OpenAI's Navier-Stokes proof sparks a credit fight with mathematicians
Tristan Buckmaster, a mathematician at New York University, publicly accused OpenAI of using his research approach to get ahead of him in solving the Navier-Stokes existence and smoothness problem, one of mathematics' hardest open questions and one that carries a $1 million bounty. OpenAI reached a solution using tens of thousands of AI agents, but Buckmaster says the company only pushed forward once it learned the equation was close to being solved, drawing on work he had done with Anthropic researcher Levent Alpoge using both OpenAI's Codex and Anthropic's Claude. OpenAI investigated the claim and amended its announcement to state it had "confirmed that Buckmaster's Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training." The company referred Wired to that announcement. Despite his accusation, Buckmaster has kept using Codex to tidy up his papers and to reconstruct the logical steps OpenAI's agents might have taken.
He isn't alone. German mathematician Andreas Thom says he was "amazed" when OpenAI announced in August that its Astra model had used techniques from his two decades of work in geometric group theory to prove a long-standing problem. When Thom emailed OpenAI researchers Mark Sellke and Sebastien Bubeck, he pointed out that the company's claim of "no progress" on the problem in the last decade ignored a 2019 paper of his and other mathematicians' work; OpenAI amended its press release as a result. Thom also asked whether his interactions with ChatGPT had been fed into training data. Sellke told him "that did not happen," but Thom says he doesn't fully trust the denial and expects he will never know for certain whether his work shaped the result. He has kept using ChatGPT to speed up writing papers, now with privacy settings changed to opt out of training.
Cornell mathematician Alex Townsend, coauthor of a forthcoming book on the field's evolution, says colleagues have been asking since August how to get access to more powerful AI models, and describes feeling "excited and nervous simultaneously" about what the tools mean for his own purpose as a researcher. Buckmaster argues that racing to solve famous problems without properly crediting the human work behind them, especially ahead of major IPOs, is "childish" and irresponsible; he plans to clean up papers he posted prematurely to beat OpenAI's announcement, one of which he calls "AI slop."
Organized pushback is building. Twenty-five Fields medalists signed an open letter saying AI companies and mathematicians are "severely misaligned," more than 4,000 people have signed the Leiden Declaration setting out recommendations for mathematicians, funders and policymakers, and more than 2,000 people with ties to Caltech called on organizers to suspend an AI math hackathon at the school that was sponsored by Anthropic and OpenAI (OpenAI has since dropped out). Thom doubts any slowdown is sustainable given the efficiency gains AI offers, and both he and Buckmaster say the field needs to figure out how to guide younger mathematicians through the shift rather than stop it.
Key facts
- NYU mathematician Tristan Buckmaster accused OpenAI of using his approach to beat him to a solution of the Navier-Stokes existence and smoothness problem, which carries a $1 million bounty; OpenAI used tens of thousands of agents to reach the result.
- OpenAI amended its announcement to state it confirmed Buckmaster's Codex prompts over the two months before the September 8, 2026 paper could not have influenced the system, including through training.
- German mathematician Andreas Thom says OpenAI's Astra model used his geometric group theory techniques, developed over two decades, to prove a problem he was working on; OpenAI revised its press release after Thom noted it had overlooked his 2019 paper.
- Both Buckmaster and Thom keep using OpenAI's Codex and ChatGPT despite their concerns, and Cornell mathematician Alex Townsend says he feels 'excited and nervous simultaneously' about the technology's effect on his field.
- Twenty-five Fields medalists signed an open letter calling AI companies and mathematicians 'severely misaligned,' more than 4,000 people signed the Leiden Declaration, and over 2,000 people tied to Caltech called to suspend an AI math hackathon sponsored by Anthropic and OpenAI, which has since dropped out.
Why it matters
AI labs are now producing headline results in pure mathematics, Navier-Stokes and a geometric group theory problem among them, faster than the field's usual mechanism for crediting the human work they build on can keep up. Andreas Thom puts it starkly: AI "kills this entire idea that you could trace back who contributed what." That strikes at a discipline organized around peer review and traceable credit.
Who it affects
Working mathematicians whose unpublished approaches and years of specialized research can be drawn into a model's output with no clear paper trail, and who, per Buckmaster and Townsend, now feel pressure to adopt paid AI subscriptions just to keep pace. It also affects OpenAI and Anthropic, whose public claims about novel proofs are being publicly challenged and, in Thom's case, corrected after the fact.
How to use it
Both Buckmaster and Thom keep relying on the same companies' tools they're at odds with, Codex and ChatGPT, to tidy up papers and reconstruct proof steps, because they say the efficiency gain is too large to pass up. Thom has since changed his privacy settings to stop his prompts being used for training, and notes that OpenAI's university and enterprise tiers default to not training on user data.
How solid is it
The account rests on on-the-record statements from Buckmaster, Thom and Townsend, plus OpenAI's own emailed reply and its amended public announcement acknowledging it examined and revised its claims. The central attribution question, whether Buckmaster's or Thom's unpublished work actually shaped the AI systems' results, remains contested: OpenAI denies it, and Thom says he expects to never know for sure.
Risks and caveats
OpenAI states flatly that Buckmaster's prompts could not have influenced its system, including through training, so the claims on both sides remain unresolved rather than confirmed. The source does not name the specific geometric group theory problem Astra is said to have solved, does not say whether the Caltech hackathon was actually suspended, does not quantify the 'efficiency gain' mathematicians cite, and gives no figure for any payout from the $1 million Navier-Stokes bounty.
“AI really kills this entire idea that you could trace back who contributed what. That is probably over.”
— Andreas Thom, mathematician