OpenAI says an experimental artificial intelligence system has produced a major mathematical result on the Navier–Stokes equations after about 10,000 AI agents worked on the problem for 88 hours.

The equations describe the movement of fluids and underpin one of mathematics’ Millennium Prize Problems. Important questions about whether their solutions always remain well-behaved have resisted mathematicians for decades.

OpenAI said its agents exchanged nearly three million messages and produced about 130 billion output tokens while tackling the problem. Based on the company’s commercial pricing, the computing effort would have cost about $10 million.

However, the result should not yet be treated as a complete solution to the Millennium Prize challenge. OpenAI said its work resolved two of four required statements, while the proof has not been independently verified or formally accepted by the Clay Mathematics Institute. The company says it does not intend to claim the $1 million prize.

The announcement has also prompted a dispute over research credit. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working on related ideas, raising questions about whether unpublished work entered into AI tools could have influenced OpenAI’s research. OpenAI has denied improperly using their work and says its approach was independently developed.