Levent Alpöge posted on X a counterexample to the Jacobian conjecture, a problem open since 1939, using Anthropic's Claude model. The counterexample consists of three polynomials that satisfy the conj…
An AI-found counterexample to the 87-year-old Jacobian conjecture in dimension three, posted by mathematician Levent Alpöge on July 19, can be verified by anyone in seconds using symbolic computation.…
Mathematician Levent Alpöge used Anthropic's Fable 5, the latest frontier AI model, to disprove the Jacobian conjecture, a long-standing open problem in algebraic geometry that had resisted solution f…
Mathematician L. Alpöge announced a polynomial counterexample to the Jacobian conjecture on July 20, 2026, crediting the AI system Fable. The Jacobian conjecture, first stated by Keller in 1939, asser…