OpenAI said Tuesday its internal AI model produced a Lean-verified proof that the Navier-Stokes fluid equations can “blow up,” using 10,000 coordinating AI agents over 88 hours.
Hours earlier, NYU mathematician Tristan Buckmaster accused OpenAI’s Sébastien Bubeck of learning about his and Anthropic researcher Levent Alpöge’s unpublished, related proof and pressuring them over credit before the announcement.
OpenAI, Bubeck, and CEO Sam Altman deny the account; Bubeck posted texts he says prove he offered Buckmaster’s team the option to publish first.
OpenAI said Tuesday its internal AI model just solved one of the biggest questions in math research—but the celebration was met with sharp criticism after claims surfaced from an NYU mathematician that the company played dirty.
OpenAI said it proved the Navier-Stokes equations, which describe how fluids move, can “blow up”—a point where the math predicts infinite speed, which can’t happen in nature.
It’s one of seven Millennium Prize Problems, each worth $1 million from the Clay Mathematics Institute.
OpenAI says the result took 88 hours and roughly 10,000 coordinating AI agents—copies of its models working the proof in parallel—checked with Lean, software that verifies a proof step by step.
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
But they may not be the ones who first found the solution.
Hours before OpenAI’s announcement, NYU mathematician Tristan Buckmaster told a different story in a four-page statement. He and Levent Alpöge, a mathematician at OpenAI rival Anthropic, had spent nearly a year using AI models to chase proofs of fluid blow-up and came up with a solution by August 22.
Buckmaster says that on September 3, amid rumors Anthropic had solved a major problem, he told a mathematician at OpenAI about the project, stressing it was personal and unaffiliated with either company
Three days later, on a call, OpenAI’s Sébastien Bubeck told him an internal model had already produced a 100-page proof for forced Navier-Stokes—the same narrow approach Buckmaster says almost nobody else was pursuing.
Buckmaster says Bubeck then offered two options: Either OpenAI publishes the day after his team does, or Buckmaster alone writes up his paper, with Alpöge left off because he works at a rival lab. When Buckmaster said he’d go public instead, he says Bubeck replied, “Why would you ruin your career?”
“If you don’t want me to be nice, then I don’t have to be nice,” Bubeck told Buckmaster, per his statement.
Buckmaster ended up publishing the research papers with his findings. Levent Alpöge was credited there, but neither researcher received credit from OpenAI—save for a quote tweet acknowledging that it could not “rule out that de-identified data derived from their usage of our products helped improve our models.”
OpenAI and Bubeck push back
Bubeck, OpenAI, and Altman all deny Buckmaster’s characterization of what happened. In a follow-up post, Bubeck shared texts proposing a coordinated release with Alpöge and offering OpenAI’s prompts, and says he acted in good faith.
“I hope it’s clear from the message that we came in with the best possible intentions,” he wrote. “I never ever asked for Levent to be removed from authorship of his own work.”
OpenAI CEO Sam Altman defended Bubeck, saying he “acted with integrity and generosity throughout,” and that OpenAI offered to let Buckmaster’s team publish first once it realized they’d only solved Euler, not full Navier-Stokes.
I spent much of the weekend talking with the team who did this work. Seb–and everyone else–acted with integrity and generosity throughout.
Initially we believed the other team had also solved the problem. We wanted to collaborate and do a joint release.
In a separate statement, OpenAI said it never saw the pair’s work before publication and accessed no specific user data. That said, the company doesn’t explicitly discard the possibility either.
Fields Medalist Terence Tao called Buckmaster and Alpöge’s underlying math a “remarkable achievement.” It’s the second AI-math story out of the same two labs this week, days after Anthropic said Claude produced a computer-checked proof of Fermat’s Last Theorem.
Buckmaster and Alpöge’s most advanced result—the version closest to the actual $1 million problem—remains unpublished pending a final Lean check. Nobody outside OpenAI has independently reviewed its 100-page proof either.
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