
OpenAI has attracted attention across the scientific community after reporting that an internal artificial intelligence system developed a proposed solution to the Navier–Stokes existence and smoothness problem, one of mathematics’ most challenging unsolved questions. The project reportedly involved approximately 10,000 AI agents working simultaneously, with the main computational effort lasting around 88 hours before additional work was undertaken to formalise the result.
The development has renewed discussions about AI’s potential to advance mathematical research, while raising questions about proof verification, research transparency and the attribution of scientific discoveries.
The Navier–Stokes equations describe how fluids, including liquids and gases, move. They are essential to numerous scientific and engineering applications, including weather forecasting, aircraft design, ocean modelling and the study of fluid behaviour. Despite their widespread use, mathematicians have yet to resolve a fundamental question concerning whether smooth solutions to the three-dimensional equations can develop singularities under the conditions specified in the problem.
The challenge is among seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000. Each carries a $1 million award for a solution that satisfies the institute’s requirements. OpenAI’s reported progress has therefore attracted considerable interest, although the company has stated that it does not intend to claim the prize for its work.
According to OpenAI’s account, the research effort expanded after the company became aware of progress on related mathematical questions. On September 1, 2026, researchers began deploying groups of AI agents to investigate several difficult mathematical problems and explore different approaches.
The agents worked in coordinated groups, with individual systems assigned specific tasks and given access to computational tools. They could also communicate with other agents within their groups, enabling multiple approaches to be explored concurrently rather than relying on a single model to develop a solution independently.
An initial result involving the related Euler equations encouraged the researchers to allocate additional computing resources to the Navier–Stokes challenge. OpenAI subsequently expanded the operation to approximately 10,000 concurrent agents. The system produced its proposed solution on September 5, following around 88 hours of work. A further 17 hours were reportedly spent formalising the proof with another AI model and the Lean proof-assistant system.
The scale of the experiment was substantial. OpenAI reported that its agents generated approximately 2.7 million messages and used around 130 billion output tokens during the Navier–Stokes investigation. Across the wider mathematical project, the figures reportedly reached approximately 4.9 million messages and 300 billion output tokens.
However, the announcement also prompted questions about the relationship between OpenAI’s work and research conducted by other mathematicians. Tristan Buckmaster of New York University and Levent Alpöge, affiliated with Anthropic, had independently made progress on a related problem involving the Euler equations.
Buckmaster raised concerns about whether information connected to the researchers’ work could have influenced OpenAI’s approach. The company denied directly accessing their specific prompts or proofs and said an internal investigation found that the relevant prompts could not have influenced its system through training. The disagreement has highlighted the challenges of establishing research priority when multiple teams investigate closely related mathematical questions.
The proposed solution must also withstand independent mathematical scrutiny. Although Lean can verify the logical steps encoded in a formal proof, specialists must still assess its assumptions, interpretation and significance. Recognition as a solution to a Millennium Prize Problem requires meeting the Clay Mathematics Institute’s publication and review requirements.
OpenAI’s experiment demonstrates how coordinated AI agents could help researchers explore difficult mathematical questions at a scale that would otherwise require considerable time and resources. Nevertheless, computational power alone does not guarantee a valid discovery. Independent verification, transparent reporting and appropriate attribution remain essential to scientific progress.
As researchers examine the implications of the reported achievement, the project has intensified debate about whether increasingly capable AI systems could reshape mathematical research and contribute to solving problems that have challenged scientists for generations.
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