OpenAI has announced a major breakthrough in mathematics, saying one of its internal AI systems has produced a solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. 

The question has remained unresolved for around 90 years and is linked to how fluids such as air and water move.

The Navier-Stokes equations are fundamental to fluid dynamics and are used in areas ranging from aircraft design and weather forecasting to studying blood flow. The central question is whether a smooth three-dimensional fluid can develop a singularity, where fluid velocity becomes unbounded in a finite period of time.

OpenAI said its system produced an analytical proof showing that an initially smooth fluid at rest can develop such a singularity in finite time. The company also produced a formalised version of the proof in Lean, a programming language used to verify mathematical arguments. OpenAI said this resolves the problem under one of the formulations included in the official Millennium Prize challenge.

The scale of the AI effort was also unusual. OpenAI said it used a multi-agent system involving around 10,000 concurrent AI agents. The agents generated about 2.7 million messages and used roughly 130 billion output tokens while working on the Navier-Stokes problem. The initial solution was produced after about 88 hours, followed by another 17 hours of Lean verification.

However, the announcement has already attracted debate within the mathematics community. Researchers Tristan Buckmaster and Levent Alpöge were working on related problems around the same time, leading to questions over originality and recognition. 

OpenAI has denied accessing their specific user data and said its proof is significantly different from their work.

OpenAI has also said it does not intend to claim the $1 million Millennium Prize. Instead, the company is presenting the achievement as evidence of how quickly AI systems are advancing in complex scientific research.

If independently validated by mathematicians, the development could become an important milestone for AI-assisted scientific discovery, showing that advanced AI systems may increasingly contribute to problems that have remained beyond human solution for decades.

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