Next-gen OpenAI model solves Navier-Stokes Millennium Challenge, mathematicians hint AI stole their work

OpenAI has claimed that an unreleased AI model has solved one of seven Millennium Prize Problems – the deepest and most difficult problems in math. But a researcher has alleged that the company may have used his data to achieve this.

In Short

• OpenAI says next-gen model solved Navier-Stokes Millennium problem
• Mathematicians allege OpenAI may have used their work to solve it
• OpenAI said 10,000 agents collaborated for 88 hours using 130 billion tokens

AI seems to have made another breakthrough, and this time it could be one of the biggest yet. On Tuesday, OpenAI announced that an unreleased AI model had solved the Navier-Stokes existence and smoothness problem – one of the seven Millennium Prize Problems that have stood as some of mathematics’ hardest unsolved questions since 2000. But New York University professor Tristan Buckmaster alleges that OpenAI may have used data from his work with Levent Alpoge, a mathematician at Anthropic, to solve it.

As per OpenAI, it used a new unreleased model to solve the problem. This model, the company says, is much more capable than even GPT-6 Astra – which some claim to be AGI. To solve the Navier-Stokes problem, OpenAI revealed that it used as many as 10,000 AI agents that worked together for 88 hours, using billions of tokens.

The Navier-Stokes equations, developed in the 19th century by Claude-Louis Navier and George Gabriel Stokes, describe how liquids and gases move and are used in areas including aircraft design, weather forecasting and the study of blood flow.

The Millennium problem asks whether smooth solutions to the equations governing three-dimensional fluid motion always stay smooth, or whether they can break down. OpenAI said its proof shows that “an initially smooth fluid at rest can develop a singularity in a finite time.” In its account, a spaghetti-like vortex becomes smaller while spinning faster and faster, with its speed growing without limit in what mathematicians call finite-time blowup.

Mathematician argues OpenAI may have used his data

The claim has immediately become both a major maths story and a controversy. If the proof holds, it would be only the second Millennium Prize Problem to be solved and the first solved by AI.

But before mathematicians had even begun reading the paper, New York University professor Tristan Buckmaster alleged that OpenAI’s account of how it reached the result overlapped uncomfortably with separate work with Levent Alpoge – using both Codex and Claude AI tools. As per Buckmaster, OpenAI only began working on solving the equation after receiving information about their work.

This raised doubts in Buckmaster’s mind whether OpenAI had used their work to train the model. “I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” he said in a statement. “I was told the model did not look up user data. I asked again, about training, and I did not get an answer.”

Though Tristan Buckmaster made it clear that he was simply explaining what he was told. “I am stating it because the alternative is to let a sequence of announcements say something I know to be false,” he added.

Later in an X post, OpenAI addressed these claims. “We (the researchers and the agents) did not see any of their (Buckmaster and Alpoge) work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem,” the company said.

However, OpenAI did not dismiss the chance that data from Codex may have been used to improve the model. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models,” it said.

How did OpenAI’s new AI model solve Navier-Stokes problem?

In a blog post, OpenAI said that its next-generation AI model was more capable than Astra in math. According to the company, Astra solved about 10 per cent of problems on its in-house maths benchmark, while the unreleased model solved closer to 50 per cent “Basically, you throw at it almost any open problem,” OpenAI researcher Sebastien Bubeck said, “and it’s a coin flip whether the model can solve it.”

The company said the model had been in training since late August. On 1 September, with the maths community buzzing over rumours that Anthropic had solved two Millennium Prize Problems, OpenAI set the model on all six remaining open questions, including the Riemann hypothesis, P versus NP and Navier-Stokes.

“We didn’t expect it to solve any,” researcher Noam Brown said. After about 50 hours, the AI had made enough progress on a Navier-Stokes-related problem for the human team to intervene, shift effort away from the other five problems and concentrate the computing power on this one.

OpenAI increased the number of AI agents from 100 to as many as 10,000. It said the Navier-Stokes effort involved 2.7 million messages between agents and 130 billion output tokens, which it described as roughly the equivalent of a million books. The company said the work was completed on Saturday and computer-verified on Sunday, and that it used “millions of dollars” in computing resources.

The competition to solve a Millennium Prize Problem had become so intense, OpenAi says, that it did not circulate the proof to outside mathematicians before publication. Though humans were not absent from the process. OpenAI researcher Dan Roberts described the role of researchers as “a bumble bee cross-pollinating across different groups and delivering different bits of information.”

The wider significance comes from the status of the problem itself. In 2000, the Clay Mathematics Institute named seven Millennium Prize Problems and offered one million dollars for each correct solution. Only one, the Poincare conjecture, had previously been solved, by Grigori Perelman, who later declined the prize money.

OpenAI said it would not seek the million-dollar award for Navier-Stokes either. “Our goal in releasing this result is to report on the substantial progress of our AI models,” the company said. “We do not intend to claim the Millennium Prize.”

This comes at a time when we are seeing rapid progress in various areas, thanks to frontier AI models. Previously, OpenAI had revealed that Astra had managed to make major breakthroughs in 10 major math problems. Later, an Anthropic staff member said that its Fable model managed to crack 5 of those problems in a single day.

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