OpenAI Says AI Solved Millennium Math Problem, but Credit Dispute Overshadows Proof

The Navier–Stokes problem involves equations that describe the flow of fluids such as water and air, and that are widely used in weather prediction. The question asks whether the equations can break down under certain conditions, mathematically implying events such as water spontaneously exploding. Physicists and mathematicians regard such a breakdown as physically unrealistic, but no one had been able to settle the question. With a $1 million prize attached, it was one of the most prominent open problems in mathematics; before OpenAI’s announcement, only one of the seven problems had been solved.

According to The New York Times, OpenAI said the proof was produced in 88 hours by a model that has not been released. The effort coordinated as many as 10,000 AI agents and may have cost millions of dollars in computing power. The company released the proof as a paper and in the formal proof language Lean, and said it did not plan to claim the monetary prize.

The result was another sign that AI is reshaping the highest levels of mathematical research, according to The New York Times, exciting some mathematicians and worrying others.

The dispute centers on work by Buckmaster and Alpöge, who spent nearly a year using publicly available OpenAI and Anthropic models to attack the Navier–Stokes problem. On Monday, Buckmaster posted a proof on Mastodon that a simplified version of the equations could break down. OpenAI then presented a proof that the full equations could break down. In a document posted alongside his proof, according to MIT Technology Review, Buckmaster said OpenAI employees offered him two options: he and Alpöge could post their own work and OpenAI would release its solution the next day, or he could work with OpenAI on a paper that excluded Alpöge from authorship because of Alpöge’s affiliation with Anthropic. Buckmaster also wrote that OpenAI employees denied that their agents had obtained transcripts of the work he and Alpöge had done with OpenAI models, but did not answer when he asked whether the models had been trained on those transcripts.

OpenAI rejected the implication. In a press briefing, OpenAI’s chief research officer, Mark Chen, said that no agents or employees had accessed Buckmaster and Alpöge’s transcripts. OpenAI researcher Sébastien Bubeck said the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge’s efforts, according to MIT Technology Review. He separately told The New York Times that the solution was “a spectacular culmination of the arc we have seen over the past twelve months.”

The question of influence is complicated by the choice of mathematical approach. MIT Technology Review reported that both the Buckmaster-Alpöge proof and OpenAI’s proof use a strategy developed by mathematicians Diego Córdoba and Luis Martínez-Zoroa. Javier Gómez-Serrano, a mathematics professor at Brown University, said that approach was already seen as promising, making it possible but not certain that the two teams arrived independently.

The dispute comes as AI models become increasingly indispensable in attacking central mathematical problems, but the scale of computation required may now exceed what most academic mathematicians can command. MIT Technology Review said the episode could be a turning point in the history of mathematics, because solving major problems may require resources available only at a few frontier AI companies, which often operate outside the collaborative norms of academic research. That leaves open what role human mathematicians will play, a question some in the field are asking.