A math problem with a $1 million bounty may have just met its match—and the solver appears to be artificial intelligence. OpenAI says one of its models not yet available to the public solved the "Navier-Stokes existence and smoothness problem," reports the New York Times. It's one of the Clay Mathematics Institute's seven Millennium Prize Problems, only one of which had been solved prior to this week. Assuming it's confirmed, just how big of a feat is it? "Today may go down as the biggest day in math in at least two decades, if not far longer," declares Scientific American.
The Navier-Stokes equations involve the motion of fluids, and OpenAI seems to have for the first time found a situation in which the rules might break down. The Times has the mind-bending upshot: "This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode." Physicists, for the record, don't think that would ever happen in the real world. Meanwhile, the breakthrough is already mired in controversy, notes Scientific American.
Mathematician Tristan Buckmaster says he and collaborator Levent Alpoge, using Anthropic's tools and building on work by Diego Córdoba and Luis Martínez-Zoroa, had essentially cracked a key related result first. He alleges OpenAI learned of their "forcing" method, raced to extend it, and then tried to sideline Alpoge from authorship. Beyond credit fights, some experts may argue the solution exploits a loophole in how the problem was originally framed.
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