OpenAI uses internal models to solve the Navier-Stokes equation problem, sparking academic controversy

In September 2026, OpenAI announced that its team used the unpublicized internal Astra model and 10,000 concurrent agents to successfully solve the problem of the existence and smoothness of the Navier-Stokes equations, which has plagued the field of mathematics for approximately 90 years. This problem is one of the seven Millennium Prize Problems with a prize of $1 million since 2000. OpenAI began training on August 28 and achieved a solution after about 88 hours on September 5. The solution was then formally verified over 17 hours, during which 4.9 million messages were exchanged and approximately 300 billion output tokens were used. Tristan Buckmaster, a professor at New York University, and his collaborators had spent nearly a year studying this problem and made a breakthrough on August 15. They subsequently accused OpenAI of cheating and published a version of their research results. OpenAI responded that its model did not access user data and that the proven results were significantly different from those of Alpog and Buckmaster.