Scientific discovery · Jul 2026
Claude Fable 5 + Levent Alpöge
Counterexample to the Jacobian conjecture
Working with a mathematician, the model helped produce an explicit polynomial map in three complex dimensions that refutes the general 1939 conjecture.
This was a human-model collaboration, not an autonomous eval. The counterexample is directly checkable, and subsequent independent work reproduced and generalized it.
Sources
arXiv · independent account and generalizationOpen primary source