AI helps Harvard mathematician crack near-century-old math problem

Levent Alpoge, a 33-year-old mathematician at Harvard University, U.S., wrote on X on July 19 that the Jacobian conjecture, long believed to be true, is in fact false. He supported the claim with a 216-character counterexample.

By the following day, the result had been independently verified and became the main topic of discussion among researchers in Imperial College London's pure mathematics department, British mathematician Kevin Buzzard told Fortune.

First proposed by German mathematician Ott-Heinrich Keller in 1939, the Jacobian conjecture states that a certain class of mathematical functions can always be reversed. It was later included in mathematician Stephen Smale's influential 1998 list of 18 major unsolved problems for the 21st century.

In his X post, which has since attracted nearly 40 million views, Alpoge wrote that part of the work was done with help from his "close friend fable during the world cup final," an apparent reference to Anthropic's Claude Fable 5 AI model, according to science magazine New Scientist.

A person stands in front of a chalkboard filled with mathematical formulas. Photo from Pexels

The finding is the latest in a series of AI-driven advances in mathematics. Since mid-2025, AI systems have rapidly expanded their capabilities, beginning with solving five of six problems at the International Mathematical Olympiad. OpenAI later disproved an 80-year-old conjecture by Paul Erdős in combinatorial geometry, while in June, 16 researchers from 15 universities issued the Leiden Declaration on Artificial Intelligence and Mathematics, calling for standards on transparency, attribution and peer review as AI reshapes the discipline.

Abhishek Saha of Queen Mary University of London said recent advances by AI in mathematics, including OpenAI's work on the Erdős conjecture, had already surprised researchers, but the Jacobian result represented a new milestone.

"Probably this is the biggest conjecture that AI has played a significant role [in proving or disproving] so far in mathematics," he says. "This is a pretty big deal. AI has [made] remarkable progress in the last year."

Buzzard described the result as "very exciting," saying it highlights the potential for large language models to become the kind of "supermathematician" envisioned years ago by Google Deep Learning scientist Christian Szegedy.

Still, some researchers cautioned that AI has yet to explain its reasoning in ways mathematicians find satisfying. "The trouble with getting current AI models to solve pure math is that you get the 'how' without the 'why'," said Akhil Mathew, a mathematician at the University of Chicago who suggested the problem to Alpoge.

"One can check out that it's correct, but it would be nice to be able to tell a story."

Ivan Fesenko of Westlake University in China told New Scientist that increasingly capable AI models are likely to solve ever more complex mathematical problems, fundamentally changing the field.

"Right now, AI can already produce master's degrees in mathematics. In one year, they will produce PhD degrees in mathematics. And then the question arises, do we really need so many mathematicians around if AI can do such things so nicely?"