OpenAI announced on Tuesday, September 8 that one of its internal, unreleased models succeeded in solving part of the Navier–Stokes equations; one of the seven "Millennium Prize Problems" for which the Clay Mathematics Institute has offered a one-million-dollar prize for each solved problem. But just hours after that announcement, a New York University mathematician accused OpenAI of misusing his private research, sparking a controversy over how much credit should be given for this scientific achievement.
What happened?
According to Eitna and OpenAI's statement, the achievement was obtained in 88 hours with the collaboration of about 10,000 AI agents working in parallel and was validated by the Lean software, which verifies mathematical proofs step by step.
Accusation of research theft
Hours before OpenAI's official announcement, Tristan Buckmaster, a mathematician at New York University, presented a different account in a four-page statement. He says that, together with Levent Alpoge, a mathematician who works at rival company Anthropic, they had spent nearly a year using AI models on a similar proof for this problem and had reached a result by August 22.
Buckmaster says that on September 3, following rumors that Anthropic had made a major breakthrough, he shared the topic of his personal project with one of OpenAI's mathematicians. He says that three days later Sebastian Bubeck, head of OpenAI's mathematics team, informed him in a call that the company's internal model had earlier produced a one-hundred-page proof for a forced version of the Navier–Stokes equations; the same limited approach that, according to Buckmaster, almost no other researcher had been pursuing.
According to Buckmaster's claim, Bubeck then presented him with two options: either OpenAI would publish its result one day after Buckmaster's team's paper, or Buckmaster would publish the paper alone and omit Alpoge's name-because of his work at the rival company.
Buckmaster says that when he indicated he preferred to publish his findings independently, he received responses from Bubeck that he described as unprofessional.
Ultimately Buckmaster and Alpoge published their research under both their names, but OpenAI said in its official message only that it could not rule out the possibility that anonymized data resulting from the two researchers' use of its products may have helped improve its models.
OpenAI's response
Bubeck, OpenAI, and Sam Altman, the company's CEO, have denied Buckmaster's account. Bubeck posted images of his messages on the social network X that he says show he had, from the start, suggested a coordinated joint publication including Alpoge and never asked for his name to be removed from the author list.
Sam Altman also wrote in support of Bubeck that he had acted with honesty and generosity throughout the episode, and that OpenAI initially believed the rival team had fully solved the Navier–Stokes problem, which is why it sought a joint release of results.
According to Altman, when it became clear that Buckmaster's team had only proved the Euler equations (the frictionless version of Navier–Stokes) and not the entire problem, OpenAI suggested they publish earlier.
OpenAI also stated in a separate declaration that it had no direct access to the two researchers' work prior to publication and did not use any specific user data; although it did not completely rule out the possibility.
The Verge reports that Terence Tao, a Fields Medal winner, described Buckmaster and Alpoge's mathematical achievement as a "remarkable success."
This was the second event this week involving AI-produced mathematical proofs by the same two rival companies; days earlier Anthropic had announced that their Claude model produced a computer-verified proof of "Fermat's Last Theorem." A more advanced version of Buckmaster and Alpoge's proof, which is closer to a full solution of the main problem, remains unpublished and awaiting final review, and OpenAI's one-hundred-page proof has not yet been reviewed by any independent body.