OpenAI published 722 mathematical manuscripts on GitHub on October 6, grouped into 372 families of related results. Produced by an unreleased internal model, the collection spans open research problems across mathematics. The papers are at different stages of verification, so the total should not be read as 722 independently confirmed breakthroughs. OpenAI Math: Manuscripts and Proof Artifacts

The company says its model was tested on approximately 4,000 problems, with each result using roughly three hours of ChatGPT Pro thinking compute on average. Some prominent results followed different procedures. The figure describes a compute equivalent for an internal model, rather than a guarantee that current ChatGPT subscribers can reproduce the work. How the Results Were Produced

The catalogue includes claimed advances on the quasi-Riemann hypothesis, a matrix multiplication exponent of at most 9/4 over the complex numbers, and Hilbert’s tenth problem over the rationals. It also lists Hodge conjecture results for specific classes of mathematical objects. These claims have defined limits: they do not establish the full Riemann hypothesis or resolve the Hodge conjecture in general. OpenAI Mathematics Results Catalogue

OpenAI has shared Lean formalizations for many proofs, enabling computer checking, while acknowledging that some unformalized results could contain issues. It plans to add more formalizations and record corrections through versioned updates. Publication gives researchers access to examine the work; it does not establish that every claim has passed independent review. OpenAI Math: Verification Status and Revisions

OpenAI has consulted an independent mathematics and AI advisory group and plans to fund workshops around AI-generated results. If the major claims withstand scrutiny, the release could expand AI’s contribution to mathematical discovery. Its lasting value will depend on what researchers can verify, understand and build upon. Sharing AI Progress in Mathematics — OpenAI

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