// MIT TECH REVIEW — INTELLIGENZA ARTIFICIALE
What OpenAI’s latest controversy tells us about the future of math
AI companies are making impressive mathematical strides. Human mathematicians are losing out.
OpenAI’s latest mathematical milestone has quickly become mired in controversy. Today, the company announced that its agents have solved one of the Millennium Prize Problems, some of the most important open problems in mathematics. Under normal circumstances, that solution would be a huge feather in OpenAI’s cap. But the announcement has been 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 if OpenAI’s models made use of the work completed by Buckmaster and Alpöge, though Sébastien Bubeck, a member of the technical staff at OpenAI, said in a press briefing that the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge’s efforts. But whether or not OpenAI’s models took advantage of Buckmaster and Alpöge’s research, this 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 our time, and solving them may demand resources only available at a couple of frontier AI companies, which often defy the norms of academic collaboration that undergird most mathematical progress. If that’s the future we are headed for, it is unclear how human mathematicians will fit into it.
The problem that OpenAI claims to have solved is known as the Navier–Stokes existence and smoothness problem. It is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. Solutions come with a one million dollar prize; before today, only one other Millennium Prize Problem had been solved.
The Navier–Stokes problem concerns a set of equations that describes how fluids, such as water and air, flow over time. The equations are widely used in the field of fluid dynamics, and they have proven powerful, but physicists and mathematicians didn’t understand them completely. 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, NYU’s Buckmaster posted a proof on the social media site 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. The proof was obtained using an internal model that dramatically outperforms the already-impressive Astra model, which was only released last week. The company says it does not plan to claim the million-dollar prize for solving the problem.
These mathematical achievements are indisputably impressive, but they have attracted far less attention than the controversy about their origins. Along with the proof, Buckmaster posted a document detailing his interactions with OpenAI employees after he heard rumors about their work and reached out to one of them. According to him, OpenAI employees presented two possibilities to him: Either he and Alpöge could post their work and OpenAI would post their Navier-Stokes solution the following day, or he could work with OpenAI on a Navier-Stokes paper that excluded Alpöge from authorship, due to his affiliation with Anthropic, OpenAI’s biggest rival. Buckmaster also wrote that he asked the employees whether the agents had obtained access to transcripts of the work that he and Alpöge had done with OpenAI models, which they denied; and whether OpenAI models had been trained on those transcripts, to which they offered no response. MIT Technology Review reached out to Buckmaster