India, Sept. 8 -- 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...