Levent Alpőge, a mathematician at the AI company Anthropic, says he used the company’s large language model Claude Fable 5 to find a counterexample to the Jacobian conjecture, according to ScienceDaily.
The Jacobian conjecture is a long-standing problem in algebraic geometry. It asks whether certain polynomial functions with a non-zero constant Jacobian determinant must always have a polynomial inverse.
According to the report, Alpőge found a three-dimensional example with a constant Jacobian determinant of -2 that sends multiple input points to the same output point, which means it is not reversible. That makes the conjecture false in every dimension above two.
The original two-dimensional version of the conjecture, first stated in 1884 and later generalized in 1939, remains unsolved. The counterexample was brief enough that other mathematicians were able to verify it easily, according to ScienceDaily.
The article says details of the prompting process have not been made public. It also notes that the finding adds to a growing list of math results linked to large language models.
