Timeline
- 8.5
OpenAI Releases 722 AI Math Manuscripts in One Batch; the Math Community Begins Verification
OpenAI has published a batch of 722 mathematics manuscripts produced by an unreleased internal frontier model, drawn from an evaluation over roughly 4,000 open research problems; many manuscripts revolve around the same core result and, when merged, correspond to 372 interrelated result families. Several directly address long-standing open problems: a proof of the Unique Games conjecture, a so-called "quasi-Riemann hypothesis" stating that the Riemann zeta function has no zeros in the region where the real part exceeds 7/8, the rational Hodge conjecture for CM abelian varieties, and the free group factor problem unsolved since the 1940s. The release extends a run of AI-driven results that have both impressed and unsettled parts of the mathematical community, and it puts long-standing open problems in front of mathematicians for review. OpenAI says verification levels differ across the results, and the independent mathematical advisory group AGMAI that consulted on the release explicitly stated it does not endorse them, so the outcomes are not settled conclusions. The manuscripts come from an evaluation of about 4,000 open research problems and were produced by an unreleased internal frontier model. Lean formalized proofs, which can be checked mechanically by computer, have been attached to the Unique Games, quasi-Riemann and free group factor results, while OpenAI says the non-formalized portions may still contain errors.
- 9.0
Sharing AI Progress in Mathematics
OpenAI published a public GitHub repository (openai/math) containing mathematical manuscripts and supporting proof artifacts, including Lean proof formalizations, produced by an internal OpenAI model. The material covers long-standing open problems such as Barnette's Conjecture and the Unique Games Conjecture. Hacker News commenters framed the release as significant: one wrote that the Unique Games Conjecture is "a seminal conjecture in Complexity Theory" and an underlying assumption for many inapproximability results, calling a valid proof "a big deal". Another commenter said he had spent considerable time attacking Barnette's Conjecture with state-of-the-art models a few months earlier and failed. One commenter, citing proofatlas.ai, said the list claims to fully solve 90 of the top 500 open problems in mathematics, with the highest-ranked among them listed as Hilbert's tenth problem over ℚ, Unique Games, Anderson-model extended states, the spacetime Penrose inequality and the nonexistence of Landau–Siegel zeros. Another commenter highlighted a polynomial-time algorithm for three-machine unit-job scheduling, an open problem since Garey and Johnson's 1979 book. These specifics come from the discussion and are not independent verification of the proofs.