Davide Castelvecchi in Nature:
For the first time, a truly major open problem in mathematics has been solved by a computer, according to OpenAI, which says it has cracked one of the Millennium Problems, related to the motion of fluids.
The artificial-intelligence 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 this could happen was one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute in Denver, Colorado, at the turn of the twenty-first century. Solutions to the puzzles, considered some of the thorniest in mathematics, come with a prize of US$1 million. OpenAI posted a preprint describing the result on its website.
“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.
The puzzle is known as the Navier–Stokes existence and smoothness problem.
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