openai/math repository README: 722 manuscripts in 372 families, ~4,000 problems, ~3h Pro compute each

README as read on 2026-10-07 (Apache-2.0; ~4.2k stars at the time):

• "722 manuscripts organized into 372 families", grouped by discipline; overview.pdf, CONTENTS.md, preprints/, a Lean library with formalization.yaml and Comparator instructions.
• Produced by "an unreleased internal OpenAI model" as part of evaluating models on open research problems, after "performance on our existing mathematical evaluations saturated".
• "On average, each result used three hours of ChatGPT Pro thinking compute"; "the model was posed approximately 4,000 problems."
• Caveats: "Not all have accompanying Lean formalizations." "Some of the unformalized results could have issues." Corrections will be released as new versions; earlier versions stay accessible.
• Exceptions to the fixed procedure: "work on a zero-free region for the Riemann zeta function and proof of the Hodge Conjecture for CM abelian varieties"; the writeup for the Re(s) > 11/12 zero-free region "was human edited for readability".
• Reasoning summaries for 10 families: 007 two-point correlations of multiplicative functions, 017 irrationality exponent of π, 087 Mahler conjectures, 102 NP-hardness at the basic SDP threshold (the Unique Games family), 159 quasipolynomial bounds for arithmetic progressions, 197 Kaplansky direct-finiteness in characteristic 2, 221 Mézard–Parisi formula, 271 spontaneous magnetization in the quantum Heisenberg ferromagnet, 287 isomorphism of free group factors, 362 3D relativistic Vlasov–Maxwell.

Note on the zeta result (CONTENTS.md, family 003): the principal paper (dated Sept 30) claims zero-freeness of ζ and all Dirichlet L-functions for Re s > 7/8 (Lean-formalized). A companion paper (dated Oct 5) gives a different proof for Re s > 11/12 and is the human-edited one. The same family includes "Uniform exclusion of Landau–Siegel zeros".

(pending: to be filled by npm run fetch-posts; views quoted above are from fxtwitter on 2026-10-07 around 05:20 UTC)