Earlier this month, OpenAI announced that it had found a solution for one of the biggest unsolved problems in math, the Navier-Stokes equations, by directing 10,000 of its powerful AI agents to work on the enigma for 88 hours straight. It was an occasion fraught with controversy, however, as mathematicians accused the company of essentially stealing their work.
That controversy is still rippling through the math world. But what has the AI’s solution taught us? Not a lot, as it turns out, because the proof it wrote, while technically correct, is borderline incomprehensible.
“So far it’s been very difficult to really extract any human understanding from this new AI proof,” James Maynard, an Oxford mathematician, told NPR.
“The paper is not written for humans,” echoed Javier Gómez-Serrano, a mathematician at Brown University who uses AI in his own research. The AI’s proof could help the field after “some serious re-writing,” he added, but “as of today, the paper doesn’t teach us much.”
The Navier-Stokes equations mathematically describe how fluids, ranging from a rush of wind to the churn of ocean currents, move and behave. They’ve been used for nearly two centuries with reliable results, but why they work remains something of a mystery. Scientists have been eager to push the equations to their limits and see if their predictions could reach a breaking point where they describe a scenario that makes no sense in the real world. Reifying the equation’s importance, the Clay Mathematics Institute in 2000 listed the Navier-Stokes as one of its six Millennium Problems, with the prize for solving it at $1 million.
OpenAI claimed that its swarm of AI agents identified a scenario in which the fluids accelerate to an infinite velocity, creating a “blow up” or singularity — something, of course, that’s impossible in the physical universe.
Hours before the announcement, NYU mathematician Tristan Buckmaster, who had been working on the Navier-Stokes problem for years, accused OpenAI of jumping on his work without notice or permission, and thereby essentially pilfering his ideas by pushing them over the finish line. He claimed that OpenAI’s work followed a similar path to his own, which he says that no one else in the field was pursuing. Because he’d been using OpenAI’s Codex tool to help with his research, he insinuated, OpenAI may have secretly accessed his notes. When he approached OpenAI about this, he claims that the company said it would credit him on its paper if he dropped his collaborator, Levent Alpöge, who was working at Anthropic.
OpenAI denied the allegations but admitted that it “cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
There’s also some groaning about the Navier-Stokes problem OpenAI says it solved. To earn the Clay Institute’s Millennium prize, mathematicians could solve either the “forced” or “unforced” version of the problem. The forced version involved an external force like gravity applied to the fluids. As laid out in a recent Scientific American piece, experts are chiefly interested in finding a purer scenario where the equations “blow up” without an external force and only with the forces within the fluid. OpenAI’s solution, however, relies on an external force. More than that, a recent proof posted by mathematicians contends that OpenAI’s solution can never lead to solving the full problem.
“The most important problem is unsolved,” Luis Silvestre, a mathematician at the University of Chicago, told SciAm. “The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.”
Still, mathematicians are in agreement that, however technical it may be, OpenAI’s solutions are valid, even if it’ll take many more weeks to unpack the AI’s ramblings.
The post Mathematicians Can’t Make Sense of How OpenAI’s Agents Solved One of the Toughest Math Problems Because the AI’s “Proof” Is Borderline Incomprehensible appeared first on Futurism.
