OpenAI announced on September 8 that its AI agents have solved the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. The equations describe how fluids flow over time and are foundational to fluid dynamics, but mathematicians had never fully understood whether they could break down under certain conditions.
The announcement was quickly overshadowed by controversy. NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge had been working on the same problem for nearly a year using publicly available AI models from both OpenAI and Anthropic. On Monday, Buckmaster posted a proof on Mastodon showing that a simplified version of the equations can indeed break down. Hours later, OpenAI presented a proof for the full equations using an internal model that reportedly outperforms its recently released Astra model.
OpenAI denies using the researchers' work directly but acknowledged being inspired to pursue the problem after hearing a rumor about their efforts. The episode raises deeper questions about the role of AI in mathematical research and whether frontier labs operating with proprietary models can coexist with the open collaboration norms that have long driven mathematical progress.
The company says it does not plan to claim the million-dollar prize associated with solving a Millennium Problem. Human mathematicians, meanwhile, are grappling with what it means when AI systems can tackle problems that have resisted solution for decades.