WASHINGTON (dpa-AFX) - OpenAI says an internal artificial intelligence system has produced a proof showing that the three-dimensional Navier-Stokes equations can develop a singularity in finite time, potentially resolving one of the seven Millennium Prize Problems in mathematics.
The Navier-Stokes equations describe how fluids move and are widely used in areas such as aircraft design, weather forecasting and blood-flow research. The longstanding problem asks whether a smooth fluid flow can remain smooth indefinitely or instead develop a singularity where fluid velocity becomes unbounded in a finite period.
According to OpenAI, its system found a solution involving a vortex that spirals inward while becoming increasingly stretched. Although the velocity grows without bound, the fluid's total energy remains finite.
The company said the mathematical terms governing acceleration, pressure, momentum transfer and viscosity become increasingly large but cancel each other in a precise way, while the external force applied to the fluid remains smooth.
OpenAI said the result was produced by a multi-agent system involving around 10,000 concurrent agents. The agents generated about 2.7 million messages and used roughly 130 billion output tokens while working on the Navier-Stokes problem. The solution was reached on September 5, followed by about 17 hours of Lean formalisation and verification.
The company said the proof establishes statements C and D in the official Millennium Prize formulation.
However, OpenAI is not seeking the $1 million prize and described the result as evidence of accelerating AI capabilities rather than a final milestone.
Copyright(c) 2026 RTTNews.com. All Rights Reserved
Copyright RTT News/dpa-AFX
© 2026 AFX News
