OpenAI announced that it had solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Problems in mathematics, with the help of a computer. In a preprint published on 8 September, the San Francisco, California-based company reported that it had presented a solution showing that the Navier–Stokes equations, the most widely used physical model of fluids, can break down. Each of the problems selected at the beginning of the twenty-first century by the Clay Mathematics Institute, based in Denver, Colorado, carries a US$1 million prize.
OpenAI computer scientist Ven Chandrasekaran said the solution showed that some fluids that are initially completely normal could reach infinite speed in a finite amount of time according to the equations. The fact that this is physically impossible in real liquids or gases indicates that the equations may not reliably reflect physical reality under certain conditions. Clay Mathematics Institute president Martin Bridson described the result as a significant development, while Luis Martínez Zoroa of CUNEF University said he found the work noteworthy.
OpenAI researchers tested their new artificial intelligence prototypes on six of the unresolved Millennium Problems. The company directed its resources toward Navier–Stokes on 1 September amid rumors that Levent Alpöge and Tristan Buckmaster had solved a version of the problem using Anthropic models. Alpöge and Buckmaster announced on 7 September that they had reached an infinite-speed result for inviscid fluids; they used the Claude, Codex and Astra models in their work. Anima Anandkumar and her colleagues at the California Institute of Technology also published a solution for the inviscid problem on the same day, using a physics-informed neural network.
OpenAI solved the simplified question in 50 hours with 1,000 artificial intelligence agents; it deployed 10,000 agents for the full problem.
Why it matters
The significance of the claim lies not only in an artificial intelligence system producing an answer to a difficult question, but also in raising the question of under what conditions a mathematical proof should be accepted. However, the result has not yet been verified by independent mathematicians; it is therefore too early to conclude that the problem associated with the Clay Mathematics Institute’s prize has actually been solved. The use of different tools and scopes for the simplified question and the full problem means that it must be clarified which version the result presented definitively covers. Competing studies published on the same day and results based on different artificial intelligence models show that the debate has not been settled by a single company’s announcement; the real test will be whether the method and result withstand independent review.
Background
OpenAI is not a new name in the FikirPilot archive: we have published 31 reports mentioning the name in the past 90 days; the most recent was dated 13 September 2026.