When AI Splits a Field

On 6 October 2026, OpenAI deposited 722 mathematical manuscripts, covering 372 distinct result families, on a public GitHub repository. The work was generated by an unreleased frontier model averaging roughly three hours of compute per solution, and includes what the company claims is meaningful progress on three of the seven Clay Millennium Prize problems. The result has split the mathematics community: some researchers — notably Dan Litt of the University of Toronto — have welcomed the volume as a windfall of new starting points; others, including Terence Tao of UCLA and a coalition of 24 Fields Medalists, have described the approach as “an assault on mathematics” carried out by an “impossibly well-resourced interloper” with little regard for the discipline’s working norms.

What OpenAI published

The deposit, on 6 October 2026, is the largest single release of mathematical manuscripts by any organisation in the modern era. The repository contains 722 papers organised into 372 “result families” — clusters of related items that fall under a single claimed result. OpenAI has said the work was produced by an internal frontier model, unspecified, that has not been released and is not generally available. On average, the company said, the model took roughly three hours of compute per problem to produce a draft solution; some items took many times that, and a small number were the result of dozens of failed attempts. Of the 372 result families, a substantial minority — OpenAI declined to give a number — are duplicates of items that had already appeared on arXiv or as accepted papers in peer-reviewed journals before October 2026.[1, 2, 3]

The repository is structured unusually. Each paper has a short English-language description and, for many of the families, an accompanying formal Lean proof. For ten selected families the release includes the model “reasoning summary” — an extended natural-language narrative of the model’s search process — the compute budget consumed, and the success rate across multiple attempted re-runs.[1, 9] The lean-proof coverage is the result of a deliberate decision by OpenAI to release the work in a form in which a small program (the Lean kernel) can check that each proof step is a valid inference from the previous one. By the standards of the Lean community this is a strong form of verification; by the standards of the AI mathematics community it is also an incomplete one, because Lean can verify the formal correctness of a proof without verifying that the statement proved is the statement the author intended.[9]

Of the seven Clay Millennium Prize problems — the seven open questions in mathematics that the Clay Mathematics Institute named in 2000 as the most consequential in the field — three receive explicit attention in the 6 October release. OpenAI said it had made “meaningful progress” on the Riemann hypothesis, the Navier–Stokes blowup problem, and the P versus NP problem, but did not claim a complete solution to any of them. The navier-stokes progress is on the same blowup side claimed in the September 2026 announcement that produced the attribution dispute; the Riemann progress is described as a tightening of explicit bounds on the density of zeros on the critical line; the P vs NP progress is described as a conditional non-existence result within a limited complexity class.[1, 3]

The fracture in the discipline

The publication has produced the sharpest public split in the mathematics community in more than a decade. On the celebratory side, Dan Litt, a professor at the University of Toronto who works in algebraic geometry, told Fortune that the release was “great for mathematics” and that he had identified several solutions of immediate interest to problems he had been thinking about himself. Other mathematicians who work on asymptotic combinatorial problems have reportedly begun reading the repository in detail and identifying items in their own areas of expertise.[1]

On the critical side, the language has escalated. Fortune‘s coverage reports that several mathematicians, including some who work on combinatorial problems, have described the approach OpenAI is taking as “an assault on mathematics” carried out by an “impossibly well-resourced interloper.” The phrase captures a particular grievance: that the company is committing substantial compute resources to problems over which individual mathematicians have laboured for years, producing proofs whose verification is outsourced back to those same mathematicians, and presenting the result in a format that resembles the academic literature without the underlying working practices of it. The criticism is not that AI can solve mathematical problems. It is that a single company, operating outside the academic incentive structure, is presenting the result of substantial but indiscriminate effort as if it were a series of individual research contributions, and asking the mathematics community to assess it on the community’s own time.[1, 4, 10]

The split has structural features as well as rhetorical ones. On one side is a working group — including Tao, the Association for Human Mathematics, and most of the senior research mathematicians who have publicly commented on the release — that argues the publication should be understood as a marketing product and treated with the corresponding reserve. On the other is a working group — including Litt, several other working mathematicians who have agreed to be quoted on the record, and the contributing group of about two dozen OpenAI researchers credited on the repository — that argues the publication is a legitimate contribution to a public-good problem (it is free to read and cite) and that the community’s response should be to engage with it on its merits.[1, 4]

The split is unlikely to be resolved quickly. The release is large enough that a definitive community-wide audit is months away, and the older Nash-and-Bourbaki tradition of patient, low-throughput individual contribution is unlikely to be replaced by the OpenAI’s high-throughput, compute-bound approach in any direct way. What has changed, as of October 2026, is that both positions are now articulated in print by senior figures, and both have institutional homes: the celebratory position has informal but wide support and the OpenAI research staff; the critical position has the senior leadership of the field through the 24-laureate letter and now the Association for Human Mathematics.[4, 5, 10]

The Navier–Stokes dispute

The most concrete flashpoint in the split, and the one that produced the strongest public accusations, is the Navier–Stokes problem. In September 2026, OpenAI announced that its frontier model had produced a proof that, under certain conditions, the three-dimensional Navier–Stokes equations admit a solution that “blows up” — becomes infinite — in finite time. This is one of the two possible resolutions to the Clay Millennium Prize problem on Navier–Stokes; the other is a proof that no such blowup occurs.[6, 7]

Hours before OpenAI’s announcement, two mathematicians publicly disclosed that they were working on the problem using AI tools, including Claude from Anthropic and Codex powered by GPT-5.6 Sol from OpenAI. Tristan Buckmaster of the Courant Institute at New York University, and Levent Alpöge, a mathematician who works for Anthropic, said that they had been pursuing a line of attack introduced by Diego Córdoba and Luis Martínez-Zoroa, and had made “considerable progress” using the AI tools to push that line of attack forward. The descriptions of the two efforts matched: a similar approach to a closely related part of the blowup question, and a publishable result, but not a complete proof.[1, 6, 7]

The accusation that followed, which Buckmaster laid out in a public statement before OpenAI’s announcement, was that the company had either intentionally or inadvertently fed his and Alpöge’s work-in-progress into its own model. OpenAI denied the allegation. The company said the training data for the frontier model that produced the proof predated the date at which Buckmaster and Alpöge had begun using Codex for Navier–Stokes work, and that the model therefore could not have received any signal about their progress through training. OpenAI also acknowledged, however, that the proof itself had been produced in a sprint that began only after rumours began circulating that Anthropic was on the verge of an announcement; the proof was the work of an unusually large multi-agent system, with up to 10,000 sub-agents working variations of the problem in parallel, coordinated by a central controller. The model had been trying the problem, in OpenAI’s account, for less than a week before the result was produced.[1, 6, 7]

Buckmaster, in response to the 6 October 2026 release, told The New York Times that the new submission made it no clearer whether OpenAI’s model had absorbed his and Alpöge’s work through some channel that he and Alpöge could not identify. The issue is, in the technical sense, unresolved. It is not a question whose answer can be obtained from the papers themselves; it is a question about the provenance of the data on which the model was trained and on the inputs the model received during the period of the sprint. The mathematics community cannot answer it; nor, so far, has any independent audit succeeded in doing so.[1, 7]

The institutional response

The response from the institutional centres of the discipline has been unusually fast. Within weeks of the September announcement, the Institute for Advanced Study in Princeton has agreed to host an independent advisory group on mathematics and AI, and OpenAI has agreed to participate in it on the group’s terms. The Advisory Group on Mathematics and AI (AGMAI) was formed in September 2026. Its members include Edward Witten, the theoretical physicist and Fields medalist; Timothy Gowers, the Cambridge combinatorialist; Terence Tao; and a small but representative group of senior research mathematicians who have agreed to participate on the condition that the group’s recommendations are not subject to OpenAI approval before release.[8, 9]

The recommendations AGMAI has released are concrete. They require, in summary, that any AI-generated mathematical proof released publicly should be in a form that resembles existing academic publication, should disclose which model and which prompt produced it, should disclose the compute budget consumed, and should disclose which related problems the model attempted but failed to solve. They require formal verification by an audited theorem prover for any item presented as a proof of a contested claim; they require that the contribution of the human authors (where applicable) be stated explicitly; and they require that the work be subjected to independent community audit before any claim of priority is acknowledged.[9]

OpenAI has adopted some of these recommendations in the 6 October release. The lean-checked proofs for many of the families are a direct response to the formal-verification requirement. The reasoning summaries and compute disclosures for the ten highlighted families are a direct response to the model-and-prompt and compute requirements. The structure of the repository — papers rather than a single document — is a partial response to the existing-academic-publication requirement. What OpenAI has not done is disclose, for every family, which problems were tried and failed, which it considers an internal matter; nor has it committed to independent community audit before announcing results it considers marketing-relevant, such as the Navier–Stokes announcement.[1, 9] The advisory group, in its initial response to the 6 October release, said only that it “reaffirms its existing recommendations for responsible disclosure” and that “the final assessment is up to the mathematics community.” It declined to endorse or condemn the release, but its refusal to endorse has been read by the critics as a quiet critique.[1, 9]

The institutional response is not only formal. Annals of Mathematics, the leading US journal of record; Inventiones Mathematicae; Acta Mathematica; and the Journal of the American Mathematical Society have between them announced new policies requiring, in essence, the same standards AGMAI has recommended. Papers submitted to these journals that depend on AI-assisted proofs are now required to include a formal-verification transcript and a disclosure of model and compute. Several journals have further required that the contribution of the human authors be stated explicitly when the contribution has been primarily the curation and editorial assembly of an AI output rather than the identification of the key idea.[9]

The Fields Medal letter

The strongest single statement against the OpenAI approach, and the document most cited by the critical side of the split, is a letter signed by 24 past winners of the Fields Medal, organised in the days after the September announcement and reported by Fortune on 15 September 2026. The letter’s principal concern is the relationship between AI-generated proofs and the conceptual contribution that has traditionally justified the credit given to mathematical research. The signatories argue that the credit system of mathematics — authorship, priority, the prize system — is designed for results whose value depends not only on the answer but on the insight that produced the answer. A proof produced by an AI tool, they argue, may carry the same answer but does not necessarily carry the same insight; and the disciplinary economy of mathematics does not have a clean way to handle a result whose authorship is disputed between a model and a curation team of human researchers.[4, 8]

The signatories have declined to call for a ban on AI assistance in mathematics — the letter does not say, for example, that no mathematical statement generated with the help of AI tooling should be acknowledged as a proof — but it has called for a clearer separation of the work of identifying a result from the work of producing a result. The implicit model is that if a model produced a proof and a human author curated and verified it, then the contribution is properly attributed to both. The OpenAI 6 October release does not consistently follow this practice. In most of the 372 result families the lead credit is taken by an OpenAI research team; in some it is shared with an academic collaborator whose original open problem was addressed; in a small number it is attributed to the AI alone. The letter is, in part, a request that this ambiguity be made unambiguous.[4, 8]

The signatories’ practical concern is what the release of indiscriminate compute-driven proofs does to the working conditions of mathematics. A discipline in which any open problem can be attempted by a single team in a single week, with results deposited into a public repository with the company’s brand attached, is not a discipline in which the standard contribution of a single research career looks like a recognisable or valued contribution. The letter is not only about credit; it is about the working conditions in which the next generation of mathematicians will be trained. The signatories’ worry is that those conditions are already changing, in ways whose long-term effects will be felt regardless of whether the current OpenAI leadership decides to continue with the same approach.[4, 8, 10]

The Association for Human Mathematics

The most concrete organisational outcome of the split is the formation of the Association for Human Mathematics, which announced itself in early October 2026 and made its first public statement in response to the OpenAI 6 October release.[5, 10] The association, which describes itself as a working group of about 200 mathematicians from research universities in North America, Europe and Asia, has three stated aims. The first is to maintain and defend the working norms of mathematics against what it calls “the commercialisation of frontier research.” The second is to provide a community-level audit infrastructure for AI-assisted proofs, so that the burden of verification does not fall entirely on individual researchers whose work has already been published. The third is to develop alternatives to the corporate-led model of mathematics research, including publicly funded infrastructures for AI-assisted proof at universities and research institutes.[5, 10]

The association’s statement on the 6 October release is sharper than the AGMAI response. The release, the association says, is “an exercise of power, not scholarship.” It characterises the rapid release of contested material to a public repository as “the antithesis of the working practice of mathematics, which is patient, careful, independent verification before claim.” It urges mathematicians to “stop working with OpenAI” until the company commits to independent community audit before release and accepts the association’s recommendations on disclosure. It also warns the broader research community about the asymmetry of attention: that a flashy claim by a senior figure at a major AI company will always get more public attention than a careful retraction by a research mathematician, and that the asymmetry is now structural.[5, 10]

Whether the association will have a long-term institutional home is unclear. Its membership is concentrated in senior figures with established positions, and the leverage it can bring to bear on AI laboratories is primarily through the withdrawal of collaborative labour. The leverage is real: mathematics is a discipline whose senior participants are scarce and whose contribution is identifiable. If a substantial fraction of the senior research community decides that collaboration with a particular laboratory is no longer worth the political cost, the laboratory loses access to the people on whose cooperation its future work depends. The association’s call for mathematicians to stop working with OpenAI is, in this sense, a call that has actual force.[1, 5, 10]

The association is not unanimous. Some of its members have privately expressed concern that an outright call to break with a leading AI laboratory is too strong, and that a more measured posture of conditional cooperation would be more effective. The association’s leadership has, for the moment, held the line. The dispute within the association is the same dispute the broader mathematics community is having with itself, transposed to the institutional scale.[10]

Math 1.0 ends

The most useful framing of the moment, in summary, is Terence Tao‘s. The 6 October release, Tao wrote in a widely circulated post on the day of the release, marks the end of “Math 1.0” — the centuries-old discipline in which proof and result were produced by individual mathematicians working at human pace on individual problems. “Math 2.0,” Tao wrote, is a discipline in which proofs are produced by AI tools acting on the prompt and verification of human mathematicians, in which many attempts are made in parallel, and in which the role of the human mathematician shifts gradually from the production of proofs to the curation, verification, and integration of AI outputs. The transition is not necessarily hostile to mathematics, but it is not the same discipline.[11, 12]

What the October 2026 episode has made clear is that the discipline has not yet worked out how to handle the transition. The advisory group, the Fields medal letter, the new Association for Human Mathematics, and the AGMAI recommendations are all parts of an attempt to work out how the discipline handles a moment in which the cost of producing mathematical claims has dropped sharply and the cost of verifying them has not. The community is, in real time, building the institutions that it will need to govern the new regime, and the building is contested.[5, 8, 9, 10]

What is not contested, by either side of the split, is that the publication has changed the discipline. The mathematics done in 2027 and after will be done in the shadow of a publicly deposited, almost-immediately-available, AI-generated thousand-paper-a-year release rate; in the shadow of a corporate actor with sufficient compute to attempt any of the open problems of mathematics at any time; in the shadow of a community that has split, not on whether AI can solve mathematical problems, but on whether the way OpenAI is solving them is a contribution to the discipline or a violation of its working norms.[1, 4, 5]

The split is not necessarily a bad outcome. Mathematics has split before — over the legitimacy of computer-assisted proof in the 1970s (the four-colour theorem), over the publication practices of the Bourbaki group in the 1960s, over the axiomatisation of set theory in the early twentieth century. Each time the split has been followed, after some years, by a normalisation that absorbs the new technique and produces a richer discipline. The difference this time is the speed of the new technique’s arrival, and the asymmetry between the speed at which claims can be produced and the speed at which they can be verified. Mathematics 1.0 ended on 6 October 2026, in Tao’s framing. Mathematics 2.0 has not yet begun.[11, 12]

Event / document	Date	Form	Significance
OpenAI announces it has “resolved” Navier–Stokes blowup	Sep 2026	Public announcement, multi-agent system	Followed by Buckmaster–Alpöge accusation of feeding their work to the model; OpenAI denial
24 Fields Medal winners sign public letter	Sep 2026 (reported 15 Sep)	Open letter	Warns that AI-proof “marketing” risks prioritising answers over insight
AGMAI formed at the Institute for Advanced Study, Princeton	Sep 2026	Hosted by IAS; Witten, Gowers, Tao members	Releases disclosure recommendations; OpenAI adopts some in the 6 Oct release
OpenAI 6 October release (ten-proofs repository)	6 Oct 2026	722 papers, 372 result families	Largest single release of mathematical manuscripts in modern era; ~3 hrs compute per solution
Community split intensifies	Oct 2026	Public statements by Litt, Tao, others	“Great for mathematics” vs. “assault on mathematics”
Association for Human Mathematics formed	Early Oct 2026	Working group of ~200 senior mathematicians	Urges mathematicians to break with OpenAI; calls for community audit infrastructure
Top journals require Lean verification + model/compute disclosure	Oct 2026	Editorial policies at Annals, Inventiones, Acta, JAMS	Mirrors AGMAI recommendations; constrains how AI-assisted proofs can be published
Tao post: “the end of Math 1.0”	6 Oct 2026	Personal blog post	Frames the moment as a transition to a discipline in which proofs are produced by AI and curated by humans
Dan Litt quote	Oct 2026	Interview with Fortune	“Great for mathematics”; eager to read solutions in his own subfields
Buckmaster–Alpöge dispute (ongoing)	Sep–Oct 2026	Public accusations and denials	Provoked the 6 Oct advisory responses; not yet resolved
OpenAI adopts partial AGMAI recommendations	6 Oct 2026	Ten summaries + many Lean proofs	Reveals model reasoning, compute, and attempt counts for ten families; declines to disclose failures

References

1. Kahn, Jeremy. “OpenAI publishes solutions to more than 370 outstanding math challenges. The results divide mathematicians but most agree: Math will never be the same.” Fortune, 7 October 2026. https://fortune.com/2026/10/07/openai-math-controversy-solutions-370-outstanding-challenges-published-criticisms-celebration/
2. OpenAI. ten-proofs. Public GitHub repository, 722 manuscripts / 372 result families, released 6 October 2026. https://github.com/openai/ten-proofs
3. “OpenAI says its internal model produced 372 math breakthroughs, nearly all from a single prompt to one AI agent, though some may have taken multiple attempts.” Techmeme summary, 8 October 2026. https://www.techmeme.com/261008/p9
4. Kahn, Jeremy. “Push for AI regulation mounts as talk of AI’s ‘existential risks’ goes mainstream - but Trump resists calls for a slowdown.” Fortune, 15 September 2026. (Primary source for the 24 Fields-medalist letter.) https://fortune.com/2026/09/15/push-for-ai-regulation-mounts-as-talk-of-ais-existential-risks-go-mainstream-but-trump-resists-calls-for-a-slowdown/
5. “The Association for Human Mathematics says OpenAI’s new math documents show power, not scholarship, and urges mathematicians to stop working with the company.” Techmeme summary, 8 October 2026. https://www.techmeme.com/261008/p2
6. Kahn, Jeremy. “OpenAI says it cracked one of math’s grand challenges. But there are troubling questions about how they did it - and what it means for us all.” Fortune, 8 September 2026. (Primary source for the Navier - Stokes sprint, the multi-agent system with up to 10,000 sub-agents, and Buckmaster’s pre-announcement statement.) https://fortune.com/2026/09/08/openai-says-it-cracked-navier-stokes-math-grand-challenge-buckmaster-accusation-cheating-intimidation-tao-lament/
7. “All the drama around AI’s takeover of mathematics.” The Verge, 8 October 2026. (Independent coverage of the AGMAI response, the Buckmaster - Alpöge dispute, and the Tao “Math 1.0 ends” framing.) https://www.theverge.com/ai-artificial-intelligence/1004933/ai-math-openai-breakthrough-solution
8. Witten, Edward; Gowers, Timothy; Tao, Terence; et al. “Open letter from 24 Fields Medalists on AI laboratories and frontier mathematical problems.” September 2026. (As reported in Fortune and The Verge; full text not publicly distributed at the time of this article.)
9. AGMAI (Advisory Group on Mathematics and AI), Institute for Advanced Study, Princeton. “Recommendations for the publication of AI-generated mathematical proofs.” First release September 2026; supplementary statement 6 October 2026. https://www.ias.edu/math/agmai
10. Association for Human Mathematics. “Statement on the OpenAI 6 October 2026 release.” Self-published statement, October 2026.
11. Tao, Terence. “The end of Math 1.0.” What’s new (blog), 6 October 2026. https://terrytao.wordpress.com/2026/10/06/end-of-math-1-0/
12. “오픈AI, 수학계에 폭탄 투하” [OpenAI drops a bomb on the mathematics community.] Fortune Korea (Korean-language summary of the original Fortune English article by Jeremy Kahn), 8 October 2026. https://news.nate.com/view/20261008n28033
13. Córdoba, Diego; Martínez-Zoroa, Luis. “On the blowup of Navier - Stokes singularities: an approach.” Annals of PDE 11(2) (2025), 1 - 40.
14. Buckmaster, Tristan; et al. “AI-assisted proofs in fluid dynamics: a partial regularity result.” arXiv:math.AP/2609.08712, September 2026.
15. Institute for Advanced Study. “Advisory Group on Mathematics and Artificial Intelligence (AGMAI) - Terms of reference and member list.” Princeton, NJ, September 2026. https://www.ias.edu/math/agmai-terms
16. OpenAI. “Early science acceleration experiments with GPT-5.” OpenAI Blog, 20 November 2025. (Earlier precursor publication; provides context for the October 2026 release.) https://openai.com/index/early-science-acceleration-experiments-with-gpt-5/
17. de Moura, Leonardo; et al. The Lean Theorem Prover. Manual and reference documentation, Microsoft Research and the Lean community. https://leanprover.github.io/
18. “four color theorem.” Standard encyclopaedic reference. (Background on the 1976 computer-assisted proof that produced a similar community split.)
19. Litt, Daniel. “On reading the ten-proofs repository.” Personal blog, October 2026. (Working mathematician’s first reactions.)
20. “AI labs and the production of mathematical claims.” Editorial, Bulletin of the American Mathematical Society, October 2026 (forthcoming).