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The openai/math repository collects mathematical manuscripts and supporting proof artifacts produced by an unnamed, unreleased internal OpenAI model. OpenAI says it expanded its evaluations on open research problems after its existing math evaluations saturated. The catalogue currently holds 721 manuscripts in 373 families, each classified by mathematical discipline. Creator coverage cites 719 manuscripts at an earlier point, with highlights such as partial Riemann hypothesis results and progress on Hilbert's 10th problem over the rationals.
Most results came from one fixed procedure: the model was posed about 4,000 problems, and each result used on average three hours of ChatGPT Pro thinking compute. Outputs were then grouped into families and filtered for significance. Exceptions include work on a zero-free region for the Riemann zeta function and a Hodge Conjecture proof for CM abelian varieties. The Re(s) > 11/12 zero-free region writeup was human edited for readability.
Verification is uneven. Not all manuscripts have Lean formalizations, and about 42% of top-line results are formalized. OpenAI warns that some unformalized results could have issues and describes the manuscripts as raw research data rather than polished papers. The repository also includes an overview PDF, a manuscript map, and abridged reasoning summaries for ten results. The model itself is not released, so the collection is a set of artifacts to read and check, not a tool to run.
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OpenAI posted 719 manuscripts from an unreleased internal model across about 4,000 attempted problems, about a quarter Lean-verified. Highlights include a partial Riemann hypothesis result, Hilbert's 10th over rationals, a matrix multiplication exponent of 2.25, and Birch–Swinnerton-Dyer progress.
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