OpenAI Claims Navier-Stokes Proof; Buckmaster Alleges Misconduct

For the second time ever, someone has claimed a solution to one of math's Clay Millennium Problems, and the announcement has landed in the middle of a fight over credit. Scientific American reports that OpenAI says an internal model has proved a form of the Navier-Stokes equations, one of the seven Clay problems each carrying a $1-million prize, while NYU mathematician Tristan Buckmaster has publicly accused OpenAI of trying to cut his collaborator out and pressuring him to stay quiet.

The math backstory: on August 15, Buckmaster and Anthropic's Levent Alpöge proved that the Euler equations, the frictionless cousin of Navier-Stokes, can blow up, extending a 'forcing' approach developed by Diego Córdoba and Luis Martínez-Zoroa. Word of that unpublished work reached OpenAI over the following week, Buckmaster says, and over the weekend a team led by Sébastien Bubeck, who leads OpenAI's math team, produced a proof that pushes the argument all the way to the full Navier-Stokes equations. "We're a little bit in shock," Córdoba told the magazine. "Yesterday and today are crazy days," said University of Chicago mathematician Luis Silvestre.

Buckmaster posted his statement Monday at 11:58 P.M. EDT. In it, he alleges that OpenAI proposed he write up a joint result as sole author while leaving Alpöge, an Anthropic employee, off the paper, and that when he threatened to make the episode public he was told, "Why would you ruin your career?" He has also raised the possibility that the OpenAI model saw drafts he had been keeping inside Codex sessions.

Bubeck has rejected the account. "We did not use their prompt or models or proof," he told Scientific American, and has separately called Buckmaster's characterization "false and inflammatory." Córdoba himself hedged on whether the prize has actually been won: "If it's done, that will be a big surprise for us." The proof is reported to lean on a forcing term that some experts view as a loophole in how the Clay problem is usually posed. Neither the Clay Mathematics Institute nor peer review has yet certified anything.