Anthropic’s Fable 5 reportedly disproved a 90-year math problem

A 90-year-old open problem in algebraic geometry may have fallen to Anthropic’s Fable 5 — but at least one mathematician says that does not mark a dramatic shift in what researchers should expect from AI.

On Sunday evening, while much of the world was watching the World Cup, mathematician Levent Alpöge posted on X that he had used Fable 5 to disprove the Jacobian conjecture. The conjecture has stumped mathematicians for nearly 90 years and was included in Stephen Smale’s 1998 list of unresolved problems known as Smale’s problems.

Mashable notes that Alpöge is part of Harvard’s Society of Fellows, and his LinkedIn profile lists an affiliation with Anthropic. The publication said it contacted Anthropic with questions about Alpöge’s work.

Fable 5 is Anthropic’s latest frontier model and the public version of Claude Mythos Preview, which Anthropic has said had such advanced cybersecurity capabilities that it was too dangerous for public release.

Professor Andrew Blumberg, who has a joint appointment in mathematics and computer science at Columbia University, told Mashable the result did not change his view of what these systems can do. Blumberg is involved in the First Proof project, which tests frontier large language models on research-level mathematics.

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“This did not cause me to update my priors about what AI can and can’t do. This is exactly the kind of thing I would expect AI to be able to do. If there was a counterexample that was concise and easy to state that people haven’t found because it’s a pain to search through all this stuff, AI will find it.”

Why a counterexample is different from a proof

Blumberg said producing a counterexample is still a meaningful achievement, but it is not the same as delivering a positive proof that helps mathematicians understand a problem more deeply.

“Suppose that Moses came down from the mountain with tablets, and on the tablet was written, 'Cancer can be cured.' Would you care? You don’t just want the answer to the question. You want to learn something from the answer. And the reason Smale thought this problem was important is because he thought that if we solved it, we would understand more things about the about the way nature is structured.”

In Blumberg’s view, the Jacobian conjecture counterexample may be important without being especially illuminating.

“This counterexample tells us essentially nothing. It’s just, you know, there are a lot of polynomials, and it’s hard for people to check them all, but it’s not hard for machines.”

Mashable compares the claim with another recent case: OpenAI said in May that an internal model had disproved the Erdős unit distance conjecture, a central conjecture in discrete geometry. Blumberg said that result appeared more useful because experts were able to unpack the disproof and build on it.

He said that may not be true here, though he also acknowledged he is not enough of an expert on the Jacobian conjecture to know whether this particular counterexample has deeper structure worth studying.

Mashable also disclosed that its parent company, Ziff Davis, filed a lawsuit against OpenAI in April 2025, alleging copyright infringement in the training and operation of its AI systems.