🤖 Claude Fable 5 helped find a counterexample to the Jacobian conjecture
Mathematician Levent Alpoge (Anthropic) claims to have found a counterexample to the Jacobian conjecture, which has remained open since 1939. The counterexample, proposed with the help of the Claude Fable 5 model, is a polynomial mapping in $\mathbb{C}^3$ with a constant Jacobian determinant equal to -2. The result has not yet undergone official peer review.
🌍 If the claim is confirmed, it will become one of the greatest breakthroughs in algebraic geometry and demonstrate a new level of LLM application in solving fundamental problems.
👤 This is an example of how frontier models are transitioning from text generation to acting as a "drafting" tool for scientists, helping to verify complex hypotheses.
Source 1: https://en.wikipedia.org/wiki/Jacobian_conjecture Source 2: https://www.explainx.ai/blog/fable-5-jacobian-conjecture-counterexample-alpoge-july-2026