Claude Fable produced a counterexample to the Jacobian Conjecture
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Fable LLM discovered a counterexample to the 85-year-old Jacobian conjecture.
A user named levent posted on X that Claude Fable produced a counterexample to the Jacobian conjecture, a long-standing problem in algebraic geometry. The polynomial map from C^3 to C^3 has a constant Jacobian determinant of -2 but maps three distinct points to the same output, proving it is not injective and thus not invertible. The post includes links to WolframAlpha verification. Grok and other users confirmed the result. The discovery implies related conjectures (Dixmier, Poisson) are also false.
What commenters are saying
Commenters confirmed the Jacobian conjecture states that a polynomial map with non-zero constant Jacobian determinant must have a polynomial inverse. The map's non-injectivity (three points mapping to the same output) disproves it. Many expressed surprise the simple counterexample was not found earlier, noting the polynomials are low-degree with small coefficients. Some attributed the discovery to LLMs' ability to brute-force search spaces that academics overlooked. A user verified both conditions in Lean 4. Skepticism was minimal, with most acknowledging the finding's validity.