OpenAI says an internal AI system has produced a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The company published its claim on 8 September, alongside a written proof and a formalisation in Lean.
The problem concerns equations used to describe fluid motion, with applications including aircraft design and weather forecasting. OpenAI says its proof shows that initially smooth fluid motion under a smooth external force can develop a singularity, where calculated speeds grow without bound within a finite time, despite viscosity.
According to the company, the successful effort involved around 10,000 concurrent AI agents. They reached the result after about 88 hours, followed by another 17 hours of Lean formalisation and verification.
OpenAI said in its announcement: “We do not intend to claim the Millennium Prize for this result.”
On 21 September, OpenAI announced that it was working with an independent mathematics advisory group to advise on reviewing and communicating emerging results. It says the group can publish its advice and its members will not be paid by OpenAI.
The mathematical result remains presented here as OpenAI’s claim: its announcements do not establish independent acceptance or a prize award.
