OpenAI solved one of the “Millennium Problems” (Navier-Stokes)

OpenAI announced on Tuesday that its latest AI technology has solved one of the “Millennium Problems,” a collection of important unanswered mathematical questions that aim to push the world’s top mathematicians to new heights. The announcement is another clear sign that Artificial Intelligence is fundamentally changing the upper levels of mathematics, long considered the pinnacle of human achievement. The change has excited some mathematicians, while also causing concern among others.

Over the past year, AI systems have solved several problems that have plagued mathematicians for decades. But those problems were nowhere near as complex as the one OpenAI’s technology has solved in recent days. The Millennium Problems are among the most extensively researched in the field. “This is a spectacular culmination of the progress we’ve seen over the past 12 months,” said OpenAI researcher Sebastien Bubeck of the company’s new solution.

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The company announced that one of its latest models, which has not yet been released to the public, took 88 hours to solve what mathematicians call the “Navier-Stokes existence and smoothness problem.” This problem involves a set of equations often used to predict weather. The equations describe the motion of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI’s proof claims to have defined just such a situation.

This would imply, at least theoretically, that the laws of physics themselves break down under certain conditions: that, for example, water could suddenly explode. But mathematicians and physicists do not believe that this mathematical analysis could actually lead to such an outcome in the physical world. The Navier-Stokes problem was one of seven “Millennium Problems” chosen by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI’s announcement, only one of the problems had been solved.

OpenAI reports that it was able to solve the Navier-Stokes problem by coordinating up to 10.000 AI agents, an extremely expensive process that can cost millions of dollars in computing power.

For those interested in the findings, the company has published the study in PDF format.

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