What OpenAI’s latest controversy tells us about the future of math

OpenAI announced that its AI agents solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. These problems are among the most important unsolved mathematical challenges, selected by the Clay Mathematics Institute in 2000, with a $1 million prize for each solution. The Navier–Stokes equations describe how fluids like water and air move over time, but mathematicians did not fully understand whether these equations could break down under certain conditions, predicting impossible states such as infinite fluid velocity. Before OpenAI’s announcement, only one other Millennium Prize Problem had been solved. OpenAI’s solution was achieved using an internal model that outperforms its publicly released Astra model, launched just one week prior. The company stated it would not claim the $1 million prize.

OpenAI’s announcement was overshadowed by accusations that it used the work of NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge without proper credit. Buckmaster posted a proof on Mastodon showing that a simplified version of the Navier–Stokes equations can break down, a major step toward solving the Millennium Problem. He claimed that OpenAI employees approached him with two options: either he and Alpöge could publish their work first, allowing OpenAI to publish its solution the next day, or they could collaborate on a paper excluding Alpöge due to his affiliation with Anthropic, OpenAI’s rival. Buckmaster also asked whether OpenAI’s models had accessed transcripts of his and Alpöge’s work, which OpenAI denied. OpenAI’s chief research officer, Mark Chen, later denied any improper access to Buckmaster and Alpöge’s transcripts.

The Navier–Stokes problem has been approached using a method pioneered by mathematicians Diego Córdoba and Luis Martínez-Zoroa. Both Buckmaster and OpenAI’s teams used this approach, raising questions about whether OpenAI’s models were influenced by Buckmaster and Alpöge’s work. Javier Gómez-Serrano, a mathematics professor at Brown University, noted that while independent discovery is possible, it is also plausible that Buckmaster and Alpöge’s research inspired OpenAI’s agents. If OpenAI’s models did rely on their work, it highlights the critical role of human research taste—the ability to identify promising research directions—in guiding AI toward breakthroughs. This suggests that human mathematicians may still play an essential role in steering AI toward solutions.

While Buckmaster and Alpöge collaborated for nearly a year using publicly available AI models, they did not achieve a full solution to the Navier–Stokes problem. In contrast, OpenAI’s team brute-forced a solution in just a few days using an internal model, but at a massive cost. Sébastien Bubeck and Mark Chen revealed that the team ran approximately 10,000 AI agents concurrently, incurring expenses in the millions of dollars. This disparity underscores the growing divide between frontier AI companies, which have the financial and computational resources to tackle complex mathematical problems, and individual mathematicians or smaller research groups, who lack such resources.