OpenAI's AI Models Solve Over 100 Longstanding Mathematical Problems

OpenAI convened around 40 mathematicians in August to discuss a remarkable development: the company's experimental AI models have solved hundreds of longstanding open problems in mathematics, a breakthrough that signals rapid progress in artificial intelligence reasoning capabilities while raising questions about verification and human understanding of the results. The Astra model, unveiled on August 1, generated machine-verifiable proofs for 10 major unsolved problems spanning group theory, quantum complexity, lattice cryptography, and extremal combinatorics. Notably, Astra disproved Connes's rigidity conjecture on von Neumann algebras, proved Ehrhart's volume conjecture, and resolved three Erdős problems—including problem 183 on multicolor Ramsey numbers—at a computational cost of roughly $2,000. More strikingly, an internal OpenAI model trained beginning August 28 reportedly resolved more than 100 open problems across most areas of mathematics within just 24 days, according to people who attended the August meeting.