OpenAI has published 722 mathematical papers produced by an unnamed internal model, organized on GitHub into 372 families spanning number theory, theoretical computer science, geometry, and mathematical physics. The claimed results include a proof of the rational Hodge conjecture for abelian varieties with complex multiplication, Kaplansky’s direct finiteness conjecture in characteristic two, and a new bound on the irrationality exponent of π. None of the papers has been peer-reviewed or independently verified, and OpenAI states that about 4,000 problems were drawn from an internal evaluation set that was expanded once existing math benchmarks stopped separating models, with each result consuming compute equivalent to roughly three hours of ChatGPT Pro in reasoning mode. Formal Lean proofs accompany 162 of the papers (a catalog OpenAI describes as partial and unverified), abridged reasoning traces accompany 10, and the company says it consulted the independent Advisory Group on Mathematics and AI at Princeton’s Institute for Advanced Study on how to release such work.

Sharing AI progress in mathematics · openai/math on GitHub

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