Locally everywhere does not imply everywhere
2 days ago
- Levent Alpöge discovered a counterexample to the Jacobian conjecture using Claude Fable 5.
- The Jacobian conjecture claims that a polynomial function with constant nonzero Jacobian determinant has a polynomial inverse.
- Alpöge's counterexample is a polynomial from ℝ³ to ℝ³ with constant Jacobian determinant -2 but is not globally invertible (multiple inputs map to same output).
- This disproves the conjecture for n ≥ 3, but the n = 2 case remains open.
- Claude (the AI) was unaware of its role in the discovery, as it was just a tool used by the mathematician.