Anthropic AI Disproves 1939 Jacobian Conjecture
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- Levent Alpöge, a mathematician at Anthropic, disproved the Jacobian conjecture with help from Fable 5 and announced the result unceremoniously in a tweet, including the explicit counterexample polynomial mapping
- The Jacobian conjecture, posed in 1939, asks whether a polynomial mapping with a nonvanishing Jacobian determinant must itself be a polynomial; Alpöge's counterexample shows it does not, settling one of algebraic geometry's central open problems
- Aaron Lou reports that an internal version of OpenAI's Codex, working without web search, independently discovered essentially the same counterexample, corroborating the result from a second AI system
- The conjecture is historically infamous for attracting incorrect proofs — @qiaochuyuan cites a 2008 paper by T.T. Moh debunking prior attempts, framing this resolution as especially notable given that history
- Jared Duker Lichtman and other mathematicians publicly vouched for the counterexample on X, while @nexuist and @vikhyatk's "tweets where decades happen" quip captured the viral reaction across Reddit (r/math, r/singularity), Hacker News, and Lobsters
Why it matters: A conjecture open since 1939 and central to algebraic geometry has been falsified by a counterexample jointly produced by a human mathematician and an AI model — and an independent second AI (Codex) arrived at the same answer without web access. The dual-AI convergence matters because it demonstrates that frontier models can now probe century-old mathematical conjectures well enough to generate novel counterexamples, not just verify proposed ones, reshaping how open math problems may be approached going forward.
