OpenAI claims to have solved part of a 90-year-old mathematics problem using an advanced internal artificial intelligence model and a swarm of 10,000 autonomous AI agents. Working concurrently for about 88 hours, the system targeted the Navier-Stokes equations, which describe how liquids and gases flow and remain one of the most elusive puzzles in fluid dynamics.
The Navier-Stokes existence and smoothness problem is one of seven Millennium Prize Problems established by the Clay Mathematics Institute, carrying a $1 million reward for a complete solution. OpenAI reported that its AI agents exchanged nearly 3 million messages and generated 130 billion tokens of output to resolve two of the four key statements required by the prize rules. The company stated that the computation cost roughly $10 million and clarified that it does not intend to claim the prize money. The proof has not yet been independently verified by the mathematics community.
The announcement has stirred debate within the research community over timing and data usage. Just before OpenAI released its findings, New York University mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published related work on the same problem. Buckmaster raised questions about whether OpenAI's internal system learned from session data they had submitted while using OpenAI's Codex tool for their own research.
OpenAI denied accessing specific user data for the solution, asserting that its proof differs significantly from the work of Buckmaster and Alpöge. However, the company acknowledged it could not entirely rule out that de-identified user data was included in model training. OpenAI team member Sebastien Bubeck also emphasized that the two research teams reached different precise results through distinct mathematical routes.