On 6 October, OpenAI published 722 mathematical manuscripts in a public GitHub repository, according to Retraction Watch. By 7 October, three of them had been withdrawn. The sequence is a useful early test of what it means to publish AI-generated mathematics at volume, and of what "released" does and doesn't tell you.

What was published

The repository, openai/math, is released under an Apache-2.0 licence. Its README describes the contents as manuscripts and supporting proof artefacts produced by an internal OpenAI model. The README says OpenAI evaluates its models on open research problems as part of development, and expanded those evaluations after performance on its existing mathematical tests saturated.

The collection is grouped into families of related papers. The README's current count is 719 manuscripts in 372 families, the figure after the withdrawals described below.

The README gives a few details of the method:

  • Most results came from the same procedure, run with what it calls an unreleased internal OpenAI model. The README doesn't name the model.
  • On average, each result used three hours of ChatGPT Pro thinking compute.
  • The model was posed approximately 4,000 problems.
  • The README names two exceptions to that fixed procedure: a zero-free region for the Riemann zeta function, and a proof of the Hodge Conjecture for CM abelian varieties.
  • The write-up of the Re(s) > 11/12 zero-free region was human edited for readability.
  • OpenAI also released abridged summaries of the model's reasoning for ten result families.

These are OpenAI's own descriptions of its own work. The README itself says the collection includes results at different stages of verification, that not all have formalisations in Lean, a programming language in which a computer checks each step of a proof, and: "Some of the unformalized results could have issues."

The withdrawal

The repository's history file records the 7 October changes. Of the paper "Algebraicity of Weil classes on split abelian eightfolds", the history file says: "a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers."

OpenAI withdrew all three manuscripts:

  • Algebraicity of Weil classes on split abelian eightfolds
  • Algebraicity of Kuga–Satake Correspondences for K3 Surfaces
  • The rational Hodge conjecture for products of K3 surfaces

The history file says the withdrawn papers now carry notices explaining the gap and linking to the archived manuscripts. It also records that OpenAI revised 14 other manuscripts, with changes ranging from repaired arguments and corrected statements to the removal of one obsolete citation. Thirteen further manuscripts were updated to cite the revised editions of companion papers.

Retraction Watch and Scientific American describe how the error surfaced in different terms. An OpenAI spokesperson told Retraction Watch the company identified the errors during an audit. Scientific American wrote that the papers were withdrawn "after experts uncovered a significant error".

How much is machine-checked

The headline figure for Lean comes from OpenAI. Its history file says that six additional formalisations, plus five other additions covering supporting results, brought the total to 300 of 719 top-line results, about 42 per cent. The README repeats "~42% top-line results formalized".

That leaves more than half the results without a Lean formalisation. Scientific American reported that the withdrawals led some to question the more than half of the proofs that aren't yet Lean-verified. The magazine also noted that, because a Lean-coded result's logic is "almost certainly sound", some papers whose English write-ups are hard to follow may still be correct.

The question of what to publish unverified has an advisory-group angle. According to Unite.AI, OpenAI said it has been consulting the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study. Unite.AI also reported that the group published its responsible-release recommendations on 29 September, and that they call on labs to make public, for each released result, the model name, the prompts, a summarised chain of thought, the time taken and the estimated compute cost. An OpenAI spokesperson told Retraction Watch that the group recommended releasing results without waiting for "full formalization", and that roughly half the results were released unconfirmed. The spokesperson added that OpenAI hoped to learn from feedback and work with the group "to understand if they have updated recommendations for release protocol moving forward".

What mathematicians said

Reaction, as reported in the first days, was mixed.

Alex Townsend, an associate professor of mathematics at Cornell University, told Retraction Watch that an error cascading through three manuscripts was not surprising, and that he suspected more would be found. His view on sequencing: "Given the skepticism of AI in the mathematics community, I think that OpenAI should have announced the manuscripts that were lean verified first."

Andrew Sutherland of MIT called the quick withdrawal "the responsible thing to do". Sutherland also told Retraction Watch: "I think the withdrawals and corrections will be viewed positively by the mathematics community, but it will take a lot more than that to earn back the trust they have lost." Speaking to Scientific American, he said: "While I expect most of these will ultimately be found to be correct, or at least correctable, we should expect some of the proofs to contain mistakes, possibly serious ones." AI Weekly quoted him on the method claims: "Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified."

Daniel Litt of the University of Toronto, quoted by AI Weekly, said: "If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us."

Others were more positive about the scale. Harvard's Michael Douglas told Scientific American: "Yesterday will be the day when a new era of math and mathematical physics began." The same piece found quality uneven. Roland Bauerschmidt of New York University said of some papers, "they're sort of this AI slop", while Hector Pasten of the Pontifical Catholic University of Chile said the papers he had looked at gave credit better than the company's earlier work.

The Association for Human Mathematics was more outspoken in its criticism. Scientific American quotes its statement: "Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power." Retraction Watch dates that statement 7 October.

OpenAI's response

An OpenAI spokesperson told Retraction Watch: "We welcome scrutiny and feedback from the mathematical community." The company said it would correct errors promptly and withdraw papers if no fixes could be found. Dan Roberts, a research lead at OpenAI, wrote on X that OpenAI will "continue to update the repo with new formalizations and with any errata we notice", according to Retraction Watch.

Where that leaves the claims

On the evidence in these reports, what is established is narrow. OpenAI published a large body of manuscripts, withdrew three after an error in one invalidated two that depended on it, revised others, and says about 42 per cent of its top-line results have Lean formalisations. Two days after the release, Scientific American wrote that scientists were "just beginning to parse through the heap". The README's own caution is the plainest summary: some of the unformalised results could have issues.

Sources

Dufresne, A. (2026) 'OpenAI Pulls Three AI-Generated Math Papers Over Sign Error', AI Weekly, 8 October 2026, available at: https://aiweekly.co/alerts/openai-pulls-three-ai-generated-math-papers-over-sign-error (Accessed: 21 October 2026).

Howlett, J. (2026) 'Mathematicians marvel, and grumble, at OpenAI's trove of new results', Scientific American, 8 October 2026, available at: https://www.scientificamerican.com/article/mathematicians-marvel-and-grumble-at-openais-trove-of-new-results/ (Accessed: 21 October 2026).

OpenAI (2026) 'history.md', openai/math repository, GitHub, entry of 7 October 2026, available at: https://raw.githubusercontent.com/openai/math/main/history.md (Accessed: 21 October 2026).

OpenAI (2026) 'README', openai/math repository, GitHub, available at: https://github.com/openai/math/blob/main/README.md (Accessed: 21 October 2026).

Reeve, J. [AI research agent byline] (2026) 'OpenAI Releases 722 Math Manuscripts From an Unreleased AI Model', Unite.AI, 6 October 2026, available at: https://www.unite.ai/openai-releases-722-math-manuscripts-from-an-unreleased-ai-model/ (Accessed: 21 October 2026).

Retraction Watch (2026) 'OpenAI withdraws three preprints a day after releasing 722 manuscripts on unsolved math problems', Retraction Watch, 8 October 2026, available at: https://retractionwatch.com/2026/10/08/openai-withdraws-preprints-722-manuscripts-unsolved-math-problems/ (Accessed: 21 October 2026).

Picture credits

  • Top picture. Institute for Advanced Study Campus, photo by Hanno Rein (CC BY-SA 3.0) (source)