OpenAI announced on September 5, 2026, that it has found a solution to a long-standing mathematical problem related to the Navier-Stokes equations, which describe fluid movement. The company utilized approximately 10,000 AI agents to solve the problem in 88 hours. This problem has been unresolved for 90 years, with significant aspects lacking proof. OpenAI described the solution as a 'milestone' in AI development, although it has not yet been independently verified or accepted by The Clay Mathematics Institute, which oversees the Millennium Prize for solving such mathematical challenges.
The new AI model, which OpenAI began training at the end of August, demonstrated advanced mathematical capabilities. Despite the rapid progress, OpenAI clarified that it does not intend to claim the Millennium Prize for this result. The AI bots exchanged nearly 3 million messages and utilized 130 billion output tokens during the process, with an estimated cost of around $10 million for the computational resources used.
OpenAI's announcement has sparked some controversy, particularly from Tristan Buckmaster, a mathematics professor at New York University, who claims that he and a colleague were also working on solutions to the same problem and that OpenAI was aware of their progress. Buckmaster stated that he found out about OpenAI's interest in their work shortly before the company's announcement. OpenAI acknowledged the concurrent work of Buckmaster and his colleague, stating that they had not accessed any of their data and that their proofs differ significantly.