A Harvard mathematician and an AI model may have cracked an 87-year-old math problem

A young mathematician teamed up with a new AI model to tackle one of the hardest open problems in mathematics, and the result is causing a stir among mathematicians and AI researchers on X.

Levent Alpöge, a 33-year-old researcher at Harvard University, spent Sunday working with Anthropic’s Fable model to defeat the “Jacobian conjecture,” a notoriously difficult problem proposed by German mathematician Eduard Ott-Heinrich Keller in 1939.

The challenge for Alpöge and Fable was to find a counterexample proving the conjecture false (a single verified counterexample would be enough). Alpöge casually announced the result on X, thanking both the friend who encouraged him to take on the problem and Anthropic’s Claude Fable, the AI model that helped him do it.

The conjecture proposes that if you start with a point on a grid represented by ordinary variables (say, x and y), then use polynomial equations—equations involving powers such as x² and y³—to create new coordinates, you should be able to reverse the process using polynomial equations and recover the original coordinates. (For a deeper explanation, visit the Wikipedia page.)

Alpöge’s counterexample is just 216 characters long. Although the work has yet to undergo the normal peer-review process, several mathematicians have reportedly confirmed the arithmetic and conducted independent checks using SymPy (a Python library for symbolic mathematics) and Lean (a formal proof assistant). Others then used additional AI systems, including OpenAI’s GPT models, to conduct their own fact-checks (sometimes to unintentionally hilarious results).

The result has prompted debate among mathematicians about AI’s role in their field. Systems that can rapidly generate counterexamples may accelerate discovery while shifting researchers’ attention toward explaining why a result is true and what it means.

AI models are increasingly being used as collaborators in mathematical research rather than simply as computational tools. Researchers use them to suggest proof strategies, fill in missing logical steps, and check arguments for errors—allowing ideas to be explored more quickly. Artificial intelligence is also accelerating the growing field of formal verification by translating proofs into computer-checkable languages such as Lean, which can verify complex theorems with a high degree of certainty. These systems can also analyze large amounts of mathematical data, identify unexpected patterns, and propose new conjectures or avenues of investigation.

Alpöge’s discovery, if verified, may offer some of the strongest evidence yet for a claim frequently made by AI executives—that advanced models will significantly accelerate mathematical and scientific discovery. It may also challenge critics who argue that transformer-based systems (including GPT and Claude), because they are probabilistic rather than deterministic, cannot be useful in exacting fields such as mathematics and science.