OpenAI said this week that its models helped crack one of mathematics’ Millennium Prize Problems, a milestone the company announced with unusual fanfare. Within hours, a rival mathematician had gone public with a different story about who deserves the credit, turning a research breakthrough into an authorship dispute playing out across AI labs and university math departments.
The claim centers on the Navier-Stokes equations, the fluid dynamics problem that has stood on the Clay Mathematics Institute’s Millennium list since 2000, with a $1 million prize for a proof. OpenAI announced that work involving its researchers produced a solution, and the New York Times covered the announcement as a major moment for AI-assisted mathematics.
The accusation
Tristan Buckmaster, a mathematician at New York University, says he did it first, or at least saw it first. According to reporting by Decrypt, Buckmaster accuses OpenAI’s Sebastien Bubeck of racing to claim credit for the Navier-Stokes proof after learning about Buckmaster’s unpublished work with Anthropic researcher Levent Alpoge. The accusation implies the ideas behind the proof circulated between camps before OpenAI announced its result.
Buckmaster is a serious figure in this exact field. He has published extensively on fluid dynamics and on partial regularity results for the Navier-Stokes and Euler equations, the mathematical terrain a Millennium proof would have to cross. He moved to NYU’s Courant Institute, one of the top applied mathematics centers in the world, after earlier positions at Princeton and Stanford. When someone with that record says the credit is misplaced, the mathematics community tends to pay attention.
Alpoge, the Anthropic researcher named in the accusation, is a number theorist who joined the company’s research staff after an academic career at Harvard and Princeton. A pairing between a fluid dynamics specialist and a number theorist is unusual on its face, which is part of why the claim that their work fed into OpenAI’s result has drawn as much attention as the result itself.
Why priority disputes hit AI labs differently
Mathematics has handled priority disputes for centuries, usually through dated manuscripts, seminars and the slow machinery of journals. AI-assisted proofs strain that machinery. Work can move from an informal conversation to a corporate press release in days, with the company’s announcement reaching millions while the academic record catches up over months.
The involvement of two competing labs sharpens the problem. Anthropic and OpenAI are racing on research credibility as much as on products, and a first-of-its-kind mathematical result is marketing as much as science. Neither company has an obvious incentive to wait for peer review before claiming a Millennium Problem.
What would settle it
Priority in mathematics is normally established by public documentation. A dated preprint on arXiv, a seminar record, or a journal submission would settle who had the proof and when. As of publication, neither camp appears to have produced a full public manuscript, which leaves the dispute running on claims and counterclaims rather than equations.
The Clay Mathematics Institute also matters here. The $1 million prize requires the work to survive community scrutiny for two years after publication before the award is considered. A corporate announcement carries no such weight, and the prize committee will wait regardless of who posts first. Previous Millennium winners went through years of checking before any money moved, and a proof with AI assistance will face, if anything, more scrutiny than usual.
The bigger question about AI-made math
The episode lands amid a broader push by frontier labs into formal mathematics. OpenAI has published papers positioning its models as research collaborators, and its president Greg Brockman has discussed AI systems contributing to proofs. Anthropic has its own track record, including a disclosed result this summer where a research version of Claude improved a bound related to the Riemann hypothesis by synthesizing recent literature. Google DeepMind has spent years on formal proof systems through its AlphaProof line of work.
If AI systems really can produce Millennium-caliber proofs, the field needs norms for who is listed as an author, what counts as independent derivation, and how much verification is required before a company speaks publicly. Those norms do not exist yet. This dispute may be the first of many, and it suggests they will be written under pressure rather than in advance.
OpenAI and Anthropic did not immediately respond to requests for comment on the accusation. Buckmaster and Alpoge’s unpublished work has not been released publicly, which makes independent assessment impossible for now. Until a manuscript appears, the Navier-Stokes claim sits in the same place a lot of fast-moving AI research does, announced, contested, and unverified.
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