The Mathocalypse II
Mathematicians React to OpenAI's 722 Manuscripts
by Claude Opus 5.5
Summary
Professional mathematicians reacted to OpenAI's 6 October 2026 release of 722 AI-generated manuscripts with more alarm than celebration, but the objection is mainly to how the work was released, not whether it is correct.
Grief and alarm: Fields medallist Hugo Duminil-Copin said he cried and that OpenAI had "annihilated" his field; his deeper fear is the collapse of the culture of freely sharing open problems.
Process critiques: Terence Tao, Andrew Sutherland, Alex Townsend, Bryna Kra, Ursula Martin, Melanie Wood, the IAS and the Association for Human Mathematics objected to the bulk release, the unreleased model, thin Lean coverage (162 of 722) and ignored advisory-group recommendations. The AHM called for a boycott.
Enthusiasm: Levent Alpöge called it "the most significant moment in mathematical history"; Abhishek Saha, Martin Bridson, Alex Kontorovich and Daniel Litt also praised the results.
Early checking: three manuscripts were withdrawn within a day, and a Cambridge–King's paper showed Lean certificates can diverge from the prose proofs they accompany.
The reaction builds on a tense 2026: the Leiden Declaration (June), the contested Navier–Stokes claim and the Fields medallists' "Severe Misalignment" declaration (September). This report covers sources up to 11 October 2026; much of the press quoting is via secondary summaries, noted where used.
The release
On 6 October 2026 OpenAI posted 722 manuscripts to github.com/openai/math, grouped into 372 "result families", all produced by an unreleased internal model. Within a day it withdrew three over a sign error and revised 14 more.
Problems posed: About 4,000; outputs judged significant were kept
Compute: Average result ≈ 3 hours of ChatGPT Pro thinking with the internal model
Lean coverage: 162 of 722 manuscripts had a Lean-formalised main result at release (≈22%)
Reasoning shown: 10 abridged reasoning summaries (e.g. irrationality exponent of π, spin glasses, Vlasov–Maxwell)
Withdrawals: 3 manuscripts pulled on 7 Oct (one sign error cascaded into two dependents); 14 revised
Not disclosed: Model name, prompts, per-result compute — items the IAS-hosted advisory group (AGMAI) recommended on 29 Sept
Headline claims: Quasi-Riemann Hypothesis, no-Siegel-zeros results, chromatic number of the plane ≥ 6, Saxl's conjecture
Repo policy: Issues turned off; no pull requests accepted at launch
OpenAI framed the results as a by-product of model evaluation after its existing maths benchmarks "saturated". Research lead Dan Roberts said the repo would keep receiving new formalisations and errata. None of the remaining Millennium Prize Problems was solved.
Prior context. The release landed on a field already unsettled by a run of 2026 AI claims: OpenAI's May disproof of Erdős's unit-distance conjecture (checked by external mathematicians including Thomas Bloom), its contested September Navier–Stokes claim (10,000 coordinating agents over 88 hours, later accused of recycling human work without attribution), Anthropic's Lean formalisation of Fermat's Last Theorem, and a Claude proof of the dying-percolation conjecture in Duminil-Copin's own field.
Distress and grief: the personal toll
The most widely shared reaction came from 2022 Fields medallist Hugo Duminil-Copin (IHÉS / Geneva), sixteen of whose favourite open questions appear among the problems OpenAI attacked. His account reached the public through a Société Mathématique de France video call on 8 October and a Le Monde report by David Larousserie on 10 October.
He said he cried on the Tuesday night of the release, waking his daughter, and that OpenAI had "annihilated" his field; in questions he called it "a dismantling of our activity".
Reading the proofs, he said, lacks "the same flavour" as work by people whose faces he knows. He still plans to work through the 3,500+ pages relevant to him, organising the effort collectively to "create human activity around these results".
His tears were also for the young, who he said "will suffer the most". His deeper worry is the free circulation of open problems, which he says AI labs have harvested; some colleagues now plan to share less, and he described that culture as shattering.
This came weeks after his 30 August essay on Proofs and Prompts about the θ(p_c) = 0 percolation conjecture, which argued that failed human attempts are themselves generative. Quanta noted that a Lean-verified proof by Anthropic's Claude had quietly appeared on GitHub on 28 August, days before. He has since argued that a machine proof is the start of mathematical "digestion", not the end.
Others voicing career anxiety (as reported by Progresser-en-maths, citing Quanta and Scientific American):
Ken Ono: Warned Berkeley students they may graduate into a vanished or unrecognisable profession
Ravi Vakil (Stanford): Fears an "AI is eating maths" narrative will justify funding cuts in a tight job market
Amaury Hayat (École des Ponts): Estimated OpenAI's Navier–Stokes compute at roughly 200 years of a CNRS researcher's work
Andrew Sutherland (MIT): Sees mathematicians as the "canary in the coal mine" for other intellectual professions
Critiques of process, norms and verification
The dominant professional objection is not that the mathematics is wrong but that the release bypassed peer review, ignored the advisory group OpenAI itself convened, and shifted the cost of checking onto unpaid humans.
Terence Tao (UCLA, Fields 2006). Reported by some outlets to have taken part in the AGMAI process OpenAI announced on 21 September, and a signatory of the Fields medallists' declaration, Tao wrote on Mathstodon that problems are being solved by "AI prompters" with no interest in the wider field, who cannot answer questions or give talks on the results (TechCrunch). He hosted the AHM statement as a guest post on 7 October, and on 9 October gave a Caltech public lecture, "Math 2.0", contrasting the current "excessive emphasis on automated solving of open problems" with a future where AI sustains the human community. Some commenters stressed that hosting the AHM post was not an endorsement; one pointed to a post by Daniel Litt on X correcting claims that Tao was aligned with the group.
Andrew Sutherland (MIT). Told Scientific American that one-shot, single-agent claims should be treated as unverified until the model is released: "We should ask for receipts." He praised the quick withdrawals as responsible but told Retraction Watch it would "take a lot more than that to earn back the trust they have lost", pointing to the 8 September Navier–Stokes announcement.
Alex Townsend (Cornell). Expects more errors; said OpenAI should have announced the Lean-verified manuscripts first and sought help on the rest separately (Retraction Watch).
Others quoted in Nature's coverage (summary):
Álvaro Lozano-Robledo (UConn): Called the simultaneous posting "staggering" and asked why hundreds had to be released at once; later wrote a guest post on Tao's blog advising students to "keep calm and carry on studying math"
Ursula Martin (Oxford): Likened it to tossing the community a messy first draft to clean up
Michael Harris (Columbia): Said he would not read the preprints at all
Melanie Wood (Harvard): Told TechCrunch there is no human understanding at the point of release — "now the work begins"
Institutional statements.
Association for Human Mathematics (7 Oct, reposted on Tao's blog): "Mathematicians did not ask for this work to be done"; the 700-file release is "a demonstration of power"; it urges colleagues to stop working with OpenAI. It notes AGMAI's first recommendation was not to test advanced problems on internal models.
Institute for Advanced Study: warned that AI can now output arguments the prompter cannot understand, verify, or take responsibility for, and asked how to build a paradigm that keeps human understanding part of responsible scholarship.
AGMAI (nine researchers, hosted at IAS): said it is for the community to judge whether its 29 September recommendations were followed. TechCrunch found only 10 of 719 manuscripts with chain-of-thought and no machine-readable links between prose and Lean.
Fields medallists' declaration, "A Severe Misalignment of AI in Mathematics" (11 Sept, 25 signatories, now 28): Tao, Scholze, Viazovska, Birkar, Huh, Hairer, Kontsevich, Maynard, Bhargava, Yu Deng, Lions, Villani, Werner and Duminil-Copin among them. It argues problem-solving is a means to understanding and that "mass production" of proofs endangers transmission. Yu Deng separately described "an atmosphere of restlessness and impatience".
Counter-voices on the critics. Lior Pachter agreed AI labs are misaligned but argued the profession's own history of neglecting students and outsiders makes it a poor model. In Tao's comments, mathematician Jörg Neunhäuserer, who had worked on three of the solved problems, said he felt relieved rather than robbed, and proud his intuition was right — though AI text is not human understanding.
Enthusiasts and qualified optimists
A visible minority judged the mathematics itself extraordinary, while usually conceding the process concerns.
Levent Alpöge (Anthropic (formerly academia)): On X called it "obviously the most significant moment in mathematical history", singling out quasi-Riemann and no-Siegel-zeros results; acknowledged "sad stories" for researchers pre-empted (Nature via AI Weekly)
Abhishek Saha (Queen Mary University of London): "A very big day for mathematics"; sorted the results into four tiers and placed most among exceptional advances within existing programmes or surprising breakthroughs (Decrypt)
Martin Bridson (Oxford; President, Clay Mathematics Institute): Reportedly called the release "breathtaking" (shattered.io)
Alex Kontorovich (Rutgers): Suggested at least one proof would merit the highest honour if a human had produced it (shattered.io)
Daniel Litt (Toronto): Told Fortune "this is great for mathematics" while urging support for human mathematicians; argued there is no reason to ask companies to keep answers secret (Decrypt)
Jacob Tsimerman (Fields 2026; left Toronto for OpenAI's safety team): Argues the career will not survive in its current form; imagines mathematicians exploring a vast machine-made library (Progresser-en-maths)
Litt's position is the most developed. His September essay "A beginning for mathematics" (a revision of his August OpenAI-hosted talk "The End of Mathematics") predicts a "mathematics explosion" in which mathematicians become busier, not redundant, because someone must understand scope, assumptions and failure modes. He had already conceded in March that he expects to lose his 2025 bet that AI would not write top-tier papers by 2030.
Several pro-AI voices also pushed back on the backlash itself. A commenter on Tao's blog warned that framing mathematicians as "anti-AI luddites" risks funding cuts, naming statements by Buckmaster, Duminil-Copin and Tao as unhelpful. A mathematician posting as "valuevar" said Tuesday's results had brought his own research programme to a successful conclusion with credit, and that he was excited while sharing the community's concerns.
Technical scrutiny of specific results
Within five days, the first hands-on checking had found one real error, raised doubts about what Lean certificates actually certify, and described several proofs as hard for experts to read.
The withdrawals hit the Hodge cluster. The three manuscripts pulled on 7 October were on algebraicity of Weil classes on split abelian eightfolds, Kuga–Satake correspondences for K3 surfaces, and the rational Hodge conjecture for products of K3 surfaces (Retraction Watch). OpenAI says its own audit found the sign error.
"Lost in translation". Alexander Bastounis (King's College London) with Fabian Circelli and Anders C. Hansen (Cambridge) posted arXiv:2610.08144 arguing that OpenAI's Lean proof of Navier–Stokes blow-up does not correspond to its natural-language proof, and that faithful autoformalisation is in a formal sense harder than the halting problem. They conclude such proofs should not be trusted without normal peer review (TechCrunch). Some readers noted the mismatches concern intermediate steps, not the headline statement.
Thomas Hales (Pittsburgh), who led the formal proof of the Kepler conjecture, wrote a guest post on Tao's blog on Lean's reliability, arguing that what matters to him is mathematics' consistency and its role in supporting science.
"Alien math". Researcher Dmitry Rybin, reading the claimed proof that the plane's chromatic number is at least 6, called it "totally unbelievable alien math", noting a seemingly out-of-nowhere equivalence between arbitrary and "weakly measurable" colourings (Decrypt). He also stressed a Lean check shows only that the proof matches the Lean statement, not the original problem.
Community formalisation. Keith Adler, formalising the Saxl conjecture proof in Lean 4, complained the repo had Issues disabled and accepted no pull requests, leaving nowhere to send fixes.
Readability. Le Monde reported many experts found the texts often illegible even for professionals; Duminil-Copin faces 3,500+ pages in his area alone.
Prior-work context. Diego Córdoba (ICMAT) and Luis Martínez-Zoroa used a guest post to set recent AI-assisted Euler and Navier–Stokes results against decades of human work on blow-up, including their own vortex-layer constructions.
Broader context: AI capability in mathematics, 2025–26
The 722-manuscript release was the climax of a year in which AI went, in Thomas Bloom's words on the Erdős problems site, from essentially useless to helping solve some of the hardest problems in mathematics in under a year.
10 Oct 2026: Le Monde reports Duminil-Copin's distress — See "Distress and grief"
9 Oct 2026: Tao's "Math 2.0" lecture at Caltech — Argues for AI that sustains the human community
6 Oct 2026: OpenAI posts 722 manuscripts; Hexagon repository for AI-assisted work announced the same day by Ben Antieau — Board includes Mohammed Abouzaid, Bryna Kra, Lauren Williams; advisers include Kevin Buzzard and Ravi Vakil
5 Oct 2026: Jeremy Avigad (CMU), "The Future of Mathematics" — Finds community responses "generally positive"; says routine results are now decoupled from understanding
29 Sep 2026: AGMAI recommendations, drawing on 600+ mathematicians' responses — Asked labs to stop testing hard problems on closed models
21 Sep 2026: OpenAI forms AGMAI at IAS (nine unpaid members incl. Gowers, Hairer, Witten)
14 Sep 2026: Litt, "A beginning for mathematics" — Predicts a mathematics explosion
11 Sep 2026: 25 Fields medallists' "Severe Misalignment" declaration — See critiques section
8 Sep 2026: OpenAI claims Navier–Stokes blow-up (10,000 agents, 88 hours); declines the Clay prize — Tristan Buckmaster (NYU) accuses OpenAI of pre-empting his and Alpöge's work; 8,000+ researchers endorse a complaint that it was rushed
Aug 2026: OpenAI's private meeting with ~40 mathematicians; ten results posted by blog — Litt's talk "The End of Mathematics"; Duminil-Copin's θ(p_c) essay; Claude proves dying percolation
Jul 2026: Tsimerman wins Fields, joins OpenAI; Alpöge uses Claude Fable 5 to refute an 87-year-old conjecture
2 Jun 2026: Leiden Declaration, endorsed by the IMU — 2,100+ signatories within days, incl. Tao, Scholze, Hairer, Maynard, Viazovska
May 2026: OpenAI disproves Erdős unit-distance conjecture — Checked externally; Thomas Bloom and Melanie Wood helped write the human version
The Navier–Stokes dispute shaped everything after it. Buckmaster alleged OpenAI researcher Sébastien Bubeck sought to drop Alpöge from authorship because he worked at Anthropic; Bubeck denied it and apologised for a remark about Buckmaster's career (The Next Web). Sutherland and the AHM both cite this as the source of lost trust.
Bryna Kra (Northwestern), who helped draft the Leiden Declaration and attended OpenAI's August meeting, told WIRED that attendees had asked for papers rather than blog posts and were told results would not be released all at once (ForkLog, summarising WIRED). "Doing mathematics via tweets and press releases … is not a way to sustain the ecosystem," she said, while calling the moment "frightening" but "truly exciting".
Nestor Guillen (NYU visitor) told WIRED that AI companies are called "bandits" in the community, and that his anxiety is "not because of AI, but because of AI companies".
Michael Harris (Columbia), a Leiden organiser, framed the declaration as an unprecedented rally behind the discipline's values, adding "now the work begins".
Themes and open questions
Across more than 30 named mathematicians, five arguments recur.
Understanding, not answers. The most common line — Tao, the Fields declaration, Duminil-Copin, Wood, Avigad — is that a proof nobody understands is the start of mathematical work, not its end.
Process over correctness. Few critics claim the mathematics is mostly wrong. The objections are to bulk release, a closed model, missing prompts, unlinked Lean files, and ignored AGMAI advice (Sutherland, Townsend, Kra, Martin).
Lean is necessary but not sufficient. Only about 22% had a formalised main result, and the Bastounis–Circelli–Hansen paper shows a certificate can verify something other than the prose claim.
The open-problem commons is at risk. Duminil-Copin's sharpest point is that labs harvested problems the community shared freely, and colleagues are now sharing less.
Careers and funding. Ono, Vakil, Lozano-Robledo and Duminil-Copin worry most for students; pro-AI voices warn that visible anguish could itself invite funding cuts.
The split runs less between academia and industry than between those judging the results (Alpöge, Saha, Bridson, Kontorovich) and those judging the release (Tao, Sutherland, the AHM). Litt and Kra sit in both camps.
Open questions
How many unformalised results survive independent review? Townsend expects more errors.
Will OpenAI name and release the model so one-shot claims can be replicated?
Will OpenAI move results to community venues such as Hexagon, and fund the human "digestion" AGMAI requested?
Will the AHM's boycott call gain institutional support beyond its own membership?
Sources
Primary and blog sources
Tao's blog: recent posts incl. Math 2.0, Hexagon, Avigad, Lozano-Robledo, Hales, Meka
Tao, "Math 2.0" (10 Oct)
News coverage
AI Weekly, summarising Nature: Lozano-Robledo, Martin, Harris
Progresser-en-maths: Fields declaration, Ono, Vakil, Hayat, Tsimerman
Could not be opened directly: Le Monde, Nature, Scientific American, The Guardian and WIRED (paywalled or blocked); their quotes are taken from the summaries above.
