OpenAI claims maths breakthrough on a famed 'Millennium Problem'

The motion of fluids is described by the Navier–Stokes equations, the focus of one of the thorniest problems in mathematics. Credit: Kertlis/Getty

For the first time, a truly major open problem in mathematics has been solved by computer, according to OpenAI, which says it has cracked one of the ‘Millennium Problems’ related to the motion of fluids.

The artificial-intelligence (AI) company in San Francisco, California, announced on 8 September that it has generated a solution to the most commonly used physical model of fluids — the Navier-Stokes equations — showing that they can break down. Whether or not this could happen was one of the seven ‘Millennium Problems’ asked by the Clay Mathematics Institute at the turn of the twenty-first century. Solutions come with a prize of US$1 million.

“It is certainly an exciting day, as we contemplate the announcement of major advances in the human understanding of mathematics,” says mathematician Martin Bridson, president of the Clay Mathematics Institute.

“Our proof does show that there exist fluids which start out perfectly normal, and under the Navier-Stokes equations, actually achieve infinite speed in a finite amount of time,” said OpenAI computer scientist Ven Chandrasekaran in a press briefing.

Because this behaviour is physically impossible for a real fluid — such as a liquid or a gas — it suggests that under certain circumstances, the equations may not be a reliable mirror of physical reality, Chandrasekaran said.

“This is, to me, the spectacular culmination of the arc we have seen over the last 12 months,” as AI solved problems of increasing complexity and importance, OpenAI mathematician Sebastian Bubeck told reporters.

A swirling vortex — involved in the solution to the Navier–Stokes existence and smoothness problem. Credit: OpenAI

The OpenAI researchers said they had been testing the ability of their latest AI prototype on all six unsolved Millennium Problems.