OpenAI just dropped 700 preprints of mathematical proofs and counterexamples

A public GitHub repository collects roughly 700 preprints released by OpenAI presenting mathematical proofs, constructions and counterexamples across a wide range of fields. The entries are organized by title and date and read like a catalog of technical manuscripts: many announce resolutions of long-standing conjectures, explicit counterexamples to famous problems, new algorithmic results, and advances in geometry, topology, analysis, combinatorics and mathematical physics. The list includes dozens of high-profile-sounding items such as counterexamples to Kaplansky-style conjectures (direct finiteness and quasitrace variants), a counterexample to Kurosh’s division-ring problem, a counterexample to Naimark’s problem in ZFC, a direct proof of optimal Max‑Cut hardness, a fully-polynomial randomized approximation scheme for perfect matchings, a nearly‑quartic separation between randomized and quantum query complexity, and algorithmic advances like low‑space subset-sum and a 2‑approximation for shortest common superstring.

The corpus also contains specialized geometric and analytic results - reductions of the Penrose inequality, Ricci‑flow constructions with finite‑time curvature blowup, manifold counterexamples and singular-set bounds - plus physics-related spectral-gap claims and percolation amplitudes derived from conformal formulas. Titles are technically specific and cover both constructive proofs and negative counterexamples, amounting to a broad, ambitious collection of purported breakthroughs and refutations for experts to examine in detail.