18/09/2026
For nearly 90 years, mathematicians have struggled with the Navier–Stokes equations—the mathematical language used to describe how fluids move, from air and water to weather, aircraft and blood flow.
The central question was simple but profound: can a perfectly smooth fluid suddenly develop an infinite-speed “singularity” in finite time?
Navier–Stokes became one of the seven Millennium Prize Problems in 2000.
Now, OpenAI says an internal AI system has produced a proof showing that such a breakdown can occur. The system used thousands of AI agents to explore mathematical approaches and formalised the result in Lean, a proof-verification language.
This is not just AI calculating faster. It is AI helping explore a problem that has challenged humanity for generations.
The proof still needs thorough independent verification—but the direction is extraordinary: machines are beginning to participate in the discovery of new mathematics.
OpenAI describes the result in its official announcement; independent mathematicians have also raised questions about verification and research ethics. OpenAI’s announcement, Quanta’s analysis
