Jacobian Conjecture claimed disproved | Anthropic researcher says Claude Fable found counterexample during World Cup final
TL;DR
Anthropic researcher Levent Alpoge posted a claimed counterexample to the Jacobian Conjecture on X — an 87-year-old problem from 1939 — crediting Claude Fable for computations during the World Cup final. The C³ map has determinant -2 everywhere yet sends three distinct points to the same image.
Anthropic researcher Levent Alpoge announced on X that the Jacobian Conjecture — a 1939 problem open for 87 years — has been disproved by a counterexample, thanks to his friend Akhil for the question and his AI friend Claude Fable for grinding through the math during the World Cup final. The conjecture states that any polynomial map ℂⁿ→ℂⁿ with a nonzero constant Jacobian determinant must have a polynomial inverse.
Alpoge's counterexample is a C³ map with Jacobian determinant identically -2 (nonzero everywhere) that nonetheless sends the three distinct points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to the same image (-1/4, 0, 0) — injectivity fails, so no polynomial inverse exists. He attached a WolframAlpha verification link. The top Hacker News thread is now full of mathematicians pressing for construction details.
Until peer review closes out, the conjecture is still open in the official record and frontier models remain draft tools, not Fields Medal committees. But an 87-year-old open problem casually knocked over while watching a World Cup final is the most surreal footnote of 2026.
via Officechai / Hacker News
Alpoge's counterexample is a C³ map with Jacobian determinant identically -2 (nonzero everywhere) that nonetheless sends the three distinct points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to the same image (-1/4, 0, 0) — injectivity fails, so no polynomial inverse exists. He attached a WolframAlpha verification link. The top Hacker News thread is now full of mathematicians pressing for construction details.
Until peer review closes out, the conjecture is still open in the official record and frontier models remain draft tools, not Fields Medal committees. But an 87-year-old open problem casually knocked over while watching a World Cup final is the most surreal footnote of 2026.
via Officechai / Hacker News
