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On Sunday evening, while most of the world was watching the World Cup final, a mathematician at Anthropic posted three polynomials on X and quietly ended an 87-year-old open problem. The Jacobian conjecture — unsolved since 1939, survivor of multiple famous false proofs, one of the problems on Steve Smale’s list for the 21st century — is false. Claude’s Fable 5 found the counterexample.
Here’s the part that made me drop what I was doing: the refutation is not a 600-page manuscript that twelve specialists will spend two years refereeing. It is three lines of algebra. I pasted them into SymPy, and my laptop confirmed the conjecture is dead in 0.1 seconds: the Jacobian determinant is exactly −2 everywhere, and three different input points crash into the same output. That’s the whole disproof. You can run it before your coffee cools.
I’ve spent two days reading the announcement thread, the MathOverflow dissection, and the blog posts mathematicians published within hours. This article covers what the conjecture said, the exact counterexample, the full verification you can run yourself, and why “counterexample hunting” is suddenly the most interesting thing frontier models do.