OpenAI says it cracked 90-year-old, Navier-Stokes maths problem in 88 hours: Here’s what happened

OpenAI claims it has solved the 90-year-old Navier-Stokes mathematics problem in just 88 hours using a new internal AI model and around 10,000 AI agents. The problem is one of the famous Millennium Prize Problems and focuses on how fluids such as water and air behave.

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OpenAI says its AI system produced a resolution after working on different versions of the problem, but the result has not yet been independently verified. The company also says it will not claim the $1 million prize attached to the problem, even as the breakthrough has triggered controversy among mathematicians.

OpenAI’s 88-hour AI effort

OpenAI said it began training a new internal model in late August after finding that it was significantly more capable at mathematics than its previous systems. On September 1, the company said it heard rumours that two Millennium Prize Problems had been solved and decided to test its model on the remaining problems.

OpenAI deployed around 10,000 AI agents to work on the Navier-Stokes problem. The agents were divided into groups and given different versions of the problem, with some asked to find a proof and others to look for a counterexample. The groups were also allowed to communicate and share useful findings.

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By September 5, around 88 hours after the first agents were launched, the system had reached what OpenAI described as a resolution to the Navier-Stokes problem. During the effort, the agents exchanged around 2.7 million messages and generated approximately 130 billion output tokens.

The initial result was then formalised and verified using GPT-6 Astra, which took another 17 hours. OpenAI says the overall effort across the problems used millions of messages and hundreds of billions of tokens.

However, OpenAI is not claiming the $1 million Millennium Prize. The company says its work addresses the relevant mathematical problem, but the result still needs to go through independent scrutiny and has not been accepted by the Clay Mathematics Institute.

Why OpenAI’s claim has sparked controversy

The announcement has also led to questions from mathematicians. NYU mathematics professor Tristan Buckmaster said he and Levent Alpöge, a mathematician at Anthropic, had been working on related problems using AI models, including OpenAI’s Codex.

Buckmaster questioned how quickly OpenAI reached a similar result after learning about their work. He also raised concerns about whether information from their Codex sessions could have influenced OpenAI’s efforts.

OpenAI has denied accessing or using its private user data. The company said no human or AI agent involved in the project looked at user data, while acknowledging that de-identified data can be used to improve its models. It maintains that its proof was independently developed and differed significantly from Buckmaster and Alpöge’s work.