OpenAI claims that it solved one of the seven Millennium Prize problems in 88 hours using an undisclosed internal model, and in the mathematics community there is strong backlash saying that “unpublished research was hijacked.”
Key point
OpenAI said it obtained a proof that the fluid equations could ‘collapse’ within a finite time by mobilizing about 10,000 AI agents.
A professor at NYU claims that “only after hearing about his unpublished results did OpenAI step in to tackle the problem.”
The Clay Mathematics Institute has not yet officially recognized this proof and continues to classify the problem as “unsolved.”
OpenAI’s Navier–Stokes proof: what came out?
In a post released on September 8, OpenAI claimed that it proved that an internal system—one that has not been made public—could cause the Navier–Stokes equations, which describe fluid motion, to collapse within a finite amount of time.
According to the company, about 10,000 autonomous agents solved the problem in parallel and produced a logical argument within 88 hours. The output was compiled into a paper draft of more than 160 pages.
The project began on September 1—right after rumors reached OpenAI that two millennium problems had been solved by other research teams. After that, GPT-6 “Astra” converted the proof into Lean, a formal logic verification language, for an additional 17 hours—turning each logical step into a form that can be mechanically verified. The executives said that the cost of this run reached the level of several million dollars.
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“I dove in after my research” — Buckmaster
Tristan Buckmaster, a professor in the Department of Mathematics at New York University (NYU), sharply criticized OpenAI, saying that it only began working to solve the problem after hearing about his unpublished research results, and that OpenAI “acted unscrupulously over a mathematical challenge that could be decisive for someone’s career.”
He has been working on the research for almost a year together with Levent Alpöge, a mathematician at the rival AI research lab Anthropic.
The issue is that the two used Codex, OpenAI’s code-writing assistant tool, during the proof process. Unless the user specifically rejects it via separate settings, this session data can be used for training OpenAI’s models.
Buckmaster and Alpeje tackled the problem by following an “extremely narrow path” that almost no one else would have chosen. He is not letting the suspicions go, saying that OpenAI’s approach and timing overlap too much with his own research. According to Buckmaster, Sébastien Bubeck, a mathematician at OpenAI, proposed a compromise that effectively sidelined Alpeje’s contribution, and even pressured him by asking, “Why are you trying to ruin your career?”
On the other hand, OpenAI denies, in its official position, that its researchers or agents could not see Buckmaster and Alpeje’s specific work details before the papers were published. While it emphasized that it did not use any individual user’s data, it acknowledged the possibility that de-identified (anonymized) data produced during product use may have been used to improve model performance. However, the company claims that “the structure and ideas of the two proofs are substantially different.”
Clay Institute: “Verification will take time”…The problem is still “unsolved”
At the same time, Terence Tao, a professor at UCLA, praised the results of Buckmaster and Alpeje but warned that this kind of competitive AI approach “risks turning mathematics into a ‘quota-filling game’ rather than something of real value.”
Abhishek Saha, a professor at Queen Mary University of London, also described the incident as “a type of situation that mathematicians typically try to avoid.” He said that the implicit ethics and community norms of pure mathematics are being shaken.
Meanwhile, Martin Bridson, director of the Clay Mathematics Institute, said in an interview with Nature that the announcement was “interesting,” but he drew a line at saying that rigorous verification would take considerable time. The institute still classifies the problem on its official website as “unsolved.”
In 2000, the Clay Institute selected seven unsolved problems and offered a $1 million prize for each. Of these, so far only the Poincaré conjecture—proven in 2003 by **Grigori Perelman**—has been officially solved. Perelman refused to accept the prize money, creating major repercussions both inside and outside academia.
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