Mathematicians vs the labs

As of 12 October the catalogue has its first retractions and the discipline has its first call for non-cooperation. OpenAI's revision log entry of October 7 withdrew three manuscripts, stating that in one "a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers". The same entry revised 14 others "with proof repairs, corrected statements, clearer hypotheses and dependencies", updated 13 more to cite revised companion papers, and recorded that "This brings the total percentage of top-line results formalized to 300 / 719 = ~42%." The README now reads "The current catalogue contains 719 manuscripts organized into 372 families", where the release was reported as 722. An OpenAI spokesperson told Retraction Watch: "Where errors are identified, we will work to correct them promptly and withdraw papers if no fixes can be found." Cornell's Alex Townsend told Retraction Watch he suspects more errors will be found, and said the Lean-verified manuscripts ought to have been announced first. The log has no entry dated later in the week.

The Association for Human Mathematics Communications Working Group, in a statement dated October 7 reposted as a guest post on Terence Tao's blog, wrote that "Mathematicians did not ask for this work to be done" and that "Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power. We urge mathematicians to discontinue their work with OpenAI and to return to a vision of science that centers human understanding." It named "The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy", and noted that OpenAI "is currently defending lawsuits against accusations of illegal plagiarism, copyright infringement, and trademark dilution". TechCrunch reported that "Just 10 of the 719 manuscripts included releases of the model's chain of thought" and that the advisory group's request for machine-readable metadata correlating the natural language and formal artifacts was "something that the frontier lab did not do with these releases". The statement carries no signatory count and records no OpenAI response.

The week's other mathematical results put the proof assistant first. Science issued "Advancing mathematics research with AI-driven formal proof search" by George Tsoukalas and 20 co-authors, volume 394 issue 6820 pages 234-239, reporting an agent that "autonomously resolved nine of 353 open Erdős problems, proved 44/492 On-Line Encyclopedia of Integer Sequences conjectures", and that "Even a basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes." SqueezeBench, from TU Wien, checks every submitted record with "two independent Lean kernels, so no referee needs to check the mathematics", and reports frontier-model agents improving every one of its twenty initial records with 82 accepted submissions, while noting that "For eight of the ten problems, at least one record is still asymptotically behind the best published bound." A separate preprint, arXiv:2610.08144, reported that the Lean proof of OpenAI's announced Navier-Stokes blow-up "does not correspond to the NL proof", while stating: "We do not make claims about the correctness of OpenAI's NL proof, we only make statements about mistranslations into Lean." No lab has published an adoption statement for the advisory group's norms.

As of this week the mathematicians have written the rules they want the labs to follow, and the Mathathon they objected to is going ahead without lab money. The Advisory Group on Mathematics and Artificial Intelligence published "Responsible Release of AI-Generated Mathematics" in late September, drawing on over 600 community replies. Its central rule is that "If AI labs produce significant mathematical results, they should responsibly release the results, as outlined in this document, as soon as possible", paired with the obligation that "AI labs that release substantial mathematical output without immediate accompanying human understanding must take responsibility for ensuring that human understanding will follow". On benchmarking against proprietary models the document states: "we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models."

The Mathathon question this storyline tracked has been answered. A joint statement published by the original student organisers, the open-letter coauthors and other members of the Caltech community set the redesigned event for 13 to 15 November 2026 under the theme "Old Problems, New Proofs", co-organised with the Foundation for Science and AI Research and with XTX Markets as lead donor. Proprietary models are permitted but open-source tools encouraged, and full disclosure and justification of model usage is required, with an explainer and a repository per submission.

On the labs' side the claims kept coming and the verification arrangements did not change. Meta published six mathematics papers written with its own model and said five of them answer previously open research questions, marking which passages were drafted by researchers and which by the model, and acknowledging a separate AI agent that reported a different counterexample to the same conjecture weeks earlier. Anthropic published a guest post describing manuscripts across many fields produced with Claude. Nothing is peer reviewed, no lab has published an adoption statement for the advisory group's norms, and the group's own framing is that it is still advising one lab on how to coordinate the release of results it has claimed.

As of 28 September one lab claim has been checked by a named outside expert and the rest have not. Anthropic published a guest post reporting that Claude computed the six-particle hexagon amplitude in planar N=4 super Yang-Mills at nine loops, past the eight-loop record, by two independent routes. Lance Dixon of SLAC and Stanford, who set the eight-loop record, validated it; the disclosure states that he validated the result independently and received Claude usage credits, and that Anthropic invited and compensated the author. The author's own conclusion is that the model did something humans turned out to be able to do as well, using known methods with more compute than people had tried, and the post reports that a group led by Song He at the Chinese Academy of Sciences obtained the majority of the same result concurrently with GPT-6 assistance. Nothing is peer reviewed and the human teams have yet to publish.

On the labs' side of the dispute the reporting norms moved slightly. OpenAI announced an Advisory Group on Mathematics and Artificial Intelligence hosted at the Institute for Advanced Study, with nine unpaid initial members who control their own membership and may go public with their views, and said in the same announcement that an internal model has resolved more than 100 additional open problems across most areas of mathematics. No independent verification of that count is reported, the problems are not listed, and the blog post states that the group will not be responsible for advising the company on how to pace its internal progress on mathematics. Only one member of the group signed the open letter that 25 Fields Medallists signed earlier in September. The Mathathon's sponsorship remains unresolved in the record and no lab has adopted the declaration's write-up norms.

As of 21 September the mathematicians have started building rather than only objecting. Terence Tao wrote that he co-founded the Foundation for Science and AI Research with private donors to support responsible uses of AI in mathematics and the other sciences, "independent of the major AI companies", and that the foundation is announcing an Open Math Model initiative with open licensed weights and code, published training methods, reproducible evaluations, documented training-data sources and releases that report failures and limitations alongside successes. The announcement says the planned gradual rollout was brought forward: "given current events and the high demand for open models, we are accelerating our schedule". No partners, compute commitments or model sizes are named, and the foundation is collecting expressions of interest.

The measurement of AI use in the field moved at the same time. Epoch AI, in an analysis updated on September 18, reports that the share of mathematics preprints on arXiv acknowledging AI rose from 4% in April to 25% in August, and that in August 6% of all papers explicitly acknowledged that AI made a substantial research contribution. Restricting to papers with at least one author who published regularly before 2023 keeps the acknowledgment rate within 1.5 percentage points of the overall figure each month. Epoch says it analysed every mathematics arXiv preprint from January 2025 to August 2026, classifying acknowledgments with one frontier model and validating with another; a human review of 200 random acknowledgments classified as substantial research or research assistance showed 93% agreement. The measure depends on voluntary disclosure. No lab has adopted the declaration's write-up norms, and the Mathathon's sponsorship remains unresolved in the record.

As of 14 September the two sides are talking past each other. Twenty-five Fields Medallists signed a declaration, published on Terence Tao's blog on 11 September, that AI labs' benchmark chasing is "severely misaligned" with mathematics; OpenAI pulled its $10,000-per-team sponsorship of Caltech's Mathathon after an open letter from Caltech mathematicians. The same week, an NVIDIA team reported an open Nemotron pipeline scoring 30 of 42 at IMO 2026 with no formal prover or tools, and the Magenta pipeline reported 100% on AIME 2025, AIME 2026 and HMMT February 2026 with Lean-checked proofs.