OpenAI has solved the Navier-Stokes Millennium problem using $15m of AI effort

OpenAI claims one of its AI models has found a solution to the Navier-Stokes problem, one of the toughest and most enduring puzzles in mathematics, sitting on the list of Millennium Prize Problems, solutions for which come with a $1 million reward. The announcement came after an unusual flurry of activity around the problem, along with a dispute around how the work came about.

The Navier-Stokes equations describe how fluids move in space, such as air over an aircraft wing or water out of a tap. Though the equations were first written down around 200 years ago, they aren’t well understood. The question posed by the Clay Mathematics Institute for the Millennium Prize Problem is to determine if the equations always work or if there are situations where they stop making sense and start spouting nonsense, what mathematicians call “blow-ups”.

To settle the question, OpenAI first set 1000 AI agents on the Euler problem, which is a cousin of the Navier-Stokes problem and a step on the path to a full solution. It took the agents 50 hours to find blow-ups in this case. They then set 10,000 agents the task of extending the blow-ups to apply to the full Navier-Stokes problem, which took just 11 hours to finish.