Key Points

• Mathematician Tristan Buckmaster says OpenAI pressured him after he and Levent Alpöge made progress on the Navier-Stokes equations using AI models.
• OpenAI claimed an internal model had produced a roughly 100-page proof following the same unusual path, according to Buckmaster. He and Alpöge had uploaded all their drafts to Codex throughout the project.
• Bubeck twice asserted he wanted Alpöge removed from authorship because he works at Anthropic, Buckmaster says. When Buckmaster refused, Bubeck allegedly asked: "Why would you ruin your career?"

Mathematician Tristan Buckmaster describes how OpenAI pressured him after information about his AI-assisted research leaked, tried to remove his co-author from the paper, and threatened him.

Tristan Buckmaster and his co-author Levent Alpöge used AI models to make major progress on one of the most famous unsolved problems in mathematics: the Navier-Stokes equations. They're part of the Clay Millennium Problems, a list of seven fundamental math questions, each carrying a million-dollar prize. Buckmaster has now published a public statement leveling serious allegations against OpenAI.

The two mathematicians had spent months working with various AI models, including Anthropic's Claude and OpenAI's Codex running GPT-5.6 Sol. By mid-August, they say they'd achieved several breakthroughs. They also believe they found a result for a specific Navier-Stokes variant, though it hasn't been published or formally verified yet. A recognized proof would be a massive deal for mathematics and a landmark for AI-assisted research.

Rumors reach OpenAI and the pressure starts

In early September, rumors about a major math breakthrough started circulating. According to Buckmaster, Alpöge got word that information about their work had been passed along to OpenAI. On September 3, Buckmaster proactively reached out to a mathematician at OpenAI to set the record straight, stressing that the work was a purely personal collaboration with no institutional agreements.

OpenAI responded the same day, asked for details, and offered compute resources. Buckmaster suggested a call the following week, but OpenAI pushed harder. On Friday, they asked if he could talk that same day. On Sunday at 12:45 p.m., they wanted to know if he was available "at any point today."

OpenAI claims its own breakthrough using the same approach

That Sunday, OpenAI's Sébastien Bubeck joined the conversation. During two phone calls, OpenAI told Buckmaster that an internal model had produced a roughly 100-page proof for the Navier-Stokes equations with forcing, according to his account.

At first, OpenAI said "very little human input" was needed. As the conversation went on, a different picture emerged, according to Buckmaster: a whole team had worked on the problem, easier problems had been used as stepping stones, and massive compute was thrown at it.

Buckmaster says the mention of forced Navier-Stokes suggested that OpenAI was pursuing the same unusual route he and Alpöge had chosen, one that he says almost nobody else was working on. He and Alpöge had put all their drafts throughout the project into OpenAI Codex sessions. When he asked whether OpenAI's model had been trained on or had access to those sessions, he says he was told the model did not look up user data. When he asked specifically about training, he says he received no answer.

OpenAI developer Noam Brown, one of the company's top minds in model development, said during the Astra launch that OpenAI had been attempting the Millennium Problems but hadn't found a solution. He added that they hadn't put much compute toward the effort. That was in early August.

Bubeck wanted to cut the Anthropic employee as co-author

OpenAI made two proposals, according to Buckmaster. In the first, Buckmaster and Alpöge post their Euler result, and OpenAI posts its own the next day, with OpenAI declaring them the "closest humans to the problem." In the second, Buckmaster alone presents the Navier-Stokes result and acknowledges an internal OpenAI model. In both scenarios, Bubeck twice "asserted" that he wanted Alpöge removed from authorship. The reason, according to Buckmaster, is that it was "so annoying" that Alpöge works at Anthropic.

Buckmaster rejected both proposals and said he'd go public if OpenAI published its result in the proposed form. The response, according to Buckmaster: "Why would you ruin your career?" When he replied that he's an academic, Bubeck allegedly said: "If you don't want me to be nice, then I don't have to be nice." Buckmaster reports that Bubeck later texted Alpöge separately, telling him: "I don't know if Tristan is being fully rational right now." Alpöge declined to engage.

Buckmaster explicitly states he isn't accusing anyone. He hasn't seen OpenAI's proof and doesn't know whether their data was used. He's sharing the facts because, as he puts it, "the alternative is to let a sequence of announcements say something I know to be false

What Buckmaster had actually wanted to talk about was something very different: that a mathematician working with a language model can now accomplish in a month what used to take much longer. "This is a Deep Blue-Kasparov moment," he writes. OpenAI has not yet responded to the allegations.

Statement