A mathematician tied to Anthropic, Levent Alpoge, claims to have found a counterexample to the Jacobian conjecture using the AI model Claude Fable 5, marking a potential breakthrough in a problem unsolved for decades.

Alpoge announced on X that he and Fable produced a counterexample, described as 216 characters long, which purportedly disproves the conjecture.

The purported disproof, aided by artificial intelligence, targets the long-standing three-variable version of the Jacobian Conjecture, with questions remaining about two-variable cases.

Independent replication and scrutiny from other experts are being emphasized as essential steps to establish the claim’s validity.

The story sits within a broader discussion of AI’s role in mathematical discovery, highlighting both its problem-solving potential and the need for human oversight for formal proofs.

AI-assisted mathematics is framed as part of a wider trend across science, capable of accelerating discovery but not replacing human insight.

The next step, beyond verifying the counterexample, is for researchers to understand why it works and what it reveals about the underlying mathematics.

Experts urge caution: a counterexample disproves the conjecture but does not automatically provide the deeper insight or constructive understanding sought in mathematics.

Formal peer review has not yet occurred, though some mathematicians have performed initial checks with tools like SymPy and Lean.

Other AI systems were used for additional checks, occasionally producing lighthearted or inconclusive results.

Verifying a solution is easier than deriving it, and questions remain about how the AI arrived at the result, possibly revealing undisclosed prompts or methods.

There is widespread caution about embracing AI-generated claims until the community validates them, given history of failed proposals.