Claude Fable helps disprove the 87-year-old Jacobian Conjecture with a 3D counterexample
AccBalanced · x · 2026-07-21
Anthropic mathematician Levent Alpöge says Claude Fable helped him find a concrete 3D counterexample to the 87-year-old Jacobian Conjecture. - The conjecture, proposed in 1939, states that any polynomial map with a constant non-zero Jacobian determinant should have a polynomial inverse. - Alpöge posted the counterexample on July 19; independent symbolic checks by multiple mathematicians reportedly confirmed it within hours. - The contradiction is straightforward: the map has constant Jacobian determinant \-2, yet it sends three distinct inputs to the same output, so it cannot be invertible. - The post also notes the conjecture has fooled serious mathematicians for decades.
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