OpenAI releases 722 math manuscripts, claiming proofs of Hilbert's tenth problem, BSD, and more
OpenAI has published a collection of 722 mathematical manuscripts covering 372 result families. The papers claim proofs of major open problems, including a negative resolution of Hilbert's tenth problem over the rationals, the full Birch–Swinnerton-Dyer formula for many elliptic curves, the quasi-Riemann hypothesis, irrationality of Catalan's constant, and the Deligne–Drinfeld conjecture. The repository includes an overview PDF and links to individual preprints, with some results formalized in Lean.
We give a negative answer to Hilbert's tenth problem over the rational numbers: no algorithm decides whether a polynomial with integer coefficients has a rational zero.