OpenAI publishes 722 math manuscripts from an unreleased internal frontier model on GitHub, claiming results on the quasi-Riemann hypothesis, the Hodge conjecture for CM abelian varieties and more

OpenAI's post "Sharing AI progress in mathematics" (https://openai.com/index/sharing-ai-progress-in-mathematics/) releases a broad set of results from an unreleased internal frontier model in the Apache-2.0 repository https://github.com/openai/math. Because existing math evals saturated, OpenAI posed roughly 4,000 open research problems; after grouping and a significance bar, the catalogue holds 722 manuscripts in 372 result families, averaging about three hours of ChatGPT Pro thinking compute per result. Headline claims include a zero-free half-plane Re s > 7/8 for all Dirichlet L-functions including zeta (family 003, branded the quasi-Riemann hypothesis, with an alternate 11/12 proof), the rational Hodge conjecture for CM abelian varieties (family 032), the irrationality exponent of pi equal to 2, both Mahler conjectures, and isomorphism of the free group factors. The zeta zero-free region and Hodge CM work fall outside the fixed procedure, and the 11/12 write-up was human-edited. 235 of 372 families link to Lean, the formalization catalogue lists 162 papers with a formalized main result, and challenges can be checked with leanprover/comparator. Ten abridged reasoning summaries are included, plus revision and citation protocols developed with advice from the IAS Advisory Group on Mathematics and AI. OpenAI cautions that some unformalized results could have issues; none is peer reviewed, and the model itself is not yet released. OpenAI will also fund workshops and programs on AI-produced results.