Here is how to understand OpenAI’s major mathematical breakthrough

One of the trickiest problems in mathematics has fallen at the hands of an advanced AI model. Following the announcement that OpenAI has resolved one tantalising aspect of the Navier-Stokes equations, researchers are now urgently trying to understand its implications.

The Navier-Stokes equations were first written down around 200 years ago and describe the behaviour of fluids. They have been instrumental in everything from building better airplane wings to creating effective artificial hearts.

Yet, our understanding of the equations is so limited that resolving a relatively simple question about them is one of the prestigious Millennium Prize Problems, where a solution means a $1 million reward. That question asks whether the Navier-Stokes equations always work or if they sometimes break down and no longer make sense.

“The equations themselves are so simple, but we understand so little,” says John Evans at the University of Colorado Boulder.

The team at OpenAI has found that the equations do sometimes fall apart, finding situations known as “blow-ups”, where the speed of part of the fluid suddenly becomes infinity. It would be like an infinite whirlpool suddenly appearing in your bath. The OpenAI team found the answer thanks to more than 10,000 AI agents working together in different configurations. About 88 hours later, they had a solution.