OpenAI's Math Proof Race Sparks Credit Dispute With NYU Mathematician
News Summary
A public dispute has broken out between OpenAI and an academic mathematician over credit for progress on the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems designated by the Clay Mathematics Institute, each carrying a $1 million award for a verified solution. NYU mathematics professor Tristan Buckmaster says OpenAI used insider knowledge of his unpublished research and pressured him during the final days before publication, while OpenAI, through researcher Sébastien Bubeck, has called the characterization "false and inflammatory" and released its own account of the exchanges.
The problem at the center of the dispute
The Navier-Stokes equations describe how fluids such as water and air move, and they underpin much of modern fluid mechanics and engineering. Despite their practical ubiquity, mathematicians have never been able to prove, in the general three-dimensional case, whether solutions to the equations always remain smooth and well-behaved or whether they can develop singularities in finite time. That open question is one of the Clay Mathematics Institute's seven Millennium Prize Problems, first listed in 2000, and it has resisted a complete resolution for decades.
Buckmaster had been working with Levent Alpöge, a mathematician employed by Anthropic, on a narrower version of the problem involving "forced" Navier-Stokes, pursuing an approach based on earlier work by mathematicians Córdoba, Martínez, and Zoroa that Buckmaster says almost no other researchers were actively exploring. On the Monday before the dispute became public, Buckmaster posted a proof showing that simplified versions of the equations can break down under certain conditions, describing the work as personal and explicitly unaffiliated with either OpenAI or Anthropic.
How OpenAI entered the picture
According to Buckmaster's account, amid circulating rumors that Anthropic researchers had made headway on a major unsolved problem, he reached out to a mathematician at OpenAI around September 3 (Eastern Time) to share informal details about his progress, again stressing that the project belonged to him personally rather than to either company. Three days later, on a call, OpenAI's Sébastien Bubeck reportedly told Buckmaster that an internal OpenAI model had already produced a roughly 100-page proof for the same forced Navier-Stokes case, using the identical, comparatively obscure Córdoba-Martínez-Zoroa approach.
Buckmaster says he found the coincidence suspicious given how few researchers were pursuing that specific method, and he has suggested that information about his and Alpöge's progress may have reached OpenAI through informal channels before the work was made public. He also says OpenAI's effort was made possible by enormous computing resources: reports indicate the company's internal agents consumed roughly 300 billion output tokens, at an estimated compute cost of about $22.5 million, running on the order of 10,000 concurrent AI agents to grind through the problem in a matter of days.
The credit dispute and disputed quotes
Buckmaster alleges that Bubeck presented him with two options in the days before publication: either OpenAI would publish its proof one day after Buckmaster and Alpöge released theirs, or Buckmaster could lead a rewritten version of the proof for publication with OpenAI, on the condition that Alpöge be left off as a credited author because he works at rival lab Anthropic. When Buckmaster resisted removing his collaborator, he says Bubeck responded with the phrase "if you don't have to be nice," and separately asked him, "why would you ruin your career?" Buckmaster also says Bubeck texted Alpöge directly, suggesting "I don't know if Tristan is being fully rational right now."
Bubeck has publicly disputed this framing. He said in a released statement that OpenAI's researchers and its automated agents "did not see any of their work through any means until they released it publicly," and separately stated, "we did not use their prompts or proofs to prompt our models or direct our agents." Bubeck said he had been trying to coordinate a joint, transparent release with Buckmaster and Alpöge rather than compete with them, and he pointed to his own text messages to Alpöge — in which he said credit should go to Alpöge and Buckmaster and offered to share OpenAI's materials — as evidence of good faith.
On the specific credit dispute, Bubeck said he never asked to remove Alpöge as an author of Alpöge's own paper. Instead, he said the disagreement was over whether Buckmaster, alone, should lead a rewrite of OpenAI's proof, and that he considered Alpöge's employment at Anthropic a conflict of interest for that particular task. Bubeck did acknowledge using language about a researcher risking "their career," calling the wording a mistake, saying he retracted it immediately, and describing it as an ill-phrased expression of concern about making unfounded accusations rather than a threat.
Reaction from the broader mathematics community
The episode has drawn concern from mathematicians who see it as symptomatic of a larger shift in how breakthroughs on famous open problems may be produced going forward. Fields Medalist Terence Tao has warned publicly that AI-driven efforts to solve major problems without transparency or collaboration "can contaminate this process to the point where it actually becomes a net negative for the progress of mathematics as a whole." Commentators have noted that traditionally, the multi-year human struggle to crack a hard problem tends to generate new techniques, spin-off results, and entire subfields of research along the way — value that can be lost if a single, well-resourced company races to a private solution using computing power far beyond what any individual academic lab could deploy.
Independent observers have also pointed out that OpenAI's approach — deploying thousands of concurrent AI agents backed by millions of dollars in compute — is simply not replicable by university researchers working with ordinary institutional resources, raising questions about how credit, priority, and collaboration norms in mathematics should evolve as AI labs increasingly compete to solve marquee open problems.
Where things stand
As of this reporting, OpenAI maintains that its proof was produced independently and that it only learned of Buckmaster and Alpöge's approach through public rumor rather than direct access to their materials. Buckmaster and Alpöge have published their own proof for the narrower forced Navier-Stokes case and have stood by their account of a pressured, compressed release timeline. Neither the full three-dimensional Navier-Stokes existence and smoothness problem, nor the associated $1 million Clay Mathematics Institute prize, has been formally resolved or awarded; the disputed proofs concern a related but narrower version of the equations.