Math & science · July 2026

Jacobian conjecture disproved

An AI-found polynomial map ends an 87-year-old conjecture.

Levent Alpöge posted an explicit three-variable polynomial map with constant Jacobian that is not injective, found with Claude Fable 5. It disproves the 1939 Jacobian conjecture in every dimension from three up; Terence Tao published an analysis two days later, and the two-variable case remains open.

See it in the living treeWikipediaSource