Scientific American: ‘AI may have just solved a million-dollar math problem’—and the field may change
Scientific American ● Covered by 18 sources
AI may have cracked a $1 million math problem tied to fluid flow. If it holds, the Navier-Stokes field may need a rethink, and credit is already messy.
Based on reporting by Scientific American — read the original for the full story.
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Today could end up being remembered as a turning point in mathematics, or at least in the way mathematicians use AI. According to a statement from Tristan Buckmaster, an artificial intelligence system has reportedly solved one of the Clay Mathematics Institute’s six open million-dollar problems: the Navier-Stokes equations, which describe how fluids move.
That matters because the question has sat at the edge of what math can prove for two centuries. The issue is simple to state and hard to settle: do these equations always describe fluid motion correctly, or can they produce mathematical blowups that real fluids would never show? The Clay Institute has put $1 million on a proof either way.
Buckmaster said he and Levent Alpöge, a mathematician and Anthropic employee, had already made major progress using an approach called forcing, which focuses on a part of the Clay problem many researchers usually ignore. He said rumors of that work reached OpenAI before the pair could publish. From there, according to Buckmaster, OpenAI used its own large language model to finish the job with a single prompt. OpenAI did not immediately comment, and later denied the allegations at a Tuesday press conference.
The path to this point runs through the Euler equations, the simpler, frictionless cousins of Navier-Stokes. Buckmaster said he and Alpöge proved on August 15 that the Euler equations blow up, then verified the proof in Lean, although the English explanation from the models was hard to read. They then tried to clean up the argument so other mathematicians could follow it. After that, Buckmaster said, OpenAI’s team pushed the forcing idea further and claimed the full Navier-Stokes result over the weekend.
Now the field is stuck with a very modern problem: the Clay problem may be solved as written, while some experts may still argue the forcing-based proof only works because of a loophole in how the problem is phrased. Buckmaster wants Martínez-Zoroa and Córdoba credited for the key idea, even saying Martínez-Zoroa deserves a Fields Medal. However this shakes out, the bigger story is obvious enough: AI labs are no longer just bragging about math ability, they may be changing what counts as a mathematical breakthrough.
My take — AI-written commentary, not fact-checked reporting
This is exactly what happens when AI labs treat mathematics like a leaderboard. The real story isn’t a heroic prompt; it’s that the credit fight started before the proof dust even settled. OpenAI, Anthropic, and everyone else would rather posture than admit the obvious: the models are now powerful enough to make the old human pecking order look a bit theatrical.
Read more about this at: Scientific American