Anthropic researcher thanks Claude for solving 87-year-old Math conjecture; says Jacobian conjecture is false
An Anthropic researcher has credited the company’s AI model, Claude Fable 5, with helping overturn one of mathematics’ longest-standing problems. Levent Alpöge, a mathematician at Anthropic, announced on X (formerly known as Twitter) that he had found a counterexample to the 87-year-old Jacobian conjecture with the help of Claude. In a post, he wrote: “Hello there the Jacobian conjecture is false.” The discovery, if confirmed by the wider mathematics community, overturns most versions of a conjecture that has remained unsolved for decades and highlights how AI is increasingly being used to make new mathematical discoveries rather than only assisting with proofs.
Anthropic researcher credits Claude for breakthrough
Levent Alpöge shared the discovery on X, saying Claude Fable 5 helped him find a counterexample to the Jacobian conjecture. The AI-assisted finding has drawn attention because the counterexample is reportedly simple enough to fit into a single social media post, making it easier for mathematicians to verify.The Jacobian conjecture was first proposed in two dimensions in 1884 by Czech mathematician Ludwig Kraus and later extended to all dimensions by German mathematician Ott-Heinrich Keller in 1939.
What is the Jacobian conjecture
The Jacobian conjecture is a well-known problem in algebraic geometry. It suggests that if a polynomial function has a constant, non-zero Jacobian determinant, then it should always have another polynomial function that reverses it.For decades, mathematicians believed the conjecture could be true, although nobody had been able to prove or disprove it completely. Many claimed proofs were later found to contain errors.According to the reported discovery, the counterexample works in three dimensions and has a constant Jacobian determinant of -2. However, the function maps multiple input points to the same output point, meaning it cannot be reversed. The finding suggests the Jacobian conjecture is false for dimensions higher than two. The original two-dimensional version of the conjecture remains unsolved.
