OpenAI publishes a catalogue of mathematics results
On 6 October 2026 OpenAI put mathematical manuscripts produced by an internal model in a public GitHub repository, with Lean formalisations of some of them. The repository's first version lists 722 manuscripts in 372 families of results; OpenAI says each result needed on average about three hours of ChatGPT Pro thinking compute. The next day three manuscripts were withdrawn because of a sign error.
Why it matters
OpenAI had shown single results of the model before; now everything is in a catalogue that mathematicians can read, check and cite, with Lean proofs where they exist and an open record of corrections. The first withdrawals show that errors turn up among the unformalised results, as the README warns. Whether the remaining claims hold, no independent check has yet been read.
What OpenAI says on its page. It is publishing a broad range of new mathematical results from an internal frontier model; it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study (see the record on the group's creation) about best practice; it publishes the results in a repository with rules for corrections and citation; it shares Lean formalisations of many proofs; and it has released 10 concise summaries of the model's reasoning, estimates of the compute used in ChatGPT Pro terms and statistics on the number of problems the model attempted. On average each result needed roughly three hours of ChatGPT Pro thinking compute. The company promises to fund workshops, conferences and programmes on making sense of the results and is working on opening access to the model responsibly. What is in the repository. The README of the first commit (6 October, 21:58 UTC) says "722 manuscripts organized into 372 families", that not all have Lean formalisations and that some unformalised results could have issues. The update of 7 October withdrew three manuscripts because of a sign error in a stabilisation-trace cancellation argument ("Algebraicity of Weil classes on split abelian eightfolds" and two dependent papers, on Kuga-Satake correspondences for K3 surfaces and the rational Hodge conjecture for products of K3 surfaces), revised 14 others, and brought the total to 719 with 300 of 719 top-line results formalised, about 42%. The README read on 21 October adds that the model was posed about 4,000 problems and that the write-up of the Re(s) > 11/12 zero-free region for the Riemann zeta function was human edited. CONTENTS.md describes result 003 as a zero-free half-plane Re s > 7/8 for all Dirichlet L-functions, which the authors call the quasi-Riemann hypothesis, with a companion proof for Re s > 11/12. What the record does not claim. The manuscripts were not read here; the descriptions of the results are OpenAI's words about its own texts, and no independent confirmation that they are correct was read here. The number of manuscripts comes from the repository, not from OpenAI's page, which gives no counts.