AI-Engine Counterexample Cracks Century-Old Jacobian Conjecture

Mathematician Levent Alpöge used Anthropic’s Claude Fable 5 to forge a concrete three-variable polynomial with Jacobian determinant -2 that is not invertible, producing a verifiable counterexample to the Jacobian conjecture (pending arXiv peer review); the episode underscores AI as a genuine research collaborator and highlights the rise of formal verification like Lean in AI-driven mathematics.