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Mathematician Claims He Solved 160-Year-Old Math Problem. Critics Say Probably Not.
An unsolved 160-year-old math problem may finally have a solution — but critics are wary.
Michael Atiyah, a prominent mathematician emeritus at the University of Edinburgh, announced yesterday (Sept. 24) at the Heidelberg Laureate Forum in Germany that he had come up with a simple proof to solve the Riemann hypothesis.
The hypothesis was first put forth by German mathematician Bernhard Riemann in 1859. Prime numbers, or those whose only factors are 1 and itself — such as 2, 3, 5 and 7— don't seem to follow a regular pattern on the number line. In other words, you couldn't figure out when the next prime number occurs by knowing some pattern. [The 11 Most Beautiful Mathematical Equations]
However, Riemann saw that the frequency of prime numbers apparently closely follows one equation that became known as the Riemann Zeta function, according to the Clay Mathematics Institute. If the equation holds true, it would describe the distribution of prime numbers all the way to infinity.
But as of now, it has been checked for only the first 10,000,000,000,000 solutions, according to the institute, and the problem remains "unsolved." The person who solves the Riemann Zeta function, or one of the other six big mysteries in math that make up the "Millennium Prize Problems," will win an award of $1 million from the Institute.
Atiyah's proof is based on an unrelated physics number called the "fine structure constant," which describes the electromagnetic interactions between charged particles, according to Science. He describes this constant using another equation called the Todd Function, to prove the Riemann hypothesis by contradiction, according to Science. In math, contradiction is one type of proof in which you assume that the "thing" you want to prove is untrue and then show how the results of this assumption are just not possible.
Atiyah, 89, has made major contributions to math and physics, winning top mathematics awards — the Fields Medal in 1966 and the Abel Prize in 2004. But in recent years he has also put forth some mathematical proofs that didn't hold up — and now many of his colleagues are critical of his new claims and say they're unlikely to hold true, according to Science.
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"The proof just stacks one impressive claim on top of another without any connecting argument or real substantiation," John Baez, a mathematical physicist at the University of California, Riverside, told Science.
In his talk, Atiyah described the many, many times people have claimed to have proved the hypothesis, only to be proven wrong. "Nobody believes any proof of the Riemann hypothesis because it's so difficult, nobody has proved it, and so why should anybody prove it now? Unless, of course, you have a totally new idea," he said.
Originally published on Live Science.
Yasemin is a staff writer at Live Science, covering health, neuroscience and biology. Her work has appeared in Scientific American, Science and the San Jose Mercury News. She has a bachelor's degree in biomedical engineering from the University of Connecticut and a graduate certificate in science communication from the University of California, Santa Cruz.