The Association for Human Mathematics (AHM) has urged mathematicians to stop working with OpenAI after the company released a large collection of AI-generated mathematics on October 6. In its October 7 statement, the group's central objection is to using a private model to tackle advanced open problems and releasing hundreds of resulting papers at once. It disputes OpenAI's claim that this publication model advances mathematics, even as the public files make individual claims available for scrutiny.

That is a position taken by AHM's Communications Working Group. It is neither a vote of the mathematical community nor a finding that every manuscript is wrong. Terence Tao reposted the text as an AHM guest statement, identifying its authorship rather than adopting it as his own statement.

The big change

  • What changed: The argument over OpenAI's repository now reaches beyond the validity of individual results. AHM challenges the company's role in choosing research problems and setting the terms on which mathematicians receive the output.
  • Why it matters: The dispute concerns who can examine the generating tool and who bears the work of checking and explaining a mass release. Those questions remain even when a particular proof is repaired or formalized.
  • What to watch: OpenAI says it will add formalizations. Independent assessment of revised claims, and any further versioned corrections, will clarify which specific results mathematicians can verify and understand.

What AHM is objecting to

AHM says mathematicians did not request the work. It calls the release of more than 700 files a display of power rather than scholarship, and asks readers to be skeptical of its value to the field. The statement also cites the independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI), saying OpenAI disregarded that group's opening request to stop testing advanced mathematics on internal models.

That reference has a clear basis. AGMAI's September 29 guidelines say frontier labs should stop testing advanced problems on proprietary models. The same document then gives conditional recommendations for releasing results if labs have already produced them: clear mathematical writing, appropriate repositories, disclosure of how the work was generated, formalization where possible, and support for human understanding. It says its recommendations drew on more than 600 survey responses and had the support of a plurality of respondents. Those facts do not turn AHM's subsequent call to stop working with OpenAI into an AGMAI directive or a field-wide decision.

In its October 6 response to the release, AGMAI explicitly said its advisory role did not endorse OpenAI's process or judge the impact of the results. It described publication as the beginning of human assessment, while saying only the mathematical community can determine how successfully its recommendations were followed. OpenAI had previously described the group as independent and said it would advise on review and communication, while not controlling the pace of the company's internal research. The difference between advice and authority matters here: AHM's criticism is a challenge to OpenAI's choices, not evidence that an outside board approved or vetoed them.

A changing record is still a record to check

OpenAI's repository says the collection contains work at different stages of verification. Its current catalogue lists 719 manuscripts in 372 families. A family can include multiple papers. The repository says some manuscripts lack Lean formalizations and some unformalized results may have issues; it reports that about 42% of top-line results are formalized. A formalization is a specified machine-checkable argument for a specified statement, not blanket confirmation of every claim in a surrounding paper, and a repository's status is not a substitute for independent mathematical review. Our earlier walkthrough of the files and proof configurations explains how to trace that scope.

The count has changed because three manuscripts were withdrawn. OpenAI's October 7 history entry attributes the withdrawals to a sign error in one proof that also affected two dependent papers. The entry records revisions to 14 other manuscripts, reference updates in 13 more and six additional formalizations. Our report on the three withdrawal notices explains the narrower conclusion: the identified arguments no longer establish those papers' claims; the notices do not disprove the mathematical statements. A withdrawn proof, a repaired manuscript and a formalized result are different statuses.

The revisions illustrate the review work that a large, unevenly formalized collection can require. That is our analysis of the repository record, not a claim made in AHM's statement. AHM opposes the decision to generate and release the collection through a proprietary model. OpenAI, meanwhile, has provided versioned material that researchers can inspect, correct and debate. Our earlier analysis of review capacity addressed the labor required to turn a large set of proposed results into understood mathematics. The present dispute adds a sharper question: whether producing that volume of work in this way serves the people expected to evaluate it.

Sources & further reading