly in quality or skewed toward extremes. What did shift was where people set their starting bar, adjusting it appropriately based on the landscape they'd seen.

In other words, people used a universal rule for how fast to lower their standards, but calibrated how high to set them in the first place.

An order of redemption

The results fit into an emerging framework in cognitive science called "resource rationality." The idea that humans aren't perfectly rational, but make good use of the limited time and brainpower they have.

"People don't do the perfect thing, but they make nearly perfect use of their constrained resources," Christian said. "I think this is a little bit more of a redemptive story about the human mind than we are used to from the 20th century."

That's a shift from the long tradition in behavioral economics emphasizing human irrationality and cognitive bias.

Christian says the findings also have implications for AI. Most AI systems assume people behave as perfectly rational agents. This study suggests that AI designed around how humans actually think — imperfectly — might work better.

Feynman died in 1988, never having published his restaurant analysis. But more than four decades after he scrawled those notes over lunch, the puzzle he left behind has finally been solved — and it turns out to say as much about the human mind as it does about what to eat.

Of the four fundamental forces of nature, gravity is the one we experience most directly ‪—‬ it's what keeps our feet on the ground and the sun in the sky. Yet we still can't pin down its exact strength. Since the 1980s, scientists have made more than a dozen measurements to calculate the precise value of gravity, and many of those numbers contradict one another.

So why is it so hard to figure out how strong gravity is?

One problem is that gravity is weak. Gravity feels strong because we constantly feel the pull of Earth. But the force of gravity between any two objects in everyday life — or any two objects that can fit in an experimental lab — is extraordinarily weak.

"It's weak, and you have to measure this against the background of the Earth's gravitational field," Stephan Schlamminger, a physicist at the National Institute of Standards and Technology, told Live Science. "If we measure gravity, we have to use everyday objects, because these are the only ones where we know the mass. What you have to do in the lab is basically use two very controlled masses, bring them close together, and measure the force between them."

In an April 2026 study, Schlamminger and colleagues replicated a precision experiment to determine the strength of gravity and calculated a value different from the previous result. They used 13 tons (12 metric tons) of mercury to run their experiment, but even then, "the change in the gravitational field was only a millionth of the change that we have here from local gravity," he said.

The team’s measured value was 6.67387x10^-11 m³kg^-1s^-2, which was 0.0235% lower than the previous result — a small difference in everyday terms, but significant in the field of metrology.

Christian Rothleitner, a physicist at the German National Metrology Institute, co-authored a comprehensive review of all gravity measurements with Schlamminger in 2017 but was not involved in the new study.

"This small force has to be determined to six or more decimal places," Rothleitner told Live Science in an email. "This is equivalent to trying to measure the weight of 7 human cells."

Physics, engineering and psychology

One explanation for the discrepancy in values could be that all of the measurements are so imprecise that the true value lies somewhere within them. But each experiment reports a small margin of error, and those ranges don't overlap.

Schlamminger thinks there are three possible reasons for this.

"I have it as a handy-dandy acronym: It's PEP: P stands for physics, E stands for engineering, and the second P stands for psychology," Schlamminger said. "It's sorted by excitement."

The least probable explanation, he said, is the physics one: Maybe there's some element of physics that scientists don't yet understand. Just as general relativity extended scientists' understanding of gravity, there may be another realm of physics yet to be discovered.

"I think it's a remote possibility, but we should not exclude it," Schlamminger said.

Then, there's the engineering explanation: Every experiment uses a slightly different setup, resulting in different values. Some use a torsion balance, a device that senses tiny forces by measuring the twisting of a small fiber. Others use pendulums or free-falling objects. Each approach has its own potential sources of error, and those mistakes are difficult to untangle from the gravitational signal.

"I personally do not believe that the reason lies in the physics, but in the measurement technology," Rothleitner said.

Human error is another part of the engineering explanation. "Such an experiment requires expert knowledge in many areas of physics and measurement technology," Rothleitner said. "You cannot be an expert in all those fields. This kind of measurement is on the cutting edge of measurement science."

The most likely possibility, Schlamminger said, relates to psychology.

"There is a driver for these people who measure these numbers to give really, really small uncertainties" — that is, margins of error — "because it makes them famous," Schlamminger said. "Because the pressure is there, the uncertainties may be a little bit too small, and that's why they don't agree with each other."

In the end, though, a precise measurement of gravity may not matter. We know the product of G times Earth's mass, and that's enough for practical applications like launching rockets into space. That may be all we need for now.

"The value of Newton's gravitational constant is rather of academic interest," Rothleitner said. "If it were different, nations would have spent much more effort in determining it better."

Schlamminger still finds it exciting, though. "We live in a society where we think everything is discovered," he said. "But if you look, there's still terra incognita. There are still problems, and the problems may be small, but they're still problems we can solve and contribute to and find mesmerizing and intriguing. And this is one of those problems."

Researchers at ETH Zurich have demonstrated a means of generating "perfect randomness" by using entangled superconducting qubits.

Creating true randomness is extremely difficult. Even the most sophisticated conventional random number generator can carry tiny biases. While in most everyday uses those biases are harmless, in cryptography — where the security of encrypted systems depends on unpredictability — even the most subtle pattern can become an exploitable weakness.

The team at ETH Zurich, led by physics professors Renato Renner and Andreas Wallraff, say they have shown how to overcome this flaw and create perfectly random numbers using quantum physics, a milestone they describe as the first certified realization of perfect randomness.

Random acts of qubits

Traditional random-number generators often rely on physical processes such as photon behavior, but those systems can still be slightly skewed and exhibit a bias that causes certain numbers to appear more frequently than others. The ETH team's approach uses quantum entanglement to push randomness beyond that limit.

The experiment revolves around two superconducting chips cooled to temperatures near absolute zero. Each chip acts as a qubit, the quantum equivalent of a binary bit. The chips are connected by a 98-foot (30-meter) tube that is also supercooled, allowing microwave photons to shuttle between them and create entanglement — a "spooky" quantum state where two particles can become linked such that measuring one instantly affects the other.

By keeping the qubits nearly 100 feet apart, the researchers ensured that, during measurement, even light-speed signals could not travel between the qubits quickly enough to influence the outcome. In the language of quantum physics, that helps preserve the integrity of the entanglement and prevents unwanted communication from spoiling the randomness.

The team then started with an imperfect random-number generator to choose the measurement basis for the qubits. After the quantum measurement, they used a special algorithm to amplify the randomness in the results. The key idea is that the quantum system can cleanse the input of bias and produce an output sequence of zeros and ones that is certifiably random, meaning its randomness is not merely assumed or inferred from standard statistical tests.

Practical randomness

The method also significantly reduces computational cost, Renner told Live Science by email.

"Our method does not really require a computation," Renner said, "as all the randomness is generated by measuring quantum bits. In this sense, the computational cost of our approach is negligible compared to that of pseudo-random number generators."

The researchers argue that the output remains perfect for all practical and analytical purposes, no matter how future methods might try to assess it.

The practical implications are significant. The ETH team compares the advance to an atomic clock for timekeeping: a physically reliable reference that other systems can rely on. Future potential applications include message encryption, digital identities, lottery systems and blockchain operations.

Renner stated that their work would be most useful in network architectures. "Our experiment would be most useful in networks where every node has access to a 'server' that implements it to produce randomness."

When a beam of light passes through a cloud of atoms, photons (particles of light) sometimes appear to spend a negative amount of time there, with light seeming to exit the cloud before it even enters. Now, physicists have confirmed this quantum quirk by asking the atoms themselves.

"This doesn't mean that we're on the verge of building a time machine or anything like that," study co-author Howard Wiseman, a theoretical quantum physicist at Griffith University in Australia, told Live Science. "It can all be understood with standard physics, but it's yet one more weird property of quantum physics that people hadn't suspected."

Photons that pass through an atomic cloud can be temporarily absorbed. They vanish as particles of light and reappear as atomic excitations — a kind of stored energy — before being reemitted. Some photons, called transmitted photons, make it through in roughly the same direction they entered Others scatter off in random directions.

Experiments dating back to 1993 had already hinted that transmitted photons tend to arrive at a detector before the center of their own pulse even enters the cloud. That implies a negative transit time.

But there was a problem with this setup: Photons at the front of a pulse may be more likely to make it through than photons at the back. If you look only at the ones that are transmitted, of course, they look early. But this left a door open for a simpler explanation.

"People were convincing themselves that this is not actually as crazy as it sounds," Wiseman told Live Science.

Confirming the crazy

In a new paper published April 13 in the journal Physical Review Letters, physicists tried a different approach. Rather than watching when a photon arrived at a detector, they monitored whether the atoms were in an excited state while the photon was passing through.

When a photon is absorbed by an atom, it is stored as energy, causing the atom to enter what physicists call an excited state. The atom remains in this excited state until it reemits the photon. Therefore, measuring the duration of the atom's excited state reveals how long the photon was absorbed by the atom.

The team measured this using a second beam of light, which picked up a tiny phase shift depending on the atoms' excitation levels. The light beam acted as a live readout of what the atoms were experiencing from moment to moment.

This atomic readout confirmed the quantum craziness of the earlier experiments.

"You get the same answer if you ask the atoms, 'How long was the photon staying with you?'” Wiseman said. "They will also tell you an answer, which is a negative time."

A million-test milestone

Getting that answer wasn't easy, because measuring quantum systems disturbs them. In this case, it potentially prevents the photon from being absorbed at all. So the team used "weak measurements," which are gentle but extremely noisy. Any single run of the experiment was swamped by noise — random fluctuations that made it impossible to tell signal from static in any individual measurement. Only after averaging roughly 1 million runs did a clear signal emerge. Across roughly seven sets of experimental parameters, the total data collection ran to approximately 70 hours.

"Even in this really simple thing — a photon interacting with atoms — people were already doing calculations on that almost 100 years ago," Wiseman said. "Just the fact that it can still show surprises after all this time is interesting."

The team's next target is the photons that don't make it through the cloud. Theory predicts that those scattered photons carry extra positive excitation time. That is enough to balance the negative time of the transmitted ones, keeping the overall average for the beam of light at zero or above. That prediction has never been tested.

Recently, a cheerful 100-year-old message in a bottle was found on the south-west coast of Australia. In it, a world war one soldier proclaimed to be "as happy as Larry."

If you're a betting person, you probably wouldn't expect great odds of this happening. A bottle cast into the ocean could end up absolutely anywhere.

If it floats to a remote location, there is little chance of somebody stumbling upon it. And if it lands somewhere more favorable where people could potentially find it, there are other issues. The message itself will deteriorate over time as light degrades it. If the bottle fills with water, it will sink and almost certainly never be found.

So, what are the chances of a message in a bottle being found and it being over 100? And what are your chances of finding this bottle?

Despite these many possibilities during a bottle's lifetime, the probability we are after is a straightforward calculation. Just count up the number of bottles with messages that have been found and are over 100 years old, and divide by the number of messages that have been sent this way (assuming we know how many are sent):

Our diagram below shows a hypothetical situation where 20 bottles are sent in total, of which six are found (indicated in gold) and one of these is over 100 years old (indicated by the "100" stamp). So, one in 20 bottles are found and over 100 years old. (Note: This is only a hypothetical calculation, not the real data.)

Instead of calculating the probability directly, another way to do it is by breaking the problem into two parts: (A) a bottle with a message is found, and (B) the found bottle is over 100. These two probabilities can be calculated separately and multiplied together to get what we want:

This is known as the "multiplication rule" of probability, and we confirm from our hypothetical numbers that (6/20)×(1/6) = 1/20, as before.

Both approaches to calculating this probability are simple. However, the direct calculation requires knowing the total number of bottles sent out, which is very difficult to know in the real world.

The multiplication rule has the advantage that it breaks the calculation into two parts. We can tackle each separately, then bring the two results together to get the probability we want. This is useful in the real-world situation where we can draw information from different sources.

First, we'll deal with the probability that a bottle with a message is found, irrespective of its age.

Experts from the Federal Maritime and Hydrographic Agency of Germany suggest a 1 in 10 chance that a message in a bottle will be found. This aligns broadly with various historical "drift bottle" experiments, where oceanographers released large numbers of bottles to understand ocean currents.

For example, studies from the 1960s and '70s in the North Atlantic Ocean led to recovery rates of 14% from the Gulf of Mexico, 8% from the Caribbean Sea and 7% from the northern Brazilian coast. A more recent and more northerly study (between Canada and Greenland) from the 2000s led to a 5% recovery rate.

We would expect the results to vary naturally from different experiments in different parts of the world. But to keep things simple, we will stick with 1/10 as the probability that a bottle with a message is found.

Now for the second piece of the calculation: of the bottles that are found, what proportion are over 100 years old?

The table below summarises data from news articles collected on Wikipedia about very old bottles with messages that have been found. However, only data on bottles over 25 years old has been collected, presumably because older bottles are more newsworthy.

So, we needed to estimate the number of 0- to 25-year-old bottles with messages ourselves — here’s how we did this.

The table shows that fewer bottles with messages are found as they get older. Messages in bottles degrade over time, which means the bottles have an increased chance of breaking and sinking, or just getting covered in layers of sediment. Plotting this data in the graph below helped us see the trend in the ages of found bottles more clearly.

We drew a line to match this observed trend in the ages of found bottles. This red line in the graph corresponds to the equation:

This equation provides an estimate of how many bottles have been found for any specific age range (where 25 = 0-to-25, 50 = 25-to-50 and so on). We are interested in the the 0- to 25-year-old bottles, so the equation suggests 46 bottles have been found in this range.

Adding up this and all of the numbers in the table gives a total of 106 bottles found, of which 12 are over 100 years old, and 12/106 is about one in ten.

Recapping the above, we have that: (A) one in ten bottles with messages are found, of which (B) one in ten are over 100 years old. Bringing these results together using the multiplication rule, we estimate the chance of a message in a bottle being found and it being over 100 years old to be (1/10)×(1/10) = 1/100.

So, if there are 100,000 bottles with messages floating around the oceans waiting to be found, we’d expect 1,000 of these to be found and be 100 or more years old. Assuming anybody in the world is equally likely to find one of these, with 8 billion people currently, that’s about a 1 in 8 million chance of you finding one – pretty unlikely.

However, some people are more persistent at message-in-a-bottle hunting than others. Following the paths of ocean currents (known as gyres) could provide clues on where to look.

Specifically, peninsulas or islands intersecting with these gyres could be good spots. For this reason, it has been suggested the Caribbean islands are ideally placed for finding bottles as they lie on the path of the North Atlantic Gyre. Which seems like a great reason to travel to the Carribean!

But let's also spare a thought for the poor soul stranded on their desert island, who surely won't appreciate the low odds of their SOS being found.

This edited article is republished from The Conversation under a Creative Commons license. Read the original article.

For the first time, researchers have detected empty voids moving faster than the speed of light — and they blazed past that cosmic speed limit without breaking the laws of relativity.

A recent study shows the voids' acceleration. Researchers used recent advances in ultrafast electron microscopy to measure voids in phonon-polariton waves zooming around inside a thin flake of boron nitride. Phonon-polaritons are quasiparticles formed from photons (quantized light) coupled with tiny vibrations, and they act like light and sound waves combined.

Waves are often visualized as a single squiggle, but in many applications, imagining them as a lake could give a better idea of what's going on. Lakes are full of waves and ripples that interfere with each other. If the waves interact when they're at their maximum height, they combine to create an even higher wave. But if they make contact when they're at their lowest points, they create deeper troughs than they would on their own.

Sometimes, waves cancel each other out, creating points where the waves' magnitude drops to zero. In a lake, this would make a temporary whirlpool (a vortex) that moves around that empty point, also called a singularity. These singularities are found throughout nature and mathematics and, since the 1970s, have been theorized to move faster than light speed in some instances, according to a recent statement from the Technion-Israel Institute of Technology.

Blazing past the limit

Einstein's theory of special relativity states that the speed of light in a vacuum ‪—‬ 299,792,458 meters per second, or about 186,000 miles per second ‪—‬ is the fastest speed information, matter and energy can travel through space. So how do singularities move faster than light speed? Because singularities are empty points of nothingness, they contain no information, no matter and no energy. They are tiny voids, so they don't have to obey the cosmic speed limit.

These voids don't just exceed the speed of light ‪—‬ they blaze past it. When two singularities encounter each other, they can sometimes exponentially speed up toward each other until their velocities approach infinity just before they cancel each other out. However, the faster they go, the harder it is to observe them. The recent study, published March 25 in the journal Nature, shows researchers doing just that.

"Our discovery reveals universal laws of nature shared by all types of waves, from sound waves and fluid flows to complex systems such as superconductors," Ido Kaminer, an electrical and computer engineering professor at the Technion-Israel Institute of Technology and a member of the research team, said in the statement.

The study's results apply to more than just tiny whirlpools; the null points act enough like particles that scientists can study them to better understand particle interactions. To do this, researchers need to know where the comparison breaks down. The new study shows the voids' need for speed is a point where the singularities stop acting like particles, since particles obey the cosmic speed limit that voids ignore.

In addition, the team's new techniques for observing very small, very fast things could light up some previously unexplored pockets across multiple scientific disciplines.

"We believe these innovative microscopy techniques will enable the study of hidden processes in physics, chemistry, and biology, revealing for the first time how nature behaves in its fastest and most elusive moments," Kaminer added.

For the first time, scientists have observed quantum entanglement in the way atoms physically move — bringing a phenomenon once described by Albert Einstein as "spooky action at a distance" into even sharper reality.

In the new study, published in the journal Nature Communications, researchers demonstrated that pairs of ultracold helium atoms can be quantum mechanically linked through their momentum — a measure of how fast and in which direction a particle moves, factoring in its mass.

Quantum entanglement is one of the strangest features of quantum mechanics. When two particles are entangled, a measurement of one instantly affects the other. Scientists had demonstrated this before in photons (packets of light) and in the internal spin states of atoms but never in the motion of particles with mass. This is important because atoms have mass, and mass responds to gravity; photons don't. Momentum-entangled atoms could one day power quantum sensors precise enough to detect space-time ripples called gravitational waves or to map Earth's interior.

Catching entanglement in the act

First, the team chose helium as their atom, because it can be held in a long-lived excited state with a lifetime of around two hours — which is “essentially infinite” in experiments that only last 20 to 30 seconds, Sean Hodgman, an experimental physicist at the Australian National University and senior author of the study, told Live Science. That internal energy means each atom hits a detector with enough force to register individually. It allows the team to reconstruct the full three-dimensional momentum of the cloud with single-atom resolution.

To create momentum-entangled atom pairs, the team started with a cloud of helium cooled to near absolute zero. Normally, atoms zip around independently. But if you cool them enough, they slow to a near standstill. Their quantum identities blur together into a single collective object called a Bose-Einstein condensate.

Then, they used tuned laser pulses to split that condensate into three groups: one kicked upward, one kicked downward, and one left stationary. As the moving clouds passed through the stationary one, pairs of atoms collided and scattered in opposite directions, forming spherical shells of correlated pairs. Physicists call it "scattering halos." At low enough density, only a single pair scatters per experimental shot. "You either have a pair at one position, or a pair at another," Hodgman said. "Your entangled state is a superposition of both."

To prove the entanglement was real, the team used a device called a Rarity-Tapster interferometer. This method, first demonstrated with photons in 1990, now extended to matter waves for the first time.

"The atoms scatter apart; then you reflect them back onto themselves and interfere with them together," Hodgman explained. "Interference only occurs if the atom is truly in a superposition of both states." The correlations the team measured cannot be explained by any classical theory.

To get their final result, the team collected data continuously for nearly a month and spent a month to a year just setting up the experiment.

"This has kind of been a long-term goal for our lab for probably 20 years or so," Hodgman said. "To be able to finally demonstrate it is really exciting."

A surreal win for quantum mechanics

The result, while exciting, mainly served to validate “textbook” physics theories, Hodgman added. Quantum mechanics predicts this exact kind of behavior, but that doesn't make it any less disorienting.

"Our brains aren't really equipped to process it," Hodgman added. "Atoms appear as smeared out at small scales, not concrete blobs or little balls. And that just seems really, really weird."

The team is already working on a stronger version of the test. But the experiment Hodgman describes as the most consequential next step involves colliding two isotopes of helium ‪—‬ helium-3 and helium-4, which are fundamentally different kinds of particles — to create pairs entangled in both momentum and mass simultaneously.

"From a quantum gravity point of view, how do you even write down the gravitational description of that kind of state?" Hodgman said. "You can't really describe it in a general relativity framework at all. These sorts of states would provide a real challenge for quantum gravity theories to explain."

Athreya, Y. S., Kannan, S., Yan, X. T., Lewis-Swan, R. J., Kheruntsyan, K. V., Truscott, A. G., & Hodgman, S. S. (2026). Bell correlations between momentum-entangled pairs of 4He* atoms. Nature Communications, 17(1). https://doi.org/10.1038/s41467-026-69070-3

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Physicists have successfully transported antimatter by truck for the first time — a milestone that allows them to study the elusive material with unprecedented precision and could eventually help to explain how matter came to dominate the universe.

The short, tightly controlled journey around the campus of the European Organization for Nuclear Research (CERN) in Geneva demonstrated that antimatter, one of the most fragile substances known to science, can be moved without being destroyed. That capability allows scientists to transport antimatter to quieter labs across Europe, where ultrasensitive experiments are less affected by interference than they are at CERN.

"This opens, in principle, an entire new universe for precision measurements outside of CERN," Stefan Ulmer, a spokesperson for the BASE (Baryon Antibaryon Symmetry Experiment) collaboration that carried out the experiment, said in a recent video.

What’s the matter with antimatter?

According to current theories, the Big Bang should have produced equal amounts of matter and antimatter. If that were the case, the two would have annihilated each other completely, leaving behind a dark, empty universe. Instead, the observable universe is puzzlingly, overwhelmingly made of matter, and physicists believe that any measurable difference between matter and antimatter could offer a crucial clue to resolving that mystery.

CERN has been producing antimatter for decades through high-energy particle collisions at its "antimatter factory." But the same powerful equipment used to create the particles also generates tiny magnetic fluctuations that can disrupt the extremely precise measurements scientists are trying to make. Relocating antimatter to more stable environments could help, but transporting it is notoriously difficult.

When antimatter comes into contact with ordinary matter, both are instantly destroyed in a burst of energy. To prevent that, scientists confine antimatter particles using carefully tuned electric and magnetic fields in a near-perfect vacuum — conditions that are challenging to maintain even in a stationary laboratory, let alone in a moving vehicle.

To test whether transport was feasible, Ulmer and his team loaded 92 antiprotons, the antimatter counterparts of protons, into a portable trap and drove them about 5 miles (8 kilometers) around CERN's campus.

Inside the device, the particles were suspended in a near-perfect vacuum and held in place by electric and magnetic fields, preventing them from touching the container walls. The team monitored the particles throughout the trip and reported that they remained stable despite road vibrations and motion, according to a CERN statement.

Even in a worst-case scenario, the experiment posed little risk. The amount of antimatter involved was extremely small, and its annihilation would have released only a negligible amount of energy. According to CERN, even all the antimatter ever produced at the facility would generate only enough energy to power a single light bulb for just a few minutes.

Beyond the Standard Model

The successful test does not immediately change how antimatter is studied, but it demonstrates that transporting it is technically feasible. That, in turn, opens the possibility of moving antiprotons to quieter laboratories across Europe, such as the Heinrich Heine University Düsseldorf in Germany, located about eight hours by road from CERN, where quieter conditions could enable more precise measurements.

Such measurements could help scientists detect even the faintest differences between matter and antimatter. If those differences exist, they could point to why matter came to dominate the universe, offer clues to physics beyond the Standard Model, and ultimately explain why anything — from stars, to planets, to people — exists at all.

"We are at the beginning of an exciting scientific journey that will allow us to further deepen our understanding of antimatter," Gautier Hamel de Monchenault, CERN's director for research and computing, said in the statement.

The Big Bang is often described as the moment everything began — a point of infinite density where the laws of physics broke down. But what if that picture is incomplete?

A new study proposes a different account of the universe's birth: Instead of an abrupt beginning from a singularity, as predicted by Einstein's theory of general relativity, the early cosmos may have passed through a more controlled high-energy phase governed by a modified theory of gravity known as QQG.

"QQG stands for quadratic quantum gravity," study co-author Niayesh Afshordi, a professor of physics at the University of Waterloo and the Perimeter Institute for Theoretical Physics, told Live Science via email. "In simple terms, it is an extension of Einstein's theory of gravity that includes additional terms which become important at extremely high energies, such as those that would have existed near the beginning of the universe."

The study was published March 18 in the journal Physical Review Letters.

Why Einstein's theory may not be enough

Einstein's theory of general relativity has been extraordinarily successful in describing gravity on large scales. It explains the motion of planets, the behavior of black holes, and the expansion of the universe. However, it struggles to explain the ultra-small world of quantum mechanics and is widely believed to contain some fundamental inconsistencies.

"The main problem is that Einstein's general relativity predicts its own failure under extreme conditions, most famously at the Big Bang singularity," Afshordi said.

At that point, densities and space-time curvature become infinite — a clear indication that the theory is incomplete. Physicists have long sought a deeper framework that can describe gravity under such conditions.

"What makes [quadratic quantum gravity] interesting is that it may provide a mathematically consistent way to describe gravity at very short distances and very high energies, where ordinary general relativity is expected to break down," Afshordi said. "In that sense, it offers a possible conservative route toward a quantum theory of gravity, while still remaining close to Einstein's theory at ordinary scales."

A universe without a singularity

In the new study, the researchers explored how QQG would reshape the earliest moments of the cosmos if it is indeed a correct completion of Einstein’s theory. Their results suggest that the universe may not have started from a singular point at all.

"Our main result is that, within quadratic gravity, the very early universe can avoid the usual Big Bang singularity and instead pass through a better-controlled high-energy phase," Afshordi said.

Rather than emerging from an infinitely dense state, the universe would have begun in a smoother, more stable configuration with finite density and finite temperature, with its precise properties depending on the particles and fields present at extremely high energies and temperatures. This avoids one of the most troubling predictions of standard cosmology.

The theory also offers a fresh perspective on cosmic inflation, the brief period of extremely rapid expansion thought to have occurred just after the Big Bang.

"In our analysis, this framework can also generate an inflation-like period without having to introduce an extra hypothetical field by hand," Afshordi said.

In standard models, inflation is typically driven by a mysterious field known as the inflaton. That field has never been directly observed. In contrast, QQG produces inflation naturally as a consequence of gravity itself.

"In other words, some of the key ingredients we normally add separately to cosmology may arise directly from the gravitational theory itself," Afshordi added.

From exotic physics to the familiar universe

One striking feature of QQG is that it behaves very differently depending on the energy scale. At extremely high energies, it follows new quantum rules. But as the universe expands and cools, it transitions back to the familiar physics described by Einstein.

The theory suggests that gravity becomes simpler at very high energies — a property known as asymptotic freedom — before evolving into the form we observe today. Eventually, the universe enters the hot, radiation-filled phase described by standard cosmology.

This framework provides a continuous bridge between an exotic early universe and the well-tested physics of later times. The key question, however, is whether this idea can be tested.

"Yes, at least in principle," Afshordi said. "The most promising tests come from cosmology, especially from the imprint of the early universe on primordial gravitational waves and the cosmic microwave background."

These ancient signals carry information about the universe's earliest moments. According to the new theory, these signals should contain subtle differences compared with predictions from standard inflation models.

"One particularly interesting aspect of our scenario is that it can lead to distinctive predictions for the gravitational-wave signal produced in the early universe," Afshordi noted. "As observational sensitivity improves over the coming years and decades, future measurements of primordial gravitational waves could begin to distinguish this kind of model from more conventional inflationary scenarios."

Although the idea is still being explored, it offers a compelling possibility: that the Big Bang may not have been a singular beginning but rather part of a deeper, quantum description of gravity. If confirmed, this framework could reshape how scientists understand the origin of the universe — replacing a breakdown of physics with a new, more complete picture of cosmic beginnings.

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Molecular vibrations can "catapult" electrons across solar materials in quadrillionths of a second‬ ‪— much faster than previously thought, a new study shows.

The findings could help scientists find more efficient ways to convert solar energy into electricity, according to the study, which was published March 5 in the journal Nature Communications.

"We're effectively watching electrons migrate on the same clock as the atoms themselves," study co-author Pratyush Ghosh, a researcher who studies ultrafast spectroscopy at the University of Cambridge, said in a statement.

Organic molecules go solar

Organic solar cells use carbon-based molecules, rather than silicon, to convert sunlight into electricity. In theory, organic solar cells could provide that electricity at lower cost than conventional solar cells, but they are much less efficient.

In a typical organic solar cell, an electron donor and an electron acceptor are sandwiched between two conductive electrodes. When light hits the cell, it generates an "exciton," an electron-hole pair. Excitons split at the interface between the donor and the acceptor, generating electricity.

To achieve fast charge transfer at the interface and limit energy loss, the donor and acceptor molecules usually have strong electronic coupling, or overlap between their electronic states, which allows charges to move easily between molecules. They also often have a large energy difference between them, but that limits the voltage available from the device.

In the new study, researchers observed ultrafast charge transfer at a junction between the electron donor and electron acceptor in an organic solar cell, without needing to conform to either of these constraints. The team used a short laser pulse to excite the electron donor, a polymer called TS-P3, and then used a different laser to measure how the system changed during charge transfer.

That charge transfer happened in 18 femtoseconds ‪—‬ about as fast as an individual molecule vibrates. A few other systems without strong driving forces exhibit charge transfer over 100 to 200 femtoseconds, but most take ten to a thousand times that long.

"Seeing it happen on this timescale within a single molecular vibration is extraordinary," Ghosh said in the statement.

A 'molecular catapult'

That similar timescale wasn't a coincidence. In a second set of laser experiments, the team found that vibrations in the polymer donor molecule launched an electron across the junction to an acceptor molecule. When the electron arrived, it triggered overlapping vibrations in the acceptor molecule. This overlap allowed charge transfer to happen much more quickly than expected, and without the need for strong coupling or a large energy difference.

"Instead of drifting randomly, the electron is launched in one coherent burst," Ghosh said in the statement. "The vibration acts like a molecular catapult. The vibrations don't just accompany the process, they actively drive it."

The findings help to explain the processes that control the speed of charge transfer and establish new strategies for designing more efficient organic solar cells and materials, the researchers wrote in the study.

"Instead of trying to suppress molecular motion, we can now design materials that use it ‪—‬ turning vibrations from a limitation into a tool," study co-author Akshay Rao, a physicist at Cambridge, said in the statement.

Today's top story

Hex appeal

Researchers in China claim to have synthesized the very first samples of "hexagonal diamond" — a mysterious and coveted material believed to be harder, stiffer and chemically tougher than natural diamond.

Scientists have been arguing about hexagonal diamonds (whose carbon atoms arrange themselves in hexagons instead of the cubic lattices seen in natural diamonds) for decades. First theorized in 1962, the diamonds were later discovered in meteorites that arrived to Earth from the mantles of shattered dwarf planets, although the evidence for this is disputed.

Now, three separate research groups appear to have made pure to nearly pure hexagonal diamond samples. If their findings are replicated consistently and can be scaled up, they could open up all kinds of new applications.

The trend

Scaling down

Climate change is making fish smaller, according to an alarming new study published in the journal Science. It warns that the shift may worsen fishery losses by 50%.

As ocean temperatures soar, fish are evolving to grow faster and mature earlier, reducing their maximum size. This in turn leads to smaller catches for fisheries, putting a vital protein source relied upon by billions of people on a very thin line.

The scientists behind the study say this is yet another reason to reduce carbon emissions, preserving millions of tons of food production that would otherwise be lost.

Three to read

1. Measles' resurgence in the US is a grim sign of what's coming [Live Science]
2. China creates a clock so accurate it could redefine the second [ScienceAlert]
3. GPS is being weaponized in electronic warfare ‪—‬ and it's putting ships at risk [Live Science]

Say it, said it

Word of the day: Zugzwang — Starting as a chess term, this German word is used in psychology and game theory to describe a situation where any move you make will worsen your position.

Quote of the day: "We are now faced with a 30-million-tonne question: we need to determine if this is just a small, natural leakage of ancient carbon, or the onset of broadscale destabilization."

Travis Drake, a carbon biogeochemist at the Swiss Federal Institute of Technology Zurich (ETH Zurich), on the detection of ancient carbon seeping into the atmosphere from the Congo Basin.

Fun and games

Today's game is Chain Word, which is a bit like another popular word game, but with science.

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Researchers in China have made what they claim to be the first samples of pure hexagonal diamond, a theorized rare variant of superstrong diamond found in meteorites from shattered dwarf planets.

Natural diamond, also called cubic diamond, has been considered the hardest natural material on Earth for so long that the Mohs hardness scale, which rates minerals' resistance to scratching, uses diamond as the scale's upper limit. It's called cubic diamond for its neat arrangements of carbon atoms in a cubic structure. In contrast, hexagonal diamond organizes carbon atoms in a lattice made of hexagons, like a honeycomb.

An elusive mineral

In 1962, researchers at the Pittsburg Coal Research Center theorized that layers of carbon atoms making up diamond could be organized in a hexagonal lattice instead of a cubic one, thanks to how carbon forms bonds with other carbon atoms. In 1967, researchers discovered hexagonal diamond — or lonsdaleite — in the lab, suspecting it could be harder than cubic diamond.

They started looking for it in a special type of diamond-rich meteorite called ureilite, which forms from the mantle of smashed dwarf planets. The first detections of hexagonal diamond in the wild were documented in a 1967 paper; three Canyon Diablo meteorites (fragments of an asteroid that created a large crater in Arizona) with about 30% hexagonal and 70% cubic diamond phases, and Goalpara meteorites (found in Assam, India) that had a small amount of hexagonal diamond.

Not everyone agrees that the Canyon Diablo lonsdaleite exists. Some scientists thought the evidence could be explained by flawed cubic diamond that was stacked chaotically, and they weren't convinced that lonsdaleite had been detected in previous studies. However, multiple recent studies have identified lonsdaleite in meteorites and in lab samples, including a 2025 study that made small amounts of it in the lab.

The biggest challenge in identifying lonsdaleite is the lack of pure samples; in many cases, it is mixed with cubic diamond, graphite and other minerals. This makes it difficult ‪—‬ or even impossible ‪—‬ to test and measure its unique properties.

The new study, published March 4 in the journal Nature, addressed this problem by creating several pure hexagonal diamond samples about 0.06 inches (1.5 millimeters) in diameter ‪—‬ big enough to measure the samples' material properties. The team found that hexagonal diamond is both stiffer and harder than cubic diamond, and that it resists oxidation much more than cubic diamond does. This means hexagonal diamond can tolerate much higher temperatures without its surface getting all gunked up by reacting with oxygen, which is important for applications like drilling.

First evidence of hexagonal diamond?

The study also provides major evidence that hexagonal diamond is a real material. According to the study, "structural and spectroscopic analyses, supported by large-scale molecular dynamical simulations, unambiguously confirm the identity of HD (hexagonal diamond)."

To make the samples, the researchers compressed very organized graphite (graphite with carbon atoms neatly arranged) for 10 hours at 20 gigapascals, or about 200,000 times Earth's atmospheric pressure at sea level, and subjected them to temperatures ranging from 2,300 to 3,450 degrees Fahrenheit (1,300 to 1,900 degrees Celsius). At higher temperatures and pressures, the lonsdaleite started morphing into cubic diamond.

Hexagonal diamond could improve processes and tools that currently rely on cubic diamond, like drilling and cutting tools, polishing abrasive coatings, and dissipating heat from electronics. Its presence in meteorites can also tell us a lot about how the meteorite formed and where it came from, giving more clues about our solar system.

The elusive material "has potential applications in many fields, for example in cutting tools, in thermal management materials and in quantum sensing", Chong-Xin Shan, co-lead of the new Nature study and a physicist at Zhengzhou University, told Nature in an article.

The new study also provides "a practical strategy for producing HD (hexagonal diamond) in bulk form," opening the way for bigger samples, more scientific exploration, and industrial applications no longer limited by cubic diamond's hardness, according to the authors.

As an irrational number, pi has no end — but that has not stopped computer engineers from chasing its eternal string of decimal places deeper into the unknown. Recently, technology media company StorageReview achieved a staggering new record, calculating 314 trillion digits of pi on a single Dell PowerEdge R7725 server that ran constantly for nearly four months.

The result shows that in modern pi calculations, the real battle is no longer just about processor speed but also storage space and efficiency. StorageReview's Dell PowerEdge R7725 server had 1.5 terabytes of memory to get the job done.

"The storage layer, specifically, is where this record was actually won," StorageReview representatives wrote in a December 2025 statement.

An irrational arms race

Previous pi records have jumped fast in the past few years, from Google Cloud's 100 trillion-digit run in 2022 to StorageReview's own 105 trillion-digit and 202 trillion-digit marks in 2024. In April 2025, Linus Media Group and Kioxia stole the crown by calculating pi to 300 trillion digits — but StorageReview reclaimed the record in November 2025.

The results were announced in time for Pi Day, March 14 (or 3/14) — a nod to the number's famous first three digits (3.14). The day has become a lighthearted tribute to math, marked by pie jokes, slices of pie, classroom contests and a public fascination with a number that never ends.

Why pi is important

Pi is a key constant in mathematics, linking every circle's circumference to its diameter. It appears in geometry, physics, engineering and statistics, showing up in everything from waves and orbits to bridges, buildings and computer models. Most people encounter pi in school as a simplified number used to find the area or circumference of a circle. But for engineers and scientists, it's a building block that helps describe how the physical world works.

Pi is considered an irrational number because it cannot be written as a simple fraction of two whole numbers. Its decimal form never ends and never settles into a repeating pattern. Mathematician Johann Lambert was the first to prove pi was irrational in 1761, showing that no fraction can exactly equal the ratio of a circle's circumference to its diameter. So, even though pi is a precise number, its decimal expansion is endless.

All those digits aren't strictly necessary for accurate calculations; NASA typically stops at 16 digits in its most precise calculations about the universe. Still, researchers challenge themselves to calculate pi to ever-more decimal places for multiple reasons. It's a way to test the limits of computers, storage and software, as a huge pi run can expose weaknesses in hardware better than many standard benchmarks. Calculating pi also helps researchers refine algorithms for handling other large calculations.

Then, of course, there's the fame of being the one to calculate pi out to the most decimal places yet. To achieve the mind-boggling result of 314 trillion digits of pi, StorageReview delivered around 280 GB/s bandwidth on its Dell server to handle the huge stream of intermediate calculations required for such a large run.

"If someone wants to take the record, we would like to see them take the whole thing: more digits, less power, shorter wall time, and the same zero-downtime reliability," the company said in the statement. "Until then, this is the benchmark for efficiency."

Pi quiz: How much do you know about this irrational number?

Researchers have developed a technology to invisibly transmit information disguised as background thermal radiation. Using a phenomenon called "negative light," they transferred 100 kilobits of data per second in a way that was completely undetectable to outside observers.

Most methods for concealing data during transfer involve hiding it among other data or encrypting it in a way that makes it impossible to read without a cipher or other means of decryption. The new technique, by contrast, makes the data almost impossible to intercept because there's no indication it's being sent at all. It can also be encrypted through traditional means to further harden security, the team wrote in a paper published March 5 in the journal Light: Science & Applications.

This hidden transfer is possible due to a phenomenon called "negative light." It relies on infrared radiation, which is the band just beyond the red end of the visible light spectrum. Infrared radiation is invisible to the naked eye, but it can be detected with thermal cameras. We experience it as heat from warm objects, and all objects emit a faint glow in the infrared.

The negative luminescence the team used could make that glow dimmer, rather than brighter. In a statement, Michael Nielsen, a professor of engineering at the University of New South Wales Sydney and lead author of the study, compared it to a flashlight that could "project darkness" as compared to background light, rather than simply turning off.

Using devices called thermoradiative diodes, the team created patterns of brighter- or darker-than-usual states that blended into typical infrared background "noise" but that can be read as data by specialized receivers.

The thermoradiative diodes were born as part of another project, in which the team proved that it was possible to generate solar power even after the sun had set. This "night-time solar" tech captured infrared radiation that Earth had absorbed during the day and was releasing at night as it cooled. The team then used thermoradiative diodes to generate a small amount of power.

While the initial transfer rate of 100 kbps is quite modest, Nielsen said higher speeds are achievable. The main hurdle was the availability of some of the sophisticated electronics the team required. In principle, there's nothing stopping this method from transferring tens of megabits per second with existing devices, with better devices and detector design pushing the speed to gigabits per second, the team said.

In fact, a commercial product delivering megabit-per-second data rates may be possible in just a few years, Ned Ekins-Daukes, a professor of photovoltaic and renewable energy engineering at UNSW and co-leader of the research, said in the statement.

By using graphene ‪—‬ a single-atom-thick sheet of carbon atoms arranged in a honeycomb pattern ‪—‬ instead of the current semiconductor material in the diodes, "we can potentially achieve data transfer rates in the gigabits-per-second range, if not hundreds of gigabits," Ekins-Daukes said.

Improved data security would have major applications in a variety of industries, including health care, defense, finance and manufacturing. Nielsen believes that virtually any communication that could benefit from security beyond standard encryption could take advantage of his team's breakthrough.

"The real advantage of this technique is that the very signal or act of communication is hidden if an outside observer doesn't have the same technology required to intercept the communication," Nielsen told Live Science in an email.

Earlier this month an artificial intelligence (AI) startup announced that their AI agent had confirmed a proof of two cases of the devilishly challenging "higher dimensional sphere-packing problem." In 2022, the proofs earned Ukrainian mathematician Maryna Viazovska a Fields Medal, one of the most prestigious prizes in math.

This was a giant step forward, and speaks to the emergence of a quiet revolution in the field.

On the surface, it may not seem so extraordinary. After all, mathematicians have long used tools to extend their abilities — abacuses, slide rules, calculators and, eventually, computers. Yet none of these tools ever replaced mathematicians; they just allowed us to refocus our attention on more interesting problems. The arrival of AI in mathematics might feel like another step in that same process. But there's a crucial difference: This time, the tools aren't just helping us calculate; they're helping us reason, or at least perform many of the routines that sit underneath human reasoning.

This represents a seismic shift in what it means to do mathematics. Instead of working unassisted, struggling at the boundaries of our own cognitive limits, we are starting to build and tune the instruments that will allow us to extend these limits, pairing human intuition with machine-level discipline. This might mean that our most sophisticated proofs won't be works a single mind can grasp; rather, they will be fully understood only in a collective mind that relies heavily on AI tools. It also means the scope of the math we can tackle will increase dramatically.

The change has been coming for a while. For years, our biggest proofs have not been the endeavours of single mathematicians. Many modern research articles in pure mathematics now rely on huge conceptual frameworks, long dependency chains, and catalogs of results that no single person can fully internalize. Computers have played a role in large proofs before, like the four-color theorem and the Kepler conjecture. But what's changing now is the level of autonomy and reliability we can expect from AI systems working alongside formal proof assistants — programs designed to check mathematical arguments.

These formal verification languages express mathematical arguments in a way a computer can check step by step, guaranteeing that every part of the proof is logically sound. Take the language Lean, for example. Unlike ordinary mathematical writing, Lean requires every definition and inference to be made explicit, and it checks each step mechanically and methodically. It's unforgiving, but in a productive way: If the argument is passed by Lean, that, in theory, means the proof doesn't have hidden assumptions or leaps of faith. Over the past few years, Lean has become a proving ground for research‑level mathematics, and mathematicians have been building "libraries" to support increasingly complex problems.

These libraries are huge collections of definitions and already‑verified theorems that have been painstakingly programmed, allowing researchers to prove new results in the language. But until recently, turning cutting‑edge proofs into machine‑checkable form required specialists to devote months or years to the work.

That's the context in which the recent formal verification of Viazovska's higher-dimensional sphere‑packing results should be understood. The sphere‑packing problem asks how tightly identical spheres can be packed together in spaces of any dimension, not just the 3D world we live in. Before Viazovska's breakthrough, the sphere‑packing problem had only been fully solved in dimensions one, two and three, with all higher‑dimensional cases remaining open. Viazovska's proofs of the eight- and 24‑dimensional sphere-packing problem, are profound pieces of mathematical insight that solve problems previously thought out of reach.

Fields Medal-level advancements

The recent important step forward is that a human-AI collaboration has now translated those arguments into fully verified Lean code, which then checked every step. The sheer scale of that achievement is astonishing; these are recent Fields Medal‑level results, and they have now been certified at a level of detail and certainty that would be impossible for individual referees, or even large human specialist teams, to reproduce unaided.

A key ingredient was Math, Inc.'s AI reasoning agent Gauss which had played a vital role in helping to turn human mathematical arguments into Lean proofs. The AI system wasn't working entirely unaided; mathematicians still had to set out the blueprint, shape the overall structure, and ensure the right concepts were in place. But once that scaffolding existed, the system could fill in the missing pieces at extraordinary speed. In the eight‑dimensional case, it completed work that the human contributors had estimated would take them months, and it did so in days. The 24‑dimensional case, which is even more intricate, followed soon after.

This is more than a technical accomplishment. It points toward a shift in the way mathematicians might organize their work. When I talked to UCLA mathematician and Fields Medalist Terence Tao, he suggested that the immediate value of AI might come not from cracking our hardest problems outright but from relieving us of the drudgery — the thousand small cases that are conceptually straightforward but too time‑consuming for any one person to tackle by hand.

Some AI systems, he argued, are already surprisingly good at handling these tasks, letting mathematicians devote their attention to strategy rather than bookkeeping. Tools like Lean matter because they give us a way to separate the creativity of generating ideas from the rigor of checking them.

AI proof expert Kevin Buzzard, of Imperial College London, expressed a complementary view. He worries, rightly, about the dangers of relying on large language models that sound authoritative without guaranteeing correctness. But he also argues that formalization offers a way through this. In Lean, if the program accepts all the steps, then it's a valid proof. This doesn't mean the computer has necessarily done something "intelligent" but rather that the formal verification language leaves no room for hidden steps or suggestive-but-incomplete arguments. The challenge, as he sees it, is that most of modern mathematics still hasn't been translated into formal libraries, so the systems don't yet have the concepts they need.

This latest step forward suggests the gap is beginning to close. The sphere‑packing project is probably the clearest demonstration yet of what is becoming possible.

None of this means mathematicians are on the brink of extinction. In fact, I suspect the opposite is true. As the space of verifiable mathematics expands, so too does the need for people who can pose good questions, create new definitions, and recognize when an argument is genuinely insightful. But we are going to have to adapt. We may find ourselves acting more like scientific-instrument builders and less like lone theorists, weaving together human intuition and AI tenacity to produce machine‑verified certainty.

Mathematics has always moved forward by partnering with assistive tools. AI doesn't change that practice; it just takes it to the next level. Mathematical concepts won't get easier to prove, but our capacity to test, verify and build upon them will surely increase.

Opinion on Live Science gives you insight on the most important issues in science that affect you and the world around you today, written by experts and leading scientists in their field.

Researchers have developed a method for steering microscopic swimming robots using light patterns and the principles of Einstein's theory of relativity. The technology is a potential first step toward deploying tiny robots in applications ranging from medicine to manufacturing.

One of the major challenges of developing microrobots for practical applications is creating ones capable of navigation without the inclusion of bulky sensors and other electronics, which would make the machines too large to operate at the desired scale (like inside a human body). In an attempt to overcome this issue, physicists at the University of Pennsylvania created "artificial space-time" to direct machines to travel in the same way that spacecraft or light does while crossing the universe.

In the study, researchers submerged 100-micron (roughly the width of a human hair) electrokinetic (EK) swimming robots in an ionized solution and tasked them with navigating a simple maze. The bots were covered with tiny solar cells with electrodes on both ends; when the solar cells were exposed to light, they powered the electrodes, which created an electric field that propelled the robots through the solution.

The challenge was to guide the microscopic machines with enough precision for them to reach a specific point in space, without being stymied by the maze's walls. That's where relativity came in. According to Einstein's theory of general relativity, gravity bends space-time around objects with mass. Light and objects follow "straight" geodesics ‪—‬ the shortest paths ‪—‬ that look bent around masses. A great example of this is gravitational lensing: Although light travels in a straight line across the cosmos, it can appear bent and magnified when passing through the gravitational well of a massive object, such as a large galaxy cluster.

"We showed that the way EK robots behave in patterned light fields is identical to the paths light follows in general relativity," lead study author Marc Miskin, an assistant professor of electrical and systems engineering at the University of Pennsylvania, told Live Science in an email. "Amazingly, you can use the robots as a gravity analog since the correspondence is exact. Alternatively, you can turn general relativity ideas around to use them to guide robots: in the same way gravity pulls objects together, you can guide robots to a specific spot."

Artificial space-time

To mimic the effect, the team modeled the maze as curved virtual space using relativity equations. Paths to the target inside the maze became simple straight lines in the model. Then, they converted the model back to a 2D light map. Dark spots naturally attracted the bots, while brighter spots repelled them. The end point of the maze was the darkest spot (a kind of faux black hole), with obstacles being more brightly lit.

Regardless of where they were initially placed, the EK bots naturally followed these geodesics, dodging walls automatically, as if sliding downhill in warped space. The team published their findings in November 2025 in the journal npj Robotics.

For Miskin, the study is a bridge between the worlds of physics and technology, "rather than a competition between them," he said. "On the one hand, relativity and light are very well understood; connecting reactive control to them invites new ways of thinking and established tools for robotics. On the other hand, general relativity and optics are also very abstract (think bending spacetime), while robotics is mechanistic and concrete (it's very easy to understand why the robot does what it does). In addition to showing how new types of robots behave according to known theories of optics, the experiments give researchers "a bit more" insight into general relativity, particularly in exploring the impact of "flat space-times" in 2D spaces, Miskin added.

While the maze study is a very early step, Miskin said practical applications may emerge over the next 10 years.

"Some use cases we're interested in exploring include checking up on teeth following a root canal, a kind of dental biopsy to make sure everything was cleared, eliminating tumors after making local measurements to confirm cells are cancerous, or even, outside of bio, assembly of microchips with tiny robotic helpers," Miskin said. "The microworld is a fascinating place; I wouldn't be surprised if these ideas are just the tip of the iceberg."

We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions?

Is it just a bigger kind of space? Is it "space-time," the popular idea which emerged from Einstein's theory of relativity?

If you have wondered what four dimensions really look like, you may have come across drawings of a "four-dimensional cube". But our brains are wired to interpret drawings on flat paper as two- or at most three-dimensional, not four-dimensional.

The almost insurmountable difficulty of visualising the fourth dimension has inspired mathematicians, physicists, writers and even some artists for centuries. But even if we can't quite imagine it, we can understand it.

What is dimension?

The dimension of a space captures the number of independent directions in it.

A line is one-dimensional. We can move along it forwards and backwards, but these are opposite, not independent, directions. You can also think of a string or piece of rope as practically one-dimensional, as the thickness is negligible compared with the length.

A surface, such as a soccer field or the skin of a balloon, is two-dimensional. There are independent directions forwards and sideways.

You can move diagonally on a surface, but this is not an independent direction because you can get to the same place by moving forwards, then sideways. The space we live in is three-dimensional: in addition to moving forwards and sideways, we can also jump up and down.

Four-dimensional space has yet another independent direction. This is why space-time is considered four-dimensional: you have the three dimensions of space, but moving forward or backward in time counts as a new direction.

One way to imagine four-dimensional space is as an immersive three-dimensional movie, where each "frame" is three-dimensional and you can also fast-forward and rewind in time.

Consider the cube

A powerful tool for understanding higher dimensions is through analogies in lower dimensions. An example of this technique is drawing cubes in more dimensions.

A "two-dimensional cube" is just a square. To draw a three-dimensional cube, we draw two squares, then connect them corner to corner to make a cube.

So, to draw a four-dimensional cube, start by drawing two three-dimensional cubes, then connect them corner to corner. You can even continue doing this to draw cubes in five or more dimensions. (You will need a large piece of paper and need to keep your lines neat!)

This experiment can help accurately determine how many corners and edges a higher-dimensional cube has. But for most of us, it will not help us "see" one. Our brains will only interpret the images as complex webs of lines in two or at most three dimensions.

Knots

We can tie knots in three dimensions because one-dimensional ropes "catch on each other". This is why a long rope wound around itself, if done right, won't come apart. We trust knots with our lives when we're sailing or climbing.

But in four dimensions, knots would instantly come apart. We can understand why by using an example in fewer dimensions, like we did with cubes.

Imagine a colony of two-dimensional ants living on a flat surface divided by a line. The ants can't cross the line: it's an impassable barrier for them, and they don't even know the other side of the line exists.

But if one day an ant, and its world, becomes three-dimensional, that ant will step over the line with ease. To step over, it needs to move just a tiny bit in the new, vertical direction.

Now, instead of an ant and a line on a flat surface, imagine a horizontal and a vertical piece of rope in three dimensions. These will catch on each other if pulled in opposite directions.

But if the space became four-dimensional, it would be enough for the horizontal piece of rope to move just a little bit in the new, fourth direction, to avoid the other entirely.

Thinking of four dimensions as a movie, the pieces of rope live in a single, three-dimensional frame. If the horizontal piece of rope shifts just slightly into a future frame, in that frame there is no vertical piece, so it can easily move to the other side of the vertical piece before shifting back.

From our three-dimensional perspective, the ropes would appear to slide through each other like ghosts.

Knots in more dimensions

Is it impossible, then, to knot a rope in higher dimensions? Yes: any knot tied on a rope will come apart.

But not all is lost: in four-dimensional space you can knot two-dimensional surfaces, such as balloons, large picnic blankets or long tubes.

There is a mathematical formula that determines when knots can stay knotted: take the dimension of the object you want to knot, double it, and add one. According to the formula, this is the maximum dimension of a space where knotting is possible.

The formula implies, for example, that a rope (one-dimensional) can be knotted in at most three dimensions. A (two-dimensional) balloon surface can be knotted in at most five dimensions.

Studying knotted surfaces in four-dimensional space is a vibrant topic of research, which provides mathematical insight into the the still poorly understood mysteries into the intricacies of four-dimensional space.

This edited article is republished from The Conversation under a Creative Commons license. Read the original article.

Physicists may have a brand-new way to measure the expansion rate of the universe — one of the biggest outstanding mysteries in cosmology — using space-time ripples predicted by Einstein.

A new study suggests that the faint gravitational wave background produced by numerous merging black holes across the universe can be used to independently measure how fast space is expanding. Even without detecting this background "hum" directly, the researchers show that it already places limits on the Hubble constant — a key quantity at the heart of one of modern cosmology's biggest puzzles.

If confirmed, the technique could settle the debate about whether we need to come up with new physics to explain the nature of the universe.

An independent test of the Hubble constant

The expansion rate of the universe, encoded in the Hubble constant, has become the focus of intense debate in recent years. Measurements based on the early universe, such as those inferred from the leftover radiation from the Big Bang (known as the cosmic microwave background), disagree with measurements derived from more nearby objects, like flickering supernovas and galaxies. This discrepancy, known as the Hubble tension, has now reached high statistical significance.

"The Hubble tension is one of the most important open problems in cosmology," Chiara Mingarelli, an assistant professor of physics at Yale University who was not involved in the new study, told Live Science via email. "Early-Universe and late-Universe measurements of the expansion rate disagree at over 5 sigma [the "gold standard" of statistical significance in physics], and we don't know why. Either there's an unidentified systematic error or new physics. Any genuinely independent measurement of the expansion rate is extremely valuable."

The new research, accepted for publication in the journal Physical Review Letters and available as a preprint, proposes such an independent method based almost entirely on gravitational waves — subtle ripples in the fabric of space-time predicted by Einstein's theory of general relativity.

"This result is very significant," study co-author Nicolás Yunes, a professor of astrophysics at the University of Illinois Urbana-Champaign, said in a statement. "Our method is an innovative way to enhance the accuracy of Hubble constant inferences using gravitational waves."

Listening to the background hum of black holes

Since 2015, detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), the Virgo interferometer, and the Kamioka Gravitational Wave Detector (KAGRA) have observed dozens of individual black hole mergers through gravitational waves. Each merger provides information about the masses of the black holes involved and their distances from Earth.

"Because we are observing individual black hole collisions, we can determine the rates of those collisions happening across the universe," lead study author Bryce Cousins, a graduate student at the University of Illinois Urbana-Champaign, said in the statement. "Based on those rates, we expect there to be a lot more events that we can't observe, which is called the gravitational-wave background." This gravitational wave background, sometimes described as a stochastic (or random) signal, is the faint, collective effect of numerous distant mergers. Its overall strength depends on how quickly the universe is expanding. A slower expansion implies larger cosmic volumes and, therefore, more mergers contributing to the background.

"It's a clever idea," Mingarelli said. "The gravitational-wave background — the collective hum of distant black hole mergers too faint to detect individually — depends on the expansion rate. A slower expansion means larger volumes, more mergers, and a louder background. So even the non-detection of this background disfavors low values of the Hubble constant."

Using current data from gravitational wave detectors, the team showed that the absence of a detected background already rules out some lower values of the Hubble constant. While the present constraints are broad, the method establishes a new framework for cosmological inference.

A new tool for cosmology

The approach builds on the concept of "standard sirens," in which individual gravitational wave events act as distance markers. But instead of relying on single bright events, the new method exploits the entire unresolved population of colliding black holes.

"It's not every day that you come up with an entirely new tool for cosmology," study co-author Daniel Holz, a professor of physics and astronomy at the University of Chicago, said in the statement. "We show that by using the background gravitational-wave hum from merging black holes in distant galaxies, we can learn about the age and composition of the universe.

"This is an exciting and completely new direction, and we look forward to applying our methods to future datasets to help constrain the Hubble constant, as well as other key cosmological quantities," Holz added.

While the new method shows promise, Mingarelli also emphasized the current limitations. "The main strength is that this is an almost entirely gravitational-wave-based measurement — independent of the electromagnetic distance ladder and the cosmic microwave background," Mingarelli said. "The limitation is that uncertainties are still large, and the result depends on the assumed black hole population model. But the authors are upfront about this and show their choices are conservative."

Looking ahead, detector upgrades are expected to significantly improve sensitivity to the gravitational wave background.

"With planned detector upgrades, the background should be detected within a few years, turning this from a lower bound into a real measurement," Mingarelli said.

If successful, this stochastic siren method could become a powerful new tool for probing the expansion history of the universe and for investigating whether the Hubble tension signals new physics or hidden systematic errors in existing measurements.

Black hole quiz: How supermassive is your knowledge of the universe?

Elevators have a strange way of messing with your sense of gravity. The moment an elevator lurches upward, you feel it in your feet. For a second, the floor presses harder than usual. When the elevator slows, that pressure eases, leaving you briefly lighter.

If you stand on a scale inside an elevator going up, the number jumps. When it slows to a stop, the number dips. On the way down, the opposite happens.

So what's really going on? Do you weigh more when the elevator goes up or when it goes down?

The short answer is that you can feel heaviest at two points: when the elevator starts moving up (accelerating upward) and when it's slowing down at the very end of a downward trip (decelerating downward). But the explanation depends on what "weight" actually means and what your body can feel.

"The word 'weight' in physics has different meanings," Miguel Morales, a physics professor at the University of Washington in Seattle, told Live Science. In physics, weight can refer to at least three related ideas: your mass (how much matter you're made of), the gravitational force pulling on you, or how hard the scale beneath you is pushing up, Morales explained.

"When you're just standing still, those can all be the same thing," Morales said. "But as soon as the elevator starts to speed up or slow down, you get three different answers. It's just physics."

Your mass never changes, no matter what the elevator does. Gravity near Earth's surface also stays essentially the same between the bottom and top of a building. What does change is the third definition: how hard the scale pushes upward. That upward push is what a scale actually measures.

Looking at gravity

This distinction reveals something counterintuitive: "You can't feel gravity. You never could," Jason Barnes, a physics professor at the University of Idaho, told Live Science.

Barnes pointed to astronauts aboard the International Space Station. "The actual gravity of the Earth up there is almost the exact same as here," he said. "But they don't feel it."

That's not because gravity disappears in orbit. At the station's altitude (about 250 miles, or 400 kilometers, above our planet), Earth's gravitational pull is still about 90% as strong as it is at the surface. The difference is that astronauts and the space station are in continuous free fall toward Earth.

The station is moving sideways at more than 17,000 mph (27,300 km/h). As it falls, Earth curves away beneath it. Instead of hitting the ground, it keeps missing it. The result is a constant fall around the planet.

Because the astronauts and the space station are falling together at the same rate, the floor never needs to push up on them. And that upward push is what we actually feel as weight (also called the normal force).

On Earth, the ground constantly prevents you from falling by pushing upward against you. In orbit, there's no such push. The astronauts are still under the influence of gravity, but nothing is stopping them from falling. Without the floor pressing upward, they feel weightless.

Why do elevators make you feel heavier or lighter?

An elevator briefly changes how hard the floor pushes back on you. When the elevator starts rising, it must accelerate you upward, too. "To start going up, that's when you feel heavier," Barnes said. "The elevator pushes back harder than normal in order to accelerate you upward."

In a typical building elevator, that extra acceleration might be about 1 meter per second squared. That is roughly one-tenth of Earth's gravity. For someone who normally weighs 150 pounds (68 kilograms), that would briefly add about 10% to the scale reading. Instead of 150 pounds, the scale might show around 165 pounds (75 kg).

Morales described the same effect from the scale's perspective. "The force of gravity hasn't changed at all," he said. "But now, in order for you to be speeding up, something's got to be pushing you harder than gravity. And so your weight on the scale will go up."

Once the elevator reaches a steady speed, the acceleration stops. Gravity and the upward push balance again, and the scale returns to its normal reading, even though you're still moving.

At the top, when the elevator slows to a stop, the opposite happens. Even though you're still moving upward, the elevator must accelerate downward slightly to slow you down.

The force of gravity hasn't changed. But because the elevator is now accelerating downward, the floor doesn't need to push up as hard to control your motion. With less upward push (normal force), the scale reading drops.

"You kind of feel yourself get a little light," Morales said.

The same pattern repeats on the way down. When the elevator accelerates downward, you feel lighter because the floor pushes up less than usual. But as it approaches the bottom and slows to a stop, the acceleration flips upward again, making you feel heavy again.

This everyday experience turns out to be connected to one of the most important ideas in modern physics.

"It is an effect that Einstein first noted when he was developing general relativity," Barnes said. That insight, known as the equivalence principle, helped Einstein understand gravity not as a force but as a consequence of acceleration and the curvature of space-time itself.

The ubiquitous squeak of sneakers on a basketball court may be caused by more than just friction, a new study suggests.

Researchers have found that the sharp chirp of rubber on a hard floor happens when tiny areas of slipping between the shoe's sole and the floor move at supersonic speeds — and, in some experiments, the process involved miniature, lightning-like sparks. What's more, the findings could lead to an improved understanding of earthquakes and aid in the design of grippy surfaces.

The new study, published Feb. 25 in the journal Nature, shows that soft rubber does not slide the way many people imagine. Instead of the whole sole sticking and then slipping at once, motion bunches into fast, wrinkle-like fronts called "opening slip pulses" that detach and reattach the rubber across the contact zone. Those repeating pulses generate the vibrations that our ears hear as squeaks.

Scientists have long explained squeaks from shoes, bicycle brakes and tires using stick-slip friction, a stop-and-go cycle in which surfaces repeatedly catch and then break free. That model works well for many hard-on-hard systems, like door hinges.

But soft materials like rubber behave differently when they slide across rigid surfaces.

To understand the physics of this process, researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) teamed up with experts from the University of Nottingham in the U.K. and the French National Center for Scientific Research. They used high-speed optical imaging and synchronized audio to watch soft rubber move quickly along smooth glass.

But what they saw was not smooth sliding. Instead, motion bunched up into opening slip pulses, sweeping across the rubber in starts and stops.

"Fundamentally, these findings challenge the long-held assumption that soft-material friction can be fully captured by simplified, one-dimensional ‘stick-slip’ models," first study author Adel Djellouli, a postdoctoral fellow at Harvard, told Live Science in an email.

Tiny lightning everywhere

The findings reveal more about the physics of friction. In classic stick-slip friction, the whole contact surface alternates between sticking and slipping. In this study, however, the motion was more localized, as only small regions opened and slipped, and then moved on, while other regions stayed in full contact.

For some experiments, the team also saw tiny flashes caused by the friction, which they described as miniature "lightning" sparks. In some tests, those sparks, or electrical discharges, appeared to trigger the slip pulses. The sparks were not the main source of the squeaking noise, but they showed how electrical energy could build up in the system when the rubber moved.

The researchers also found that the rubber's shape, more than its movement, was the main determinant of the squeak's pitch.

When flat rubber blocks slid across the glass, the slip pulses were irregular, producing a broad "whoosh" rather than a clean squeak. But when the researchers added thin ridges to the rubber, the ridges confined the pulses and made them repeat at regular intervals.

In effect, the ridges acted like guides, channeling the pulses into a repeating cycle. This locked the sound into a specific frequency, or tone. The team found that this squeak frequency depended mainly on the height of the rubber ridges.

In fact, the pattern was so reliable that the team designed blocks of different heights and used them to play the Imperial March theme from "Star Wars" by hand.

"When it came time to actually play the Star Wars theme song, we had to rehearse for three solid days to get the video right," said Djellouli. "None of us are exactly trained in making music with squeaky rubber blocks, so getting the timing and technique down took a lot of practice. I think the funniest part was the relief in the lab when we finally finished the recording after three days of constant, high-pitched squeaking. Our colleagues were very happy to finally have some quiet again!"

What sneakers may have in common with earthquakes

The findings have implications beyond shoe design. The slip pulses in the experiments share key features with rupture fronts in earthquakes, where sections of a fault suddenly break and slide at very high speeds.

"Soft friction is usually considered slow, yet we show that the squeak of a sneaker can propagate as fast as, or even faster than, the rupture of a geological fault, and that their physics is strikingly similar," study co-author Shmuel Rubinstein, a professor of physics at the Hebrew University of Jerusalem and a visiting professor at SEAS, said in a statement.

Beyond shedding light on the physics of earthquakes, the work could help engineers design surfaces that switch between slippery and grippy states on demand.

"Tuning frictional behavior on the fly has been a long-standing engineering dream," Katia Bertoldi, a professor of applied mechanics at Harvard, said in the statement. "This new insight into how surface geometry governs slip pulses paves the way for tunable frictional metamaterials that can transition from low-friction to high-grip states on demand."

At a secret meeting in 2025, some of the world's leading mathematicians gathered to test OpenAI's newest large language model, o4-mini.

Experts at the meeting were amazed by how much the model's responses sounded like a real mathematician when delivering a complex proof.

"I've never seen that kind of reasoning before in models," Ken Ono, a professor of number theory at the University of Virginia said at the time. "That's what a scientist does."

But was the artificial intelligence (AI) model being given more credit than it deserved? And do we run the risk of accepting AI-derived proofs without fully understanding them?

Ono acknowledged that the model might be giving convincing — but potentially incorrect — answers.

"If you say something with enough authority, people just get scared," Ono said. "I think o4-mini has mastered proof by intimidation; it says everything with so much confidence."

In the past, confidence and the appearance of a good argument were good signs because only the best mathematicians could make convincing arguments, and their reasoning was usually sound. That has changed.

"If you were a terrible mathematician, you would also be a terrible mathematical writer, and you would emphasize the wrong things," Terry Tao, a mathematician at UCLA and the 2006 winner of the prestigious Fields Medal, told Live Science. "But AI has broken that signal."

Naturally, mathematicians are beginning to worry that AI will spam them with convincing-looking proofs that actually contain flaws that are difficult for humans to detect.

Tao warned that AI-generated arguments might be incorrectly accepted because they look rigorous.

"Unfortunately, the AI is much better at sounding like they have the right answer than actually getting it … right or wrong; they will always look convincing," Tao said.

He urged caution on the acceptance of AI '"proofs." "One thing we've learned from using AIs is that if you give them a goal, they will cheat like crazy to achieve the goal," Tao said.

While it may seem largely abstract to ask whether we can truly "prove" highly technical mathematical conjectures if we can't understand the proofs, the answers can have significant implications. After all, if we can't trust a proof, we can't develop further mathematical tools or techniques from that foundation.

For instance, one of the major outstanding problems in computational math, dubbed P vs. NP, asks, in essence, whether problems whose solutions are easy to check are also easy to find in the first place. If we can prove that, we could transform scheduling and routing, streamline supply chains, accelerate chip design, and even speed up drug discovery. The flip side is that a verifiable proof might also compromise the security of most current cryptographic systems. Far from being arcane, there is real jeopardy in the answers to these questions.

Proof is a social construct

It might shock non-mathematicians to learn that, to some extent, human-derived mathematical proofs have always been social constructs — about convincing other people in the field that the arguments are right. After all, a mathematical proof is often accepted as true when other mathematicians analyze it and deem it correct. That means a widely accepted proof doesn't guarantee a statement is irrefutably true. Andrew Granville, a mathematician at the University of Montreal, suspects there are issues even with some of the better-known and more scrutinized human-made mathematical proofs.

There's some evidence for that claim. "There have been some famous papers that are wrong because of little linguistic issues," Granville told Live Science.

Perhaps the best-known example is Andrew Wiles' proof of Fermat's last theorem. The theorem states that although there are whole numbers where one square plus another square equals a third square (like 3²+4²=5²), there are no whole numbers that make the same true for cubes, fourth powers, or any other higher powers.

Wiles famously spent seven years working in almost complete isolation and, in 1993, presented his proof as a lecture series in Cambridge, to great fanfare. When Wiles finished his last lecture with the immortal line "I think I'll stop there," the audience broke into thunderous applause and Champagne was uncorked to celebrate the achievement. Newspapers around the world proclaimed the mathematician's victory over the 350-year-old problem.

During the peer-review process, however, a reviewer spotted a significant flaw in Wiles' proof. He spent another year working on the problem and eventually fixed the issue.

But for a short time, the world believed the proof was solved, when, in fact, it hadn't been.

Mathematical verification systems

To prevent this sort of problem—where a proof is accepted without actually being correct—there's a move to shore up proofs with what mathematicians call formal verification languages.

These computer programs, the best known example of which is called Lean, require mathematicians to translate their proofs into a very precise format. The computer then goes through every step, applying rigorous mathematical logic to confirm the argument is 100% correct. If the computer comes across a step in the proof it doesn't like, it flags it and doesn't let go. This encoded formalization leaves no room for the linguistic misunderstandings that Granville worries have plagued previous proofs.

Kevin Buzzard, a mathematician at Imperial College London, is one of the leading proponents of the formal verification. "I started in this business because I was worried that human proofs were incomplete and incorrect and that we humans were doing a poor job documenting our arguments," Buzzard told Live Science.

In addition to verifying existing human proofs, AI, working in conjunction with programs like Lean, could be game-changing, mathematicians said.

"If we force AI output to produce things in a formally verified language, then this, in principle, solves most of the problem," of AI coming up with convincing-looking, but ultimately incorrect proofs, Tao said.

Buzzard agreed. "You would like to think that maybe we can get the system to not just write the model output, but translate it into Lean, run it through Lean," he said. He imagined a back-and-forth interaction between Lean and the AI in which Lean would point out errors and the AI would attempt to correct them.

If AI models can be made to work with formal verification languages, AI could then tackle some of the most difficult problems in mathematics by finding connections beyond the scope of human creativity, experts told Live Science.

"AI is very good at finding links between areas of mathematics that we wouldn't necessarily think to connect," Marc Lackenby, a mathematician at the University of Oxford, told Live Science.

A proof that no one understands?

Taking the idea of formally verified AI proofs to its logical extreme, there is a realistic future in which AI will develop "objectively correct" proofs that are so complicated that no human can understand them.

This is troubling for mathematicians in an altogether different way. It poses fundamental questions about the purpose of undertaking mathematics as a discipline. What is ultimately the point of proving something that no one understands? And if we do, can we be said to have added to the state of human knowledge?

Of course, the notion of a proof so long and complicated that no one on Earth understands it is not new to mathematics, Buzzard said.

"There are papers in mathematics where nobody understands the whole paper. You know, there's a paper with 20 authors and each author understands their bit," Buzzard told Live Science. "Nobody understands the whole thing. And that's fine. That's just how it works."

Buzzard also pointed out that proofs that rely on computers to fill in gaps are nothing new. "We've had computer-assisted proofs for decades," Buzzard said. For instance, the four-color theorem states that if you have a map divided into countries or regions, you'll never need more than four distinct colors to shade the map such that neighboring regions are never the same colors.

Almost 50 years ago, in 1976, mathematicians broke the problem into thousands of small, checkable cases and wrote computer programs to verify each one. As long as the mathematicians were convinced there weren't any problems with the code they'd written, they were reassured the proof was correct. The first computer-assisted proof of the four-color theorem was published in 1977. Confidence in the proof built gradually over the years and was reinforced to the point of almost universal acceptance when a simpler, but still compute-aided, proof was produced in 1997 and a formally verified machine-checked proof was published in 2005.

"The four-color theorem was proved with a computer," Buzzard noted. "People were very upset about that. But now it's just accepted. It's in textbooks."

Uncharted territory

But these examples of computer-assisted proofs and mathematical teamwork feel fundamentally different from AI proposing, adapting and verifying a proof all on its own — a proof, perhaps, that no human or team of humans could ever hope to understand.

Regardless of whether mathematicians welcome it, AI is already reshaping the very nature of proofs. For centuries, the act of proof generation and verification have been human endeavors — arguments crafted to persuade other human mathematicians. We're approaching a situation in which machines may produce airtight logic, verified by formal systems, that even the best mathematicians will fail to follow.

In that future scenario — if it comes to pass — the AI will do every step, from proposing, to testing, to verifying proofs, "and then you've won," Lackenby said. "You've proved something."

However, this approach raises a profound philosophical question: If a proof becomes something only a computer can comprehend, does mathematics remain a human endeavor, or does it evolve into something else entirely? And that makes one wonder what the point is, Lackenby noted.

Heavy collisions at the Large Hadron Collider (LHC) have revealed the faintest trace of a wake left by a quark slicing through trillion-degree nuclear matter — hinting that the primordial soup of the universe may have literally been more soup-like than we thought.

The new findings from the LHC's Compact Muon Solenoid (CMS) collaboration show the first clear evidence of a subtle "dip" in particle production behind a high-energy quark as it traverses quark-gluon plasma — a droplet of primordial matter thought to have filled the universe microseconds after the Big Bang.

A study describing the results, published Dec. 25, 2025, in the journal Physics Letters B, provides a tantalizing look at the universe in its first moments.

Re-creating early-universe conditions in the lab

When heavy atomic nuclei collide at near-light speed inside the LHC, they briefly melt into an exotic state known as quark-gluon plasma.

In this extreme environment, "the density and temperature is so high that the regular atom structure is no longer maintained," Yi Chen, an assistant professor of physics at Vanderbilt University and a member of the CMS team, told Live Science via email. Instead, "all the nuclei are overlapping together and forming the so-called quark-gluon plasma, where quarks and gluons can move beyond the confines of the nuclei. They behave more like a liquid."

This plasma droplet is extraordinarily small — about 10^-14 meters across, or 10,000 times smaller than an atom — and vanishes almost instantly. Yet within that fleeting droplet, quarks and gluons — the fundamental carriers of the strong nuclear force that holds atomic nuclei together — flow collectively in ways that resemble an ultrahot liquid more than a simple gas of particles.

Physicists want to understand how energetic particles interact with this strange medium. "In our studies, we want to study how different things interact with the small droplet of liquid that is created in the collisions," Chen said. "For example, how would a high energy quark traverse through this hot liquid?"

Theory predicts that the quark would leave a detectable wake in the plasma behind it, much as a boat slicing though water would. "We will have water pushed forward with the boat in the same direction, but we also expect a small dip in water level behind the boat, because water is pushed away," Chen said.

In practice, however, disentangling the "boat" from the "water" is far from straightforward. The plasma droplet is tiny, and the experimental resolution is limited. At the front of the quark's path, the quark and plasma interact intensely, making it difficult to tell which signals come from which. But behind the quark, the wake — if present — must be a property of the plasma itself.

"So we want to find this small dip in the back side," Chen said.

A clean probe with Z bosons

To isolate that wake, the team turned to a special partner particle: the Z boson, one of the carriers of the weak nuclear force — one of the four fundamental interactions, along with the electromagnetic, strong, and gravitational forces — responsible for certain atomic and subatomic decay processes. In certain collisions, a Z boson and a high-energy quark are produced together, recoiling in opposite directions.

Here's where the Z boson becomes crucial. "The Z bosons are responsible for the weak force, and as far as the plasma is concerned, Z just escapes and is gone from the picture," Chen said. Unlike quarks and gluons, Z bosons barely interact with the plasma. They leave the collision zone unscathed, providing a clean indicator of the quark's original direction and energy.

This setup allows physicists to focus on the quark as it plows through the plasma, without worrying that its partner particle has been distorted by the medium. In essence, the Z boson serves as a calibrated marker, making it easier to search for subtle changes in particle production behind the quark.

The CMS team measured correlations between Z bosons and hadrons — composite particles made of quarks — emerging from the collision. By analyzing how many hadrons appear in the "backward" direction relative to the quark's motion, they could search for the predicted wake.

A tiny-but-important signal

The result is subtle. "On average, in the back direction, we see there is a change of less than 1% in the amount of plasma," Chen said. "It is a very small effect (and partly why it took so long for people to demonstrate it experimentally)."

Still, that less-than-1% suppression is precisely the kind of signature expected from a quark transferring energy and momentum to the plasma, leaving a depleted region in its wake. The team reports that this is the first time such a dip has been clearly detected in Z-tagged events.

The shape and depth of the dip encode information about the plasma's properties. Returning to her analogy, Chen noted that if water flows easily, a dip behind a boat fills in quickly. If it behaves more like honey, the depression lingers. "So studying how this dip looks … gives us information on the plasma itself, without the complication of the boat," she said.

Looking back to the early universe

The findings also have cosmological implications. The early universe, shortly after the Big Bang, is believed to have been filled with quark-gluon plasma before cooling into protons, neutrons and, eventually, atoms.

"This era is not directly observable through telescopes,” Chen says. "The universe was opaque back then.” Heavy-ion collisions provide "a tiny glimpse on how the universe behaved during this era," she added.

For now, the observed dip is "just the start," Chen concluded. "The exciting implication of this work is that it opens up a new venue to gain more insight on the property of the plasma. With more data accumulated, we will be able to study this effect more precisely and learn more about the plasma in the near future."

Scientists have used the loudest gravitational-wave signal ever recorded to put Albert Einstein's more than 100-year-old theory of gravity to its toughest test yet — and once again, it passed.

The signal, called GW250114, came from the merger of two black holes — each about 30 times the mass of the sun — about 1.3 billion light-years from Earth. The event caused ripples through space-time, called gravitational waves, which washed over Earth on Jan. 14, 2025, and were detected by the U.S.-based Laser Interferometer Gravitational-Wave Observatory (LIGO).

Scientists say the event closely resembles the one that resulted in the first direct detection of gravitational waves in 2015. That suggests the black holes in both mergers were similar in size and distance from Earth.

However, this new signal was recorded with roughly three times the clarity of that groundbreaking 2015 discovery, allowing scientists to test Einstein's theory of general relativity more rigorously than ever before.

"It was very clearly the loudest event," Keefe Mitman, a postdoctoral researcher at the Cornell Center for Astrophysics and Planetary Science and co-author of the new paper, told Live Science. "This one event provided more information than everything we've seen before regarding certain tests of general relativity."

The signal's exceptional clarity stems from a decade of steady upgrades to the detectors, Mitman said. Those improvements reduced noise from sources that once interfered with cosmic signals, including seismic vibrations and even passing trucks. As a result, the detectors were sensitive enough to the minuscule distortions in space-time — changes 700 trillion times smaller than the width of a human hair — caused by the recently detected black hole merger.

The findings are detailed in a study published Jan. 29 in the journal Physical Review Letters.

A black hole's "ring"

Because the recently detected signal was so clear, Mitman and his colleagues could zoom in on a fleeting stage after the merger known as the "ringdown." During this phase, the newly formed black hole briefly vibrates — much like a struck bell — emitting gravitational waves in distinct patterns, or "tones," that encode key properties of the black hole, including its mass and spin.

In GW250114, researchers detected the two primary tones predicted for such a merger. Each tone yielded an independent measurement of the black hole's mass and spin — and both matched, effectively verifying general relativity, the team reported in the study.

For the first time, scientists also confidently identified a more subtle, short-lived "overtone" that appears right at the start of the ringing — another feature long predicted by general relativity.

"This event made it very, very obvious that, indeed, this prediction of general relativity was present in the signal, which was really exciting," Mitman told Live Science.

Had the measurements disagreed, he added in a statement, "we would have had a lot of work to do as physicists to try to explain what's going on and what the true theory of gravity would be in our universe."

Earlier analyses of the same event, published in September 2025, confirmed another major prediction rooted in general relativity that Stephen Hawking proposed more than 50 years ago. Hawking predicted that a black hole's surface area — the size of its event horizon — can never shrink, even though enormous amounts of energy escape during a merger as gravitational waves.

In GW250114, scientists estimated that the two original black holes had a combined surface area of about 93,000 square miles (240,000 square kilometers) — roughly the size of Oregon. After the merger, the resulting black hole had a surface area of about 155,000 square miles (400,000 square km) — closer to the size of California — which is consistent with Hawking's prediction.

The golden age

Despite general relativity's repeated success at describing large-scale cosmic phenomena, physicists suspect the theory cannot be the complete description of gravity in our universe. For example, it cannot explain dark matter or dark energy, which are needed to hold galaxies and their clusters together and to explain the universe's accelerating expansion, respectively. Nor does it reconcile cleanly with quantum mechanics, the framework that governs nature at the smallest scales.

Scientists hope gravitational waves from energetic black hole mergers might someday show subtle deviations from Einstein's predictions, which could potentially reveal new physics.

The ringdown phase is especially promising for such tests, Mitman said. Many "beyond-Einstein" theories predict slightly different vibration patterns during the ringdown phase — so measuring more than one tone, as his team did with GW250114, can help scientists place constraints on any possible deviations from general relativity.

If a discrepancy were to be found, researchers could compare the data with predictions from alternative theories of gravity to determine which, if any, matches reality.

"There has to be some way to resolve this paradox to make our theory of gravity consistent with our theory of quantum mechanics," Mitman said in the statement.

Next-generation detectors, including the proposed Einstein Telescope in Europe and the U.S.-based Cosmic Explorer, will be 10 times more sensitive than current facilities. In addition to detecting more events like GW250114, these detectors will be able to observe lower-frequency gravitational waves, which correspond to more massive black holes, thereby allowing scientists to probe entirely new classes of these cosmic behemoths.

Researchers are also looking ahead to the European Laser Interferometer Space Antenna (LISA), which is expected to observe gravitational waves from supermassive black holes at the centers of galaxies. Planned for launch in 2035, LISA is expected to detect a flood of events and could reveal dozens of distinct tones within a single black hole merger event, Mitman said.

"We're living in the regime where we don't have enough data, and we're kind of just twiddling our thumbs waiting for more data to come in," Mitman said. "Once LISA is online, we'll be overwhelmed."

If funding for gravitational-wave science continues, he added, "we're going to see more and more of these golden events and really start to learn wonderful things about the nature of gravity in our universe."

Albert Einstein quiz: What do you know about the life of the famous theoretical physicist?

An ice-bound "ghost particle" detector at the South Pole just got a major upgrade.

The IceCube Neutrino Observatory has expanded for the first time in its 15 years of service. Technicians have added more than 600 new instruments to the bottom of the detector, which now consists of 92 strings of neutrino detectors buried in a cubic kilometer of ice near Amundsen-Scott South Pole research station.

The observatory is designed to search for high-energy neutrinos — nicknamed "ghost particles" because they are nearly massless and chargeless subatomic particles that zip through space and matter at nearly the speed of light. Neutrinos are everywhere; about 100 trillion pass through every person on Earth every second. But because they rarely interact with the matter they pass through, they're hard to detect.

Scientists would like a better understanding of neutrinos because they're produced in important processes, like the Big Bang that kick-started the universe, the nuclear fusion that powers stars, and the supernova explosions that signal violent stellar deaths.

At IceCube, scientists detect tiny flashes of light that occur when neutrinos do interact with matter and produce secondary particles. This requires a remote and quiet environment, which is readily available at the South Pole, as well as a lot of transparent matter in which to detect the light — in this case, ice. IceCube scientists have already successfully traced the arrival of a single neutrino from a blazar, a distant galaxy surrounding a supermassive black hole. They've also used the particles to map all of the matter in the Milky Way.

In 2019, the U.S. National Science Foundation (NSF) approved funding to upgrade the detector from 86 to 92 strings of detectors. The six new strings hold new detector modules with multiple types of photosensors in each module. It took three 10-week field sessions from 2023 to 2026 to drill more than a mile into the Antarctic ice and place the sensors.

The new sensors will allow scientists to more precisely measure properties such as neutrino oscillations, which happen when neutrinos formed by cosmic rays in Earth's atmosphere change into different types. This will improve their ability to measure cosmic rays and to detect neutrinos from extraplanetary sources, such as supernovas, according to the IceCube Collaboration. Researchers will also be able to better calibrate the detector retrospectively, which will allow them to refine previously collected data from the past 15 years.

"This upgrade will secure the nation's continued leadership in neutrino physics for years to come, paving the way for new cosmic discoveries," Marion Dierickx, director of the NSF's Antarctic Astrophysics and Geospace Sciences Polar Cyberinfrastructure program, said in a statement.

Scientists just watched a bizarre phase of matter turn into an even stranger one. For the first time, they saw a superfluid turn into a supersolid — a transition they weren't sure was even possible.

In a Jan. 28 study in the journal Nature, researchers observed a group of excitons — quasiparticles that combine an electron and an electron hole — transforming from a superfluid into a supersolid and back again. It is the first time excitons have been seen condensing into a supersolid, undergoing a reversible phase transition the way water can transform from a liquid to ice and back.

Secret phases of matter

There are many more phases of matter than the typical three we encounter every day (gases, liquids and solids), although most of these other matter states exist only under extreme conditions. Superfluids are one type that occurs only when some particles, like helium isotopes and excitons, are cooled to just above absolute zero — the complete absence of heat. They're not quite liquids — they flow without resistance from friction — and when stirred, they form tiny eternal tornadoes called quantum vortices.

Supersolids, on the other hand, are a state of matter theorized to exist when superfluids are cooled even more. They keep superfluidity's zero viscosity, but instead of particles moving around in a liquid-like blob, they form an orderly structure, like a crystal lattice, while maintaining their ability to flow and form quantum vortices.

Supersolids have been made in labs before, including in 2021, when researchers created 2D supersolid dysprosium and in 2024 when they saw quantum vortices in a supersolid. However, they achieved this only by using extra equipment and energy to force particles into an orderly lattice. The new study, by contrast, demonstrates a natural phase transition.

"For the first time, we've seen a superfluid undergo a phase transition to become what appears to be a supersolid," Cory Dean, a physicist at Columbia University and co-author of the study, said in a statement.

Exploring new boundaries

To do it, researchers put two pieces of graphene — which is like a very thin sheet of paper made entirely of carbon atoms — very close together. Then, they added a strong magnetic field and cooled the system to form an exciton "soup."

When cooled to between 2.7 and 7.2 degrees Fahrenheit (1.5 to 4 degrees Celsius) above absolute zero, the excitons formed a superfluid. When cooled more than that, the excitons changed into an electrically insulative mysterious new phase that the team suspects is the theorized supersolid state.

"Superfluidity is generally regarded as the low-temperature ground state," Jia Li, a physicist at the University of Texas at Austin and co-author of the study, said in the statement. "Observing an insulating phase that melts into a superfluid is unprecedented. This strongly suggests that the low-temperature phase is a highly unusual exciton solid."

The team is looking at other materials to test, as well as finding new ways to measure and study the exciton supersolid state.

"For now, we're exploring the boundaries around this insulating state, while building new tools to measure it directly," Dean said. Further study will help scientists understand how supersolids and superfluids behave, deepen our understanding of particle physics and work toward applications of higher-temperature supersolids.

Physicists have put thousands of atoms into a "Schrödinger's cat" state — smashing the record for the most macroscopic object to be observed in a quantum state.

In a new study, researchers observed nanoparticles of 7,000 sodium atoms acting as a cohesive wave, pushing the strange world of quantum mechanics to new limits. Building on this research, future experiments could finally put biological molecules into a quantum state, opening up new ways to investigate their physical properties.

In the experiment, the team produced a beam of sodium nanoparticles and aimed it at a narrow slit. Their results, published Jan. 21 in the journal Nature, show that the sodium nanoparticles spread out to produce an interference pattern, exhibiting the strange quantum behavior known as wave-particle duality. These sodium nanoparticles have now collectively set the record for the most macroscopic objects to be observed in a quantum superposition.

"Usually when people think of quantum mechanics, they associate it with small, tiny things, maybe photons, maybe electrons," lead study author Sebastian Pedalino, a physicist at the University of Vienna, told Live Science. "But quantum mechanics itself doesn't state any limits. And that's what we are testing."

Both here and there

In the quantum realm, particles can be both here and there. This strange phenomenon is known as quantum superposition.

The quantum physicist Erwin Schrödinger likened this to placing a cat in a sealed box with a vial of poison that is set to be released when a radioactive source decays, meaning the cat could be killed at any moment after the box has been sealed. This puts the cat into a superposition of being both dead and alive. It is only if the box is opened and the cat is observed that the superposition collapses and the cat is defined as either dead or alive.

Incredibly, this is how particles behave at the quantum scale; they are in multiple places at once and act as both a particle and a wave until they are observed.

This bizarre world raises a question: Where is the boundary between the quantum world and the one we observe every day? At what point does a particle start acting like a wave?

The reason we don't see quantum superposition all around us is because of a process called decoherence. If something in a quantum superposition interacts with its environment, it will decohere and no longer be both here and there; instead, it will be forced into one place. Larger objects are constantly interacting with their environment, so they can't maintain a quantum superposition. So the real challenge when trying to observe larger particles acting as a wave is to isolate them so they can stay in a coherent quantum superposition.

Searching for interference

For the new study, Pedalino attempted to observe the large nanoparticles of sodium in a quantum superposition. To do this, he and his team converted a few grams of sodium into a beam of nanoparticles, which he then aimed at a narrow slit.

If the sodium nanoparticle was in a quantum superposition, this would mean that it spread out like a wave after passing through the slit. This would then produce an interference pattern. However, if it decohered and started acting like a normal particle, the sodium would pass straight through the slit and the team would see a flat line.

"For two years, I was looking at flat lines," Pedalino said. "We were trying to see the interference pattern, but we had flat lines. And in the end, the flat line is not really helpful, as it is inconclusive."

Finally, the single line they had been seeing on the detector widened and became the unmistakable interference pattern that meant the sodium nanoparticles were behaving as both particles and waves.

"That moment was unbelievable," Pedalino said. "It was already late in the night, and I called my professor. And he came back to the lab, and we took measurements until 3 a.m., when we ran out of the sodium."

The team determined the "macroscopicity" — a quantity that describes how much a quantum object pushes into the classical world — of the sodium nanoparticles to be 15.5, beating the previous record for macroscopicity by an order of magnitude.

This discovery opens the door for future experiments where scientists could feasibly observe biological materials, such as a virus or proteins, in a quantum superposition. The experiment represents a major step forward and brings this strange quantum phenomenon tantalizingly close to the real world.

Two of the universe's most mysterious particles may be colliding invisibly throughout the cosmos — a discovery that could solve one of the biggest lingering problems in our standard model of cosmology.

Those two elusive components — dark matter and neutrinos (or "ghost particles") — are ubiquitous throughout the cosmos, yet they remain poorly understood. In a study published Jan. 2 in the journal Nature Astronomy, an international team of researchers found evidence that dark matter and neutrinos may collide, transferring momentum between them in the process.

This surprising interaction may help to explain why the universe is less populated by dense regions, like galaxies, than predicted — in other words, the universe is less "clumpy" than cosmologists think it should be, the researchers said in a statement.

Dark matter and neutrinos remain a riddle

Dark matter is the mysterious, invisible substance that constitutes 85% of the matter in the universe. As its name suggests, dark matter does not emit light, so its existence has been only indirectly inferred from its gravitational influence, as observed in cosmological surveys.

Neutrinos are subatomic particles with infinitesimally low masses and no electric charge, so they very rarely interact with other particles. They're produced by various nuclear processes, including stellar fusion and supernovas, in prodigious quantities: Every second, approximately 100 billion neutrinos pass through each square centimeter of your body, Live Science previously reported.

Yet dark matter and neutrinos should not interact, according to the leading model of cosmology, known as the lambda cold dark matter model (lambda-CDM). This standard model aims to theoretically explain the large-scale structure of the cosmos.

Cosmological conundrum

However, this recent study provides new evidence that dark matter and neutrinos may interact after all, as other researchers have posited over the past two decades.

If dark matter and neutrinos do collide, and transfer momentum to one another in the process, this discovery would inspire a rethink of the lambda-CDM model. Such collisions could also help to explain the "S8 tension," a mismatch between the expected and actual "clumpiness" of the universe.

"This tension does not mean the standard cosmological model is wrong, but it may suggest that it is incomplete," Eleonora Di Valentino, study co-author and a senior research fellow at the University of Sheffield in the U.K., explained in the statement. "Our study shows that interactions between dark matter and neutrinos could help explain this difference, offering new insight into how structure formed in the Universe."

The mismatch stems from researchers' findings that the current cosmos isn't as packed together as predicted, based on observations of the cosmic microwave background (CMB) — the first light in the universe, emitted when the cosmos was only 380,000 years old.

"The statement that cosmic structures are 'less clumped' is best understood in a statistical sense, rather than as a change in the appearance of individual galaxies or clusters. It refers to a reduced efficiency in the growth of cosmic structures over time," study co-author William Giarè, a cosmologist at the University of Hawaii, told Live Science via email.

Unraveling multiple threads of evidence

The researchers tried to unite evidence from energy and density fluctuations in the CMB and from baryon acoustic oscillations (BAO) — pressure waves "frozen" in time from the beginning of the cosmos — with more recent observations of the universe's large-scale structure.

The early-universe data come from the Atacama Cosmology Telescope in Chile and the European Space Agency's space-based Planck telescope, which was designed to study the CMB. The later-universe data come from the Victor M. Blanco Telescope in Chile and the Sloan Digital Sky Survey, a two-decade effort to create a 3D map of millions of galaxies across more than 11 billion light-years.

The researchers also incorporated cosmic shear data from the Dark Energy Survey. Cosmic shear is the distortion of distant celestial objects due to weak gravitational lensing, which occurs when massive foreground structures bend the fabric of space-time and alter the paths of light traveling from those distant celestial objects to our detectors.

Finally, the researchers combined these data and modeled the evolution of the universe. When accounting for collisions between dark matter and neutrinos and the resulting momentum exchange, the simulations generated a model universe that better agrees with real observations.

There's reason to remain cautious, however, as the interaction between dark matter and neutrinos has only a 3-sigma level of certainty — meaning there is a 0.3% chance that this result is a fluke. Though short of the scientific gold standard of 5 sigma, it is significant enough to warrant additional research because, if confirmed, the interaction would prove a "fundamental breakthrough in cosmology and particle physics" — and a potential solution to the cosmic clumpiness quandary.

"The final verdict will come from upcoming large sky surveys, such as those from the Vera C. Rubin Observatory, and more precise theoretical work," research team leader Sebastian Trojanowski, a theoretical physicist at the National Centre for Nuclear Research in Poland, explained in a separate statement. "These will allow us to determine whether we are witnessing a new discovery in the dark sector or whether our cosmological models require further adjustment. However, each of these scenarios brings us closer to solving the mystery of dark matter."

In January 1816, the secretary general of the Paris Academy of Sciences sent Marie-Sophie Germain a strange letter.

In it, he acknowledged that she had won the institute's prestigious "Grand Mathematics Prize" for her mathematical work describing how sound waves travel across 2D surfaces. And yet, the letter offered no congratulations, noted condescendingly that she was the only entrant, and admitted that she had not received tickets to attend the prize ceremony set to occur two days later. He grudgingly acknowledged that, if needed, handwritten tickets could be hastily produced.

Germain did not attend the ceremony.

"The class of mathematical and physical sciences of the Institute held its public session today, a very large assembly that attracted without doubt those desiring to see virtuoso of a new kind, Miss Sophie Germain, to whom the prize for elastic membranes was to be awarded. The expectation of the public was disappointed: the young lady did not go to take the trophy that no one of her gender has ever received in France," the newspaper Journal des Débats reported about the event that day.

The award was the culmination of a decade of work by Germain, a self-taught polymath. Born to a wealthy merchant's family, she became interested in math while reading books in her father's library during a period of seclusion during the French revolution.

Her parents were not pleased with her "unladylike" pursuit. They banked the fires that kept the house toasty and took away her warm clothes, hoping that she'd be too cold and uncomfortable to study. But when they went to sleep, she'd grab candles and cover herself in quilts to continue her math research. She taught herself number theory and calculus that way.

When the École Polytechnique opened in 1794, women were barred from attending, but the notes from lectures were publicly available. She began reading those notes and submitting answers to problems from the lectures under the pseudonym "Antoine August LeBlanc." Under her pseudonym, Germain also began corresponding with some of the leading mathematicians of her day, including Carl Friedrich Gauss and Joseph-Louis Lagrange.

Around 1806, she became intrigued by the physics behind a perplexing experiment. In his 1787 book, physicist and musician Ernst Chladni, often called the "father of acoustics," described a phenomenon in which a person can sprinkle sand across a glass plate and then drag a violin bow across various surfaces and edges. Not only could the plate be played like a violin, but varied geometric patterns formed in the sand depending on how the plates were bowed.

The French institute had offered a prize three years running to mathematically describe the "Chladni figures" that formed. No one else bothered to attempt a solution, with most believing the existing math of the day insufficient to explain the phenomenon.

Germain, however, submitted her proposed solutions all three years. Her third proposal, submitted in 1816, was titled "Research on the Vibrations of Elastic Plates." Though "awkward and clumsy" given the math available at the time, it was still a brilliant insight into the subject of 2D harmonic oscillation, or stably moving waves.

Germain ultimately decided to skip the ceremony because she felt the committee didn't sufficiently respect her work. For instance, her leading rival, Siméon Poisson, was part of the award committee and refused to discuss the problem with her or talk with her in public. Not all of Germain's contemporaries were so dismissive, however; Lagrange and Gauss strongly supported her work.

"But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius," Gauss wrote when he discovered her gender.

Germain would continue with her solitary math research for decades.

Her work with French mathematician Adrien-Marie Legendre was a major advance in the proof of Fermat's Last Theorem, which states that no three positive integers (a, b, c) can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.

Germain showed that Fermat's Last Theorem held for a special class of prime numbers, now called Germain primes, in which both p and 2p+1 are prime. Her work formed the foundation for the eventual, complete solution produced by Andrew Wiles in 1994. Nonetheless, Germain's theorem was mentioned only in a footnote in Legendre's work.

In 1831, her longtime correspondent and mentor Gauss pushed for the University of Göttingen to give Germain an honorary degree. She died of breast cancer a few weeks before she could be given the award.

On a December day, Richard Feynman gave a fun little lecture at Caltech — and dreamed up an entirely new field of physics.

During the talk, entitled "Plenty of room at the bottom," he described the enormous potential that could be realized if scientists could manipulate and control things at a "small scale."

How small? Feynman went on to discount advances of the time, such as writing the Lord's Prayer on the head of a pin, as trivial.

"But that's nothing; that's the most primitive, halting step in the direction I intend to discuss. It is a staggeringly small world that is below," Feynman said in his lecture. Rather, he suggested, people could write the entire 24-volume encyclopedia on the head of a pin, and elegantly showed that there's enough space there to write it legibly and read it out.

He then explored the possibility of a number of then-futuristic ideas: electron microscopes capable of manipulating individual atoms, ultracompact data storage, miniaturized computers, and powerful, ingestible biological machines that travel into organs like the heart, find defects, and repair them with tiny knives. He proposed a number of ways to create these small-scale innovations, including manipulating light and ions.

He ended the lecture by offering a reward of $1,000 to anyone who could miniaturize the text in a book 25,000-fold, such that it could be read using an electron microscope. He offered another $1,000 to anyone who could make a motor no bigger than 1/64th of an inch cubed.

The latter of these prizes was scooped up the following year by engineer William McLellan, who created a 250-microgram motor composed of 13 parts. In his award letter, Feynman congratulated McLellan on the feat but joked that he shouldn't "start writing small," lest he solve the first challenge, too and expect to receive the other $1,000 prize.

"I don't intend to make good on the other one. Since writing the article I've gotten married and bought a house!" Feynman wrote.The former challenge was eventually solved in 1985, when Stanford graduate Thomas Newman miniaturized the first page of the Dickens classic "A Tale of Two Cities." Feynman did, ultimately, pay up for the second prize.

Feynman's Caltech talk is now mythologized as having ushered in the field of nanotechnology. And yet, the term "nanotechnology" itself was not coined until 15 years after his talk, when scientist Norio Taniguchi penned a paper about manipulating material at the atomic scale.

In that 1974 paper, Taniguchi described nanotechnology as "the processing of separation, consolidation, and deformation of materials by one atom or one molecule." Many science historians now argue that the field was following its own trajectory, and that Feynman's talk, while prescient, wasn't the actual driver of future innovations. Prior to 1980, his talk was cited less than 10 times.

Whether it drove innovation or not, since Feynman's famous lecture, many of his predictions have proven true. The scanning tunneling microscope manipulated individual xenon atoms in 1990. Computers more powerful than he described now sit in our pockets, rather than taking up whole rooms. And indeed, tiny nanobots have been designed that can repair damaged blood vessels.

The human body is extraordinarily complex, with several openings and a few exits. But exactly how many holes does each person have?

It sounds like a simple enough question to answer — list the openings and add them up. But it's not quite that easy once you start considering questions like: "What exactly is a hole?" "Does any opening count?" And "why don't mathematicians know the difference between a straw and a doughnut?"

Before we start counting, we need to agree on what constitutes a "hole." Katie Steckles, a lecturer in mathematics at Manchester Metropolitan University in the U.K. and a freelance mathematics communicator, told Live Science that mathematicians "use the term 'hole' to mean one like the hole in a donut: one that goes all the way through a shape and out the other side."

But if you dig a "hole" at the beach, your aim is probably not to dig right through to the other side of the world. Many people would think of a hole as a depression in a solid object. But "this isn't a true hole, as it has an end," Steckles said.

Similarly, mathematical communicator James Arthur, who is based in the U.K., told Live Science that "in topology, a 'hole' is a through hole, that is you can put your finger through the object."

When digging a tunnel under the sea, like the Channel Tunnel that connects the U.K. and France, engineers started off by digging two openings. But as soon as those two digging projects joined up, the Channel Tunnel became a fundamentally different object (what Arthur and engineers would call a "through hole") — like a straw, or a tube with an opening at either end.

And if you ask people how many holes a straw has you will get a range of different answers: one, two and even zero. This is a result of our colloquial understanding of what constitutes a hole.

To find a consistent answer, we can turn to mathematics. And the problem of classifying how many holes there are in an object falls squarely within the realm of topology.

To a topologist, the actual shapes of objects are not important. Instead, "topology is more concerned with the fundamental properties of shapes and how things connect together in space," Steckles said.

In topology, objects can be grouped together by the number of holes they possess. For example, a topologist sees no difference between a golf ball, a baseball or even a Frisbee. If they were all made of plasticine, or putty, they could theoretically be squashed, stretched or otherwise manipulated to look like each other without making or closing any holes in the plasticine or sticking different parts together, Steckles argued.

However, to a topologist, these objects are fundamentally different to a bagel, a doughnut or a basketball hoop, which each have a hole through the middle of them. A figure of eight with two holes and a pretzel with three are different topological objects again.

A useful way to get into the mathematicians' way of thinking about the straw problem is to "imagine our straw is made of play dough," Arthur said. "Let's take this straw and slowly squish the top down and down and down towards the bottom, making sure the hole in the middle stays open. We will squish it until we are in a shape that looks like a doughnut." Mathematicians, Arthur said, would say that "the straw is homeomorphic to a doughnut."

The long, thin aspect ratio of the straw, and the fact that the two openings are relatively far apart, are perhaps what gives rise to the suggestion of two holes. But to a topologist, bagels, basketball hoops and doughnuts are all topologically equivalent to a straw with a single hole. "The hole in a straw goes all the way through it, and the opening at the other end is just the back of that same hole," Steckles said.

Back to the human body

Armed with the topologists' definition of a hole, we can tackle the original question: How many holes does the human body have? Let's first try to list all the openings we have. The obvious ones are probably our mouths, our urethras (the ones we pee out of) and our anuses, as well as the openings in our nostrils and our ears. For some of us, there are also milk ducts in nipples and vaginas.

There are also four less-obvious openings that we all have in the corners of eyelids closest to our nose — the four lacrimal puncta, which drain tears from our eyes into our nasal cavities. At an even smaller scale there are the pores that enable sweat to escape our bodies and sebum to lubricate our skin. In total there are potentially millions of these openings in our bodies, but do they all count as holes?

To make the question interesting, think about whether we could pass a very thin string into one hole and out of another. If we set the size of this string to be about 60 microns (60 millionths of a meter) then it's possible that the string could enter an opening as small as a pore. However — and this is key — it wouldn't be able to leave. It wouldn't be able to come out the other end. It would be blocked by the cells at the bottom of the pore — too thick to pass through into the vasculature that supplies the pore.

"They're not actually holes in the topological sense, as they don't go all the way through," Steckles said. "They're just blind pits."

By this definition we can rule out all the pores, milk ducts and urethras. We couldn't thread a string in one of these openings and out of another. Even the ears canals have to go as they are separated from the rest of the sinuses by the ear drums.

"We have our mouth, our anus, and then our nostrils. They are four of the … openings that form a hole," Arthur said. "But we actually have eight. The remaining four come from the tear ducts, we each have two in each eye, an upper and a lower."

But this doesn't mean eight holes. Steckles pointed out ."When the holes that pass through a shape connect together inside the shape, it makes it harder to count how many there are."

Looking at underwear

A pair of underwear, for example, has three openings (one for the waist and one for each of the two legs), but it's not immediately clear how many holes a topologist would say it has. "A useful trick is to think about flattening it out," Steckles said. — "If we were to stretch the waistband of the pants out onto a big hula hoop, we'd see the two trouser legs sticking down, each being one hole."

So despite having three openings, the pair of underwear has only two holes. "So when the holes connect together in the middle, there's one fewer hole than there are openings," Steckles argued. Correspondingly, topology tells us that, despite eight interconnected openings, the human body has seven different holes.

But there might be one more. Although often counted as a blind hole, the vagina leads to the uterus, which then leads to one of two fallopian tubes. These tubes are open at the far end and lead to the peritoneal cavity near the ovary. It is the job of the finger-like projections of the funnel-shaped infundibulum at the end of the fallopian tube to catch the egg when it is released from the nearest ovary. However, it has been demonstrated that eggs released from one ovary can be captured by the fallopian tube on the other side, so that passage between the two open ends of the fallopian tubes is possible. Our tiny string could therefore be threaded all the way through the female reproductive tract and back out, counting as one more hole.

So the mathematician's answer is that humans have either seven or eight holes.

In the end, the question is not just about counting openings but about understanding connections. Topologically speaking, our bodies are less like Swiss cheese and more like a carefully constructed onesie for an octopus.

Human skeleton quiz: What do you know about the bones in your body?

On this day, chemists discovered a substance 900 times more radioactive than uranium. Their research led to unprecedented medical breakthroughs and worldwide fame — but it would also kill one of them.

Marie Curie was a medical student at the Sorbonne, a university in Paris, when she decided to study the new field of radiation for her thesis. In 1895, Wilhelm Röntgen discovered powerful "Röntgen rays," which would eventually be dubbed X-rays. The following year, Henri Becquerel accidentally discovered much weaker rays emitted by uranium salts would fog up photographic plates just like light rays did — even in the absence of light.

Curie realized that she wouldn't have to read a long list of prior papers on the newfangled subject before diving into experimental work, according to the American Institute of Physics. Curie's husband, Pierre, found her a workspace in a musty, crowded storeroom at his institution, the Paris Municipal School of Industrial Physics and Chemistry. He soon became so fascinated with her research that he abandoned his own to pursue hers.

Key to Marie Curie's research was the piezoelectric quartz electrometer. The device, invented by her brother-in-law, Jacques Curie, measured the weak electrical currents produced by radioactivity.

"Instead of making these bodies act upon photographic plates, I preferred to determine the intensity of their radiation by measuring the conductivity of the air exposed to the action of the rays," Curie wrote in a 1904 article for Century magazine.

The damp storeroom messed with her results, but she ultimately discovered that the intensity of this radiation depended on the concentration of uranium in the minerals she studied. She speculated that something intrinsic to the atomic structure of uranium must be at play.

Working with her husband Pierre and Gustave Bémont, the head of chemistry at the Higher School of Industrial Physics and Chemistry of the City of Paris, they began to study pitchblende, a black mineral rich in uranium often found in deposits alongside silver.

Curie noticed that it could be much more radioactive than uranium ore itself.

"How could an ore, containing many substances which I had proved inactive, be more active than the active substances of which it was formed? The answer came to me immediately: The ore must contain a substance more radioactive than uranium and thorium, and this substance must necessarily be a chemical element as yet unknown," Marie Curie wrote in Century magazine in 1903.

Marie Curie deduced that whatever this mysterious substance was, it had to exist only in small quantities yet have a remarkable level of what she had dubbed "radio-activity." The trio decided to try to separate pitchblende, which can be composed of up to 30 minerals, into its constituent parts to identify the radioactive substance. They used the light spectra of different substances to try to isolate and identify the ingredients.

In July, they pinpointed one mineral that was around 60 times more "radio-active" than uranium, which they named polonium. And on Dec. 21, they found another — called radium — that was an unprecedented 900 times more radioactive than uranium. They described both new substances during a talk at the French Academy of Sciences on Dec. 26.

The Curies would go on to isolate the radioactive elements over the next several years, while working in a poorly ventilated shed in the courtyard across from the original storeroom.

Their research on radiation earned the Curies and Becquerel the Nobel Prize in Physics in 1903. (Marie was originally going to be passed over, but she received the prize only after her husband, Pierre, insisted the committee credit her work.) Marie would earn another Nobel Prize in 1911, this time in chemistry, for her work on radium.

Pierre was killed by a horse-drawn carriage in 1906, but Marie would go on to advocate for the use of X-rays in medicine — including developing vehicles that could provide mobile X-rays for soldiers on the battlefield during World War I. She also noted that radium killed off diseased cells faster than healthy ones, a principle that would later inspire the development of radiotherapy for cancer treatment.

Radium caused frequent radiation sickness and burns in both Curies. Marie's radiation exposure likely killed her; she died in 1934 at age 66 due to aplastic anemia, a type of leukemia that can be caused by radiation damage to bone marrow. The notebook she used to document her 1898 discovery is still radioactive and is stored in a lead box.

Whether you're cooking up chemistry, getting physical with physics or bending your mind over mathematics, one thing that remains constant is, well, constants. Some numbers are so fundamental to the way we conduct science that we'd be lost without them, and their discovery has helped us better understand the world around us.

So how many of these key figures do you know? Try our new quiz and find out. We'll be dropping another number in the mix every day for you to guess, and if you prove yourself to be a numberphile, maybe you'll make it to the top of our leaderboard. All you need to do is register and your score will be saved, and be sure to leave a comment and share how you got on (but no spoilers please).

Try more science quizzes

—Live Science crossword: Test your knowledge on all things science with our weekly, free puzzle!

—Periodic table of elements quiz: How many elements can you name in 10 minutes?

—How quickly can you name all 12 Apollo astronauts that walked on the moon?

In October 2024, news broke that Facebook parent company Meta had cracked an "impossible" problem that had stymied mathematicians for a century.

In this case, the solvers weren't human.

An artificial intelligence (AI) model developed by Meta determined whether solutions of the equations governing certain dynamically changing systems — like the swing of a pendulum or the oscillation of a spring — would remain stable, and thus predictable forever.

The key to the problem was finding Lyapunov functions, which determine the long-term stability of these systems.

Meta's work made headlines and raised a possibility once considered pure fantasy: that AI could soon outperform the world's best mathematicians by cracking math's marquee "unsolvable" problems en masse.

After looking under the hood, however, mathematicians were less impressed. The AI found Lyapunov functions for 10.1% of randomly generated problems posed to it. This was a substantial improvement over the 2.1% solved by previous algorithms, but it was by no means a quantum leap forward. And the model needed lots of hand-holding by humans to come up with the right solutions.

A similar scenario played out earlier this year, when Google announced its AI research lab DeepMind had discovered new solutions to the Navier-Stokes equations of fluid dynamics. The solutions were impressive, but AI was still some distance from solving the more general problem associated with the equations, which would garner its solvers the $1 million Millennium Prize.

Beyond the hype, just how close is AI to replacing the world's best mathematicians? To find out Live Science asked some of the world's best mathematicians.

While some experts were dubious about AI’s problem solving abilities in the short term, most noted that the technology is developing frighteningly fast. And some speculated that not so far into the future, AI may be able to solve hard conjectures — unproven mathematical hypotheses — at a massive scale, invent new fields of study, and tackle problems we never even considered.

"I think what's going to happen very soon — actually, in the next few years — is that AIs become capable enough that they can sweep through the literature at the scale of thousands — well, maybe hundreds, tens of thousands of conjectures," UCLA mathematician Terence Tao, who won the Fields Medal (one of mathematics' most prestigious medals) for his deep contributions to an extraordinary range of different mathematical problems, told Live Science. "And so we will see what will initially seem quite impressive, with thousands of conjectures suddenly being solved. And a few of them may actually be quite high-profile ones."

From games to abstract reasoning

To understand where we are in the field of AI-driven mathematics, it helps to look at how AI progressed in related fields. Math requires abstract thinking and complex multistep reasoning. Tech companies made early inroads into such thinking by looking at complex, multistep logical games.

In the 1980s, IBM algorithms began making progress in games like chess. It's been decades since IBM's Deep Blue beat what was then the world's best chess player, Garry Kasparov, and about a decade since Alphabet's DeepMind defeated the period's best Go player, Lee Sedol. Now AI systems are so good at such mathematical games that there's no point to these competitions because AI can beat us every time.

But pure math is different from chess and Go in a fundamental way: Whereas the two board games are very large but ultimately constrained (or, as mathematicians would say, "finite") problems, there are no limits to the range, depth and variety of problems mathematics can reveal.

In many ways, AI math-solving models are where chess-playing algorithms were a few decades ago. "They're doing things that humans know how to do already," said Kevin Buzzard, a mathematician at Imperial College London.

"The chess computers got good, and then they got better and then they got better," Buzzard told Live Science. "But then, at some point, they beat the best human. Deep Blue beat Garry Kasparov. And at that moment, you can kind of say, 'OK, now something interesting has happened.'"

That breakthrough hasn't happened yet for math, Buzzard argued.

"In mathematics we still haven't had that moment when the computer says, 'Oh, here's a proof of a theorem that no human can prove,'" Buzzard said.

Mathematical genius?

Yet many mathematicians are excited and impressed by AI's mathematical prowess. Ken Ono, a mathematician at the University of Virginia, attended this year's "FrontierMath' meeting organized by OpenAI. Ono and around 30 of the world's other leading mathematicians were charged with developing problems for o4-mini — a reasoning large language model from OpenAI — and evaluating its solutions.

After witnessing the heavily human-trained chatbot in action, Ono said, "I've never seen that kind of reasoning before in models. That's what a scientist does. That's frightening." He argued that he wasn't alone in his high praise of the AI, adding that he has "colleagues who literally said these models are approaching mathematical genius."

To Buzzard, these claims seem far-fetched. "The bottom line is, have any of these systems ever told us something interesting that we didn't know already?" Buzzard asked. "And the answer is no."

Rather, Buzzard argues, AI's math ability seems solidly in the realm of the ordinary, if mathematically talented, human. This summer and last, several tech companies' specially trained AI models attempted to answer the questions from the International Mathematical Olympiad (IMO), the most prestigious tournament for high school "mathletes" around the world. In 2024, Deepmind's AlphaProof and AlphaGeometry 2 systems combined to solve four of the six problems, scoring a total of 28 points — the equivalent of an IMO silver medal. But the AI first required humans to translate the problems into a special computer language before it could begin work. It then took several days of computing time to solve the problems — well outside the 4.5-hour time limit imposed on human participants.

This year's tournament witnessed a significant leap forward. Google's Gemini Deep Think solved five of the six problems well within the time limit, scoring a total of 35 points. This is the sort of performance that, in a human, would have been worthy of a gold medal — a feat achieved by less than 10% of the world's best math students.

Research-level problems

Although the most recent IMO results are impressive, it's debatable whether matching the performance of the top high school math students qualifies as "genius-level."

Another challenge in determining AI's mathematical prowess is that many of the companies developing these algorithms don't always show their work.

"AI companies are sort of shut. When it comes to results, they tend to write the blog post, try and go viral and they never write the paper anymore," Buzzard, whose own research lies at the interface of math and AI, told Live Science.

However, there's no doubt that AI can be useful in research-level mathematics.

In December 2021, University of Oxford mathematician Marc Lackenby's research with DeepMind was on the cover of the journal Nature.

Lackenby's research is in the area of topology which is sometimes referred to as geometry (the maths of shapes) with play dough. Topology asks which objects (like knots, linked rings, pretzels or doughnuts) keep the same properties when twisted, stretched or bent. (The classic math joke is that topologists consider a doughnut and a coffee cup to be the same because both have one hole.)

Lackenby and his colleagues used AI to generate conjectures connecting two different areas of topology, which he and his colleagues then went on to try to prove. The experience was enlightening.

It turned out that the conjecture was wrong and that an extra quantity was needed in the conjecture to make it right, Lackenby told Live Science.

Yet the AI had already seen that, and the team "had just ignored it as a bit of noise," Lackenby said.

Can we trust AI at the frontier of math?

Lackenby's mistake had been not to trust the AI enough. But his experience speaks to one of the current limitations of AI in the realm of research mathematics: that its outputs still need human interpretation and can't always be trusted.

"One of the problems with AI is that it doesn't tell you what that connection is," Lackenby said. "So we have to spend quite a long time and use various methods to get a little bit under the hood."

Ultimately, AI isn't designed to get the "right" answer; it's trained to find the most probable one, said Neil Saunders, a mathematician who studies geometric representation theory at City St George's, University of London and the author of the forthcoming book "AI (r)Evolution" (Chapman and Hall, 2026), told Live Science.

"That most probable answer doesn't necessarily mean it's the right answer," Saunders said.

AI's unreliability means it wouldn't be wise to rely on it to prove theorems in which every step of the proof must be correct, rather than just reasonable.

"You wouldn't want to use it in writing a proof, for the same reason you wouldn't want ChatGPT writing your life insurance contract," Saunders said.

Despite these potential limitations, Lackenby sees AI's promise in mathematical hypothesis generation. "So many different areas of mathematics are connected to each other, but spotting new connections is really of interest and this process is a good way of seeing new connections that you couldn't see before," he said.

The future of mathematics?

Lackenby's work demonstrates that AI can be helpful in suggesting conjectures that mathematicians can then go on to prove. And despite Saunders' reservations, Tao thinks AI could be useful in proving existing conjectures.

The most immediate payoff might not be in tackling the hardest problems but in picking off the lowest-hanging fruit, Tao said.

The highest-profile math problems, which "dozens of mathematicians have already spent a long time working on — they're probably not amenable to any of the standard counterexamples or proof techniques," Tao said. "But there will be a lot that are."

Tao believes AI might transform the nature of what it means to be a mathematician.

"In 20 or 30 years, a typical paper that you would see today might indeed be something that you could automatically do by sending it to an AI," he said. "Instead of studying one problem at a time for months, which is the norm, we're going to be studying 10,000 problems a year … and do things that you just can't dream of doing today."

Rather than AI posing an existential threat to mathematicians, however, he thinks mathematicians will evolve to work with AI.

"We've had situations in the past where entire fields of mathematics became basically solvable by computer," Tao said. At one point, we even had a human profession called a "computer," he added. That job has disappeared, but humans just moved on to harder problems. "It didn't mean mathematics died," Tao said.

Andrew Granville, a professor of number theory at the University of Montreal, is more circumspect about the future of the field. "My feeling is that it's very unclear where we're going," Granville told Live Science. "What is clear is that things are not going to be the same. What that means in the long term for us depends on our adaptability to new circumstances."

Lackenby similarly doesn't think human mathematicians are headed for extinction.

While the precise degree to which AI will infiltrate the subject remains uncertain, he's convinced that the future of mathematics is intertwined with the rise of AI.

"I think we live in interesting times," Lackenby said. "I think it's clear that AI will have an increasing role in mathematics."

A record-breaking investigation, using a particle detector a mile underground in South Dakota, may have revealed new insights about dark matter, the mysterious substance believed to make up most of the matter in the universe.

Using the largest dataset of its kind, the experiment — called LUX-ZEPLIN (LZ) — constrained the potential properties of one of the leading candidates for dark matter with unprecedented sensitivity. The research did not uncover any evidence of the mysterious substance, but will help future studies avoid false detections and better hone in on this poorly understood piece of the universe.

"This quest is to try to solve this huge problem, this huge missing piece that we have in terms of understanding our universe," Rick Gaitskell, head of the particle astrophysics group at Brown University and part of the LZ research team, told Live Science.

The results, released Monday (Dec. 8), have been submitted to the journal Physical Review Letters and are available as a preprint via arXiv. The results were also presented at a scientific talk at the Sanford Underground Research Facility, where LZ's detector is hosted.

WIMPs vs. neutrinos

The team had two goals for the new study: to elucidate the properties of a low-mass "flavor" of proposed dark-matter particles called weakly interacting massive particles (WIMPs), and to see if the detector could view solar neutrinos — nearly mass-less subatomic particles produced by nuclear reactions inside the sun. The team suspected that the detection signature of these particles could be similar to that predicted by certain models of dark matter, but needed to spot the solar neutrinos to know for sure.

Before the experiment, which took 417 days to perform between March 2023 and April 2025, the detector's sensitivity was upgraded to search for rare interactions with fundamental particles. A cylindrical chamber filled with liquid xenon was the theater for action. Researchers could watch for either WIMPs or neutrinos colliding with the xenon, either of which produces flashes of photons, along with positively charged electrons.

The experiment pushed forward the science for both the WIMP and neutrino questions. For the neutrinos, researchers improved their confidence that a type of solar neutrino, known as boron-8, is actually interacting with the xenon. This knowledge will help future studies avoid false detections of dark matter.

Physics discoveries typically must reach a confidence level called "5 sigma" to be considered valid. The new work achieved 4.5 sigma — a considerable improvement over sub-3-sigma results reported in two detectors last year. And that was especially notable given that boron-8 detections happen only about once a month in the detector, even when monitoring 10 tons of xenon, Gaitskell said.

As for the dark matter question, however, the researchers didn't find anything definitive for the low-mass types of WIMPs they were seeking. Scientists would have known it if they saw it, the team said; if a WIMP hits the heart of a xenon molecule, the energy of the collision creates a distinctive signature, as best as models predict.

"If you take a nucleus, it is possible for dark matter to come in and actually simultaneously scatter from the entire nucleus and cause it to recoil," Gaitskell explained. "It's known as a coherent scatter. It has a particular signature in the xenon. So it's those coherent, nuclear recoils that we're looking for."

The team did not detect this signature in their experiment.

Doubling the run

The experiment continues now, with a longer run ongoing until 2028. By then, the detector will have collected a record-breaking 1,000 days of data. Longer runs give researchers a better chance of catching rare events.

The detector will hunt not only for more solar neutrino or WIMP interactions but also other physics that may fall outside the Standard Model of particle physics said to describe most of the environment around us.

Gaitskell emphasized that the role of science is to keep pushing forward even when "negative" results arise.

"One thing I've learned is, don't ever assume that nature does things in the way that you think it should, exactly," said Gaitskell, who has been studying dark matter for more than four decades.

"There are plenty of elegant [solutions] that you would say, 'That's so beautiful. It has to be true.' And we tested them … and it turned out, nature ignored it and nature did not want to go down that particular route."

Editor's note: This article was updated on Dec. 10 at 5 p.m. ET with a correction. The detector's next run won't begin in 2028, but rather end then, after a cumulative 1,000 days of data have been collected.

Live concerts, fireworks and roaring stadium crowds can reach dangerously high volumes — loud enough to cause permanent hearing loss. But what was the loudest sound ever recorded on Earth?

The answer depends on what you mean by "sound" and whether you include old historical reports or only trust measurements made with modern scientific instruments.

The 1883 eruption of Krakatau (also spelled Krakatoa), a volcanic island in Indonesia, is often considered the loudest sound in history. People heard the blast more than 1,900 miles (3,000 kilometers) away, and barometers around the world picked up its pressure wave. At 100 miles (160 km) away, the eruption reached an estimated 170 decibels — enough to cause permanent hearing damage. At 40 miles (64 km) away, the boom was strong enough to rupture eardrums, sailors reported.

Typically, people can tolerate sounds up to around 140 decibels, beyond which sound becomes painful and unbearable. Hearing damage can occur after listening to 85 decibels for a few hours, 100 decibels for 14 minutes or 110 decibels for two minutes, according to the National Institutes of Health. Meanwhile, a vacuum cleaner is around 75 decibels, a chainsaw is about 110 decibels and a jet engine is approximately 140 decibels.

Modern estimates suggest that the Krakatau blast reached about 310 decibels. At this level, sound waves no longer behave like normal sound (which causes particles to vibrate and creates areas of compression and rarefaction). Instead, at around 194 decibels, they turn into shock waves — powerful pressure fronts created when something moves faster than the speed of sound. Krakatau's shock wave was so strong that it circled the planet seven times.

But Michael Vorländer, a professor and head of the Institute for Hearing Technology and Acoustics at RWTH Aachen University in Germany and president of the Acoustical Society of America, said we don't really know how loud the Krakatau eruption was at its source because no one was close enough to measure it.

"Assumptions can be made about sound propagation, but these are extremely uncertain," he told Live Science in an email.

Another contender for the loudest sound is the 1908 Tunguska meteor explosion over Siberia that flattened trees across hundreds of square miles and sent pressure waves around the world. The Tunguska explosion was approximately as loud as the Krakatau blast — at circa 300 to 315 decibels — but like the Krakatau eruption, the Tunguska blast was recorded only by instruments that were very far away.

Loudest sound in the modern era

If you limit the question to the modern era — that is, when scientists have had a global network of barometers and infrasound sensors — a much more recent event takes the grand prize.

"I believe the 'loudest' sound recorded is the January 2022 eruption of Hunga, Tonga," David Fee, a research professor at the Geophysical Institute at the University of Alaska Fairbanks, told Live Science in an email. "This massive volcanic eruption produced a sound wave that traversed the globe multiple times and was heard by humans thousands of miles away, including in Alaska and Central Europe."

Milton Garces, founder and director of the Infrasound Laboratory at the University of Hawaii, agrees. "If you were to reframe the question as, 'What is the loudest sound recorded in the modern digital epoch?', then without a doubt the loudest sound was from Tonga in '22," he told Live Science in an email.

One of the closest scientific stations to the underwater eruption — located in Nukua'lofa, about 42 miles (68 km) away — recorded a pressure jump of about 1,800 pascals. (A 200 megaton chemical explosive blast would create about 567 pascals overpressure at a distance of about 560 miles, or 737 km, Garces explained.) If you were to try to turn that into a normal "decibel" number at 3 feet (1 meter) from the source, you'd get about 256 decibels. But Garces said that would be bad science, because this wasn't a normal sound wave at all. Close to the source, it acted more like fast-moving air being pushed outward by the explosion. The Tonga blast was simply too big to fit into the normal decibel scale.

Human-made sounds

Strangely, the most powerful pressure wave in recent history was mostly inaudible to people because it was beyond the range of human hearing, Fee noted.

Scientists have tried to create huge pressure waves in laboratories. In one experiment, researchers used an X-ray laser to blast a microscopic water jet, which produced a pressure wave estimated at about 270 decibels. (That's even louder than the launch of the Saturn V rocket that carried Apollo astronauts to the moon, which was estimated at about 203 decibels.)

However, the laser experiment was done inside a vacuum chamber, so the 270-decibel pressure wave was completely silent. Sound waves need a medium — such as air, water or solid material — to travel.

"Pressures in a vacuum chamber are kinda cheating," Garces said. "That's like pressure in space: a supernova may generate huge radiation pressure, but it would not radiate as what we call sound."

"For the most powerful sound-like wave recorded in the modern era," Garces said, "Tonga 2022 is the champ."