'Alien's language' problem that stumped mathematicians for decades may finally be close to a solution

An aerial photograph of a crop circle design — Crop circles, like this one in England, are sometimes misinterpreted as alien messages. They've got nothing on the complexity of the Inter-universal Teichmüller Theory — a math proof so complicated it's been dubbed the "alien's language".

(Image credit: Abstract Aerial Art via Getty Images)

Imagine this scenario: Scientists have intercepted a transmission from an alien race. It's clear that the message comes from an intelligent being, but everything about it — the syntax, the grammar, the context — is unintelligible to us Earthlings.

That's how most mathematicians feel about the Inter-universal Teichmüller Theory (IUT), a proof introduced by mathematician Shinichi Mochizuki over a decade ago in an attempt to solve the famous ABC conjecture, one of the most famous unsolved problems in number theory, which deals with the sum of prime numbers and has implications on many other conjectures.

Mochizuki developed IUT in the early 2000s and published it across a series of four preprints in 2012. The proof is over 2,000 pages long, and Mochizuki claims it offers a solution to the ABC conjecture. If proven, the conjecture could help clarify other major mathematical enigmas, such as Fermat's Last Theorem — a nearly 400-year-old theorem that states no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The theorem was first solved by mathematician Andrew Wiles in 1995, but Zhou's new framework could prove the theorem in much fewer steps.

However, IUT employs concepts and symbols that are wholly unique in the world of math. In other words, Mochizuki essentially created his own mathematical language — and it confounded many of the world's leading mathematicians. A few brave souls, including mathematician Ivan Fesenko, have chipped away at parts of it and lent some credence to Mochizuki's claims. Yet despite existing for over a decade, IUT has not been fully verified by peer review because it is so difficult to understand.

Enter Zhou. He has a background in mathematics, having studied graph theory as a doctoral candidate, but he ultimately left before completing his degree to work as a software engineer. However, this didn't diminish his interest in pure math. He became obsessed with IUT, studying the theory in his spare time despite a busy workweek. Over the course of five months, he detailed several refinements and new applications in a paper, which he sent to both Mochizuki and Fesenko. The work, if correct, proves the majority of cases of generalized Fermat's Last Theorem, using principles from IUT.

The mathematicians were impressed; Fesenko even offered to fly him out to Westlake University in China, where he works. Zhou accepted the offer and is currently working under Fesenko's tutelage on furthering the proof. There are myriad potential applications of this work, ranging from cryptography and quantum computing to a better understanding of space-time — but only if they're comprehensible to other researchers.

Joanna Thompson is a science journalist and runner based in New York. She holds a B.S. in Zoology and a B.A. in Creative Writing from North Carolina State University, as well as a Master's in Science Journalism from NYU's Science, Health and Environmental Reporting Program. Find more of her work in Scientific American, The Daily Beast, Atlas Obscura or Audubon Magazine.