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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