A Mathematician Used Claude Fable to Disprove the 87-Year-Old Jacobian Conjecture in a Few Hours - Glitchwire

What the report says

Glitchwire reported that Levent Alpöge, identified as a number theorist at Anthropic and a former Harvard Society of Fellows Junior Fellow, posted on X on July 20, 2026, claiming to have found a counterexample to the Jacobian conjecture with help from Anthropic’s Fable model. The article says Alpöge credited both a friend named Akhil, who raised the problem, and “Fable” for work done during the World Cup final.

The Jacobian conjecture concerns polynomial maps from an n-dimensional space to itself: if the Jacobian determinant is a nonzero constant, the conjecture asks whether the map must have a polynomial inverse. Glitchwire described it as a major longstanding problem in algebraic geometry, noting that a generalized form dates to 1939 and that the problem appeared on Steve Smale’s 1998 list of important mathematical challenges.

According to the article, Alpöge’s posted example is a three-dimensional polynomial map with constant Jacobian determinant -2, but it sends three different input points to the same output point. If verified, that would rule out invertibility and therefore disprove the conjecture. Glitchwire said Alpöge included Wolfram Alpha links and that Wikipedia was updated soon afterward, but also emphasized that the claim was still awaiting formal peer review and arXiv verification.

The report frames the episode as a potentially significant example of AI being used as a mathematical research collaborator rather than only for benchmark performance. Separately from Glitchwire’s claims, standard mathematical practice requires careful independent checking before a purported solution or counterexample to a famous open problem is accepted.