Claude Fable5 helps find a Jacobian conjecture counterexample

机器之心 · wechat · 2026-07-20

Anthropic researcher Levent Alpoge says Claude Fable5 helped him find a counterexample to the Jacobian conjecture.

He posted a concrete polynomial map \(C^3 \to C^3\) whose Jacobian determinant is constantly -2, yet it maps three distinct inputs to the same output, so it cannot be globally invertible.
The post went viral in math and AI circles, with mathematicians and HN users quickly checking the arithmetic.
The article explains why the conjecture has resisted proof for 85 years, notes that the result is still awaiting formal peer review, and discusses the bigger question of whether the model is merely retrieving prior math or genuinely contributing new discovery.
It also connects the story to Zhang Yitang, whose own PhD work was derailed by a faulty lemma related to the conjecture.

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