Claude Fable Shatters 87-Year-Old Jacobian Conjecture

Anthropic mathematician Levent Alpöge used Claude Fable to discover a counterexample to one of mathematics' most stubborn open problems. Announced via tweet during the World Cup final.

The Jacobian Conjecture — one of mathematics' most stubborn open problems — has fallen. And it fell not in a peer-reviewed journal, but in a tweet posted during the World Cup final.

Levent Alpöge, a mathematician at Anthropic with a Princeton PhD (advised by Fields Medalist Manjul Bhargava), announced on X that he used Claude Fable to find a counterexample disproving the conjecture. His opening line: "hello there the jacobian conjecture is false."

The conjecture, first posed by Ott-Heinrich Keller in 1939 and traced even earlier to Ludwig Kraus in 1884, claimed that any polynomial map from C^n to C^n with a non-zero constant Jacobian determinant must be invertible. It survived decades of assault — false proofs were published, degree-100 verifications held, and generations of mathematicians burned years on it.

Alpöge's counterexample is strikingly simple: a degree-7 polynomial map in just three dimensions. Commenters on Hacker News noted that a graduate student in 1997 could have found it with a three-day computer search — but nobody did.

Multiple AI models independently verified the result, each reportedly going through cycles of disbelief before accepting what they were seeing. Claude Code checked its own arithmetic four times. "This is a rare instance where feeding this groundbreaking information into an LLM gives them psychosis," one HN user observed.

Wikipedia editors are already locked in an edit war over whether to update the article. But the mathematics community on Hacker News is nearly unanimous: the counterexample is straightforwardly verifiable — tedious, but doable by hand. As one commenter put it, this isn't a complicated proof; it's a straightforwardly checkable certificate of a solution.

The conjecture that survived Keller, Abhyankar, Moh's degree-100 verification, and five published wrong proofs appears to have died via tweet during the World Cup final.

Sources: Wikipedia — Jacobian Conjecture, Alpöge's Announcement on X