Algebraic Geometry

Claude Fable 5 surfaces a three-variable counterexample that topples the 87-year-old Jacobian conjecture

Mathematician Levent Alpöge, using Anthropic's large language model Claude Fable 5, has found a three-variable counterexample to the 87-year-old Jacobian conjecture. This disproof, a compact formula with a Jacobian determinant of -2, invalidates the conjecture in dimensions above two, though the two-dimensional version remains open. The discovery highlights the potential of AI in finding unexpected mathematical objects.