A remarkably simple three-dimensional function has exposed an unexpected limit to a century-old mathematical conjecture, as an AI-assisted counterexample disproves the Jacobian conjecture above two dimensions while leaving its original two-dimensional form open. Levent Alpöge, a mathematician at the artificial intelligence company Anthropic, announced that he had found a counterexample to the Jacobian conjecture, a famous and long-standing problem in algebraic geometry, using Anthropic’s large language model Claude Fable 5, which had been released to the public only weeks earlier. The Jacobian conjecture concerns functions built from polynomials, where a non-zero constant Jacobian determinant implies the existence of a polynomial inverse function. The two-dimensional version was stated by Czech mathematician Ludwig Kraus in 1884, and it was generalised to any number of dimensions by German mathematician Ott-Heinrich Keller in 1939. Fields Medallist Stephen Smale included it in his 1998 list of Mathematical Problems for the Next Century. During its long history, the conjecture has been the subject of many claimed proofs, including by Beniamino Segre and Wo.