Anthropic mathematician says Fable 5 cracked an 87-year-old conjecture

Levent Alpöge, a mathematician at Anthropic, posted on July 19 that he and a collaborator found a counterexample to the Jacobian Conjecture. The conjecture has been open since 1939.

That matters for mathematicians trying to figure out whether AI can do real research work or just win benchmarks. Most "AI does math" claims land as a score or a proof too dense for outsiders to check. This one is a specific object: a degree-7 counterexample in three variables, verifiable by hand instead of trusted on faith.

Mathematicians had estimated any counterexample would need degree 200 or higher. Alpöge and his collaborator, working with Claude Fable 5, landed on degree 7. The Hacker News thread built around the post moved fast, and most of the argument wasn't over whether the math checks out. It was over how much of the search Fable 5 actually drove versus how much the two mathematicians steered by hand.

That's the right question to ask about any AI math claim, and it's probably not one outsiders can answer. Nothing in the thread settles it either way.

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The hand-checkable part is the real claim here, and it's testable. If independent mathematicians outside Anthropic don't publish a check of the degree-7 counterexample soon, that's telling. It would mean the "verify it yourself" pitch did more work than actual verification.