OpenAI claims huge maths breakthrough on a famed ‘Millennium Problem’

On 8th September, OpenAI announced that its artificial intelligence has solved a famed mathematical puzzle known as the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The San Francisco-based company stated that its AI has generated a solution indicating that the equations governing the motion of fluids can break down and lead to infinite speed in a finite amount of time.

This behavior contradicts the physical reality, as such infinite speeds are impossible for real fluids. Mathematician Martin Bridson, president of the Clay Mathematics Institute, commented on the significance of the breakthrough. OpenAI researchers tested their latest AI prototype on all six unsolved Millennium Problems, but focused on the Navier–Stokes problem after rumors circulated about mathematicians Levent Alpöge and Tristan Buckmaster potentially solving a version using AI models from Anthropic.

On 7th September, Alpöge and Buckmaster released a paper suggesting a solution to the fluid equations achieving infinite speed, but in a simplified case with no viscosity. Anima Anandkumar and her team at the California Institute of Technology also released a solution for the zero-viscosity problem using a physics-informed neural network.