AI-Generated Tiny 3D Formula Upends Century-Old Jacobian Conjecture
A three-dimensional polynomial with a constant Jacobian determinant (-2) serves as a counterexample to the Jacobian conjecture in dimensions greater than two, while the two-dimensional case remains open. Discovered by Levent Alpöge using Anthropic’s Claude Fable 5, the remarkably simple formula is easy to verify and highlights AI’s potential to uncover surprising mathematical objects, signaling a new avenue for AI-assisted breakthroughs in mathematics.
