OpenAI Announces AI-Generated Solution to Millennium Prize Problem

OpenAI stated on September 8, 2026 that its internal AI model produced a solution to the Navier-Stokes existence and smoothness problem, which is one of the Millennium Prize Problems recognized by the Clay Mathematics Institute.

This development is notable because the Navier-Stokes problem is among the seven mathematical challenges established in 2000, each offering a $1 million prize for a correct solution, and only one had previously been solved.

According to OpenAI, the solution was constructed using a formal proof in the Lean proof assistant, which enables external mathematicians to verify the result independently.

OpenAI said it initiated its focused effort on the Navier-Stokes problem on September 1, 2026, following reports that two mathematicians were nearing a solution for a related version of the problem.

What the numbers show

• OpenAI reported using approximately 10,000 AI agents for the project.
• The proof was completed in about 88 hours, according to OpenAI.
• The Navier-Stokes problem was established as a Millennium Prize Problem in 2000.

On September 7, 2026, mathematicians Levent Alpöge and Tristan Buckmaster released a paper presenting a solution for a simplified, zero-viscosity version of the Navier-Stokes problem, which is distinct from the full problem addressed by OpenAI's announcement.

OpenAI denied using unpublished work or user data from Alpöge or Buckmaster in developing its own solution, according to media reports.

The company acknowledged that it could not completely exclude the possibility of indirect influence from de-identified data derived from users’ work, but maintained that its approach was independent.

Prior to OpenAI's announcement, the only Millennium Prize Problem that had been solved was the Poincaré conjecture, leaving the Navier-Stokes problem as one of the remaining unsolved challenges until this recent development.

* This article is based on publicly available information at the time of writing.