A compact formula in three dimensions with a Jacobian determinant equal to -2 has toppled the 87-year-old Jacobian conjecture, a long-standing open problem in algebraic geometry. Levent Alpöge, a mathematician at Anthropic, shared the counterexample almost offhandedly on X while much of the world was winding down from the FIFA World Cup Final. The tool behind the find was Claude Fable 5, Anthropic's large language model, which had been publicly available for just a few weeks. The Jacobian conjecture concerns polynomial functions that shuffle points in space; when the Jacobian determinant is always a non-zero constant, the conjecture asserts there must exist another polynomial function that reverses the first one. The two-dimensional version was first stated in 1884 by Czech mathematician Ludwig Kraus, and German mathematician Ott-Heinrich Keller extended it to arbitrarily many dimensions in 1939. Fields Medallist Stephen Smale included it on his 1998 list of Mathematical Problems for the Next Century. Proofs announced over the decades, including attempts by Beniamino Segre and Wolfgang Gröbner, each collapsed due to subtle flaws. Computational efforts verified the conjecture holds in two dimensions for polynomials up to degree 100, but the general case remained unresolved. Everyone knew a short counterexample might exist, as writing down functions that merge points is simple enough, as is writing down polynomial mappings whose Jacobian determinant is constant.