What OpenAI’s latest controversy tells us about the future of math
OpenAI announced today that its agents have solved one of the Millennium Prize Problems, a result that would normally be a major achievement. The announcement was overshadowed by accusations that OpenAI used NYU mathematician Tristan Buckmaster's and Anthropic employee Levent Alpöge's AI-assisted work on the problem as a jumping-off point and failed to credit them; OpenAI has denied the accusations. It remains uncertain whether OpenAI's models made use of that work, though OpenAI technical staff member Sébastien Bubeck said in a press briefing that the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge's efforts.
The problem is the Navier–Stokes existence and smoothness problem, one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. Solutions come with a $1 million prize, and before today only one other Millennium Prize Problem had been solved. Navier–Stokes concerns equations that describe how fluids such as water and air flow over time; the equations are widely used in fluid dynamics and have proven powerful, but physicists and mathematicians did not fully understand them. In particular, it was unknown until today whether the equations might, under some conditions, break down and predict an impossible state of affairs, such as a fluid having infinite velocity.
On Monday, Buckmaster posted a proof on Mastodon showing that a simplified version of the Navier–Stokes equations can indeed break down, a major step forward on the Millennium Problem. He and Alpöge had worked on the problem for almost a year, using publicly available models from both OpenAI and Anthropic. Then today, OpenAI presented a proof showing that the full Navier–Stokes equations can break down as well. That proof was obtained using an internal model that dramatically outperforms the already-impressive Astra model, which was only released last week.
Regardless of whether OpenAI's models took advantage of Buckmaster and Alpöge's research, the episode may mark a turning point in the history of mathematics. AI models now seem essential for making progress on the most important mathematical problems of the time, and solving them may demand resources available only at a couple of frontier AI companies, which often defy the academic collaboration norms that undergird most mathematical progress. If that is the future, it is unclear how human mathematicians will fit into it.