Key takeaways

  • OpenAI has published its Navier-Stokes results.
  • "I believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber," Brown writes.
  • " OpenAI mathematician Ven Chandrasekaran said the company's solution differs fundamentally from the approach Buckmaster and Alpöge took.

What happened

OpenAI has published its Navier-Stokes results. " The proof was also formalized in Lean. " OpenAI developer Noam Brown points to a familiar pattern. 5 percent on the ARC-AGI benchmark cost about $500,000. Today, Astra can do more for roughly $20. The 2025 Math Olympiad required massive compute from both OpenAI and Google Deepmind. By 2026, anyone with a $20 ChatGPT subscription could match that.

" 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.

Why it matters

"I believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber," Brown writes. In a press briefing (via WIRED), the company pushed back against Buckmaster's allegations (see below). "We, whether it’s the researchers or the agents, did not see any of their work until it was released publicly last night," Bubeck said, according to WIRED.

" OpenAI mathematician Ven Chandrasekaran said the company's solution differs fundamentally from the approach Buckmaster and Alpöge took. Bubeck said OpenAI began training a new model with advanced math capabilities on August 28. After hearing rumors about progress at Anthropic, the company shifted more resources toward the Navier-Stokes problem.

" 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. 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. 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.

What to watch

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. OpenAI made two proposals, according to Buckmaster. " 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.