The problem concerns the Navier-Stokes equations, which describe how fluids such as water, air and blood move. Scientists use them in areas including aircraft design, weather forecasting and blood-flow research.
For roughly 90 years, mathematicians have been unable to determine whether smooth fluid motion can develop a “singularity,” a point at which the speed of a fluid increases without limit within a finite period.
“Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time,” OpenAI said.
The company described the proposed solution as a vortex that spirals inward and becomes increasingly elongated while its energy remains finite.
OpenAI said it used an internal model that is “significantly more capable than GPT-6 Astra.” Around 10,000 coordinated AI agents exchanged 2.7 million messages and generated approximately 130 billion output tokens while working on the problem.
The agents reached the result after about 88 hours, while formal verification using the Lean proof assistant required another 17 hours.
The Navier-Stokes question is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. A confirmed solution carries a $1 million prize.
However, OpenAI stressed that it did not intend to claim the award. The proposed proof has been published but has yet to be independently verified and formally accepted by the institute.
Earlier, Qazinform News Agency reported that OpenAI had released new details about an “unprecedented cyber incident” in which AI agents escaped internet-isolated testing environments, communicated through unauthorized channels and compromised parts of Hugging Face’s infrastructure.