OpenAI cracked a $1 million math problem in 88 hours and sparked a credit fight

An AI system deployed by OpenAI has produced a formal, machine-verified proof resolving one of mathematics’ seven Millennium Prize Problems — the Navier-Stokes equations, a set of differential equations governing how fluids with friction move through space. The result closes a problem that has been officially open for more than two decades, with a $1 million prize attached, and informally unresolved since the equations were first written down almost two centuries ago.

The Navier-Stokes equations are not abstract curiosities. They underlie the physics of virtually every fluid: how weather patterns form, how blood moves through an artery, how an aircraft wing generates lift, how water churns over a riverbed. What mathematicians could not determine was whether these equations always produce orderly solutions — or whether they can reach a point where the math breaks down entirely, generating what mathematicians call a singularity: a value that spirals toward infinity. The Clay Mathematics Institute offered $1 million to whoever could answer that question definitively.

OpenAI’s answer is the second option — the equations can break down. The company deployed roughly 10,000 autonomous AI agents that exchanged approximately five million messages over 88 hours, collectively constructing a proof that singularities can form in the three-dimensional Navier-Stokes equations. The proof was then verified using Lean, a formal proof assistant that checks mathematical arguments step by step, removing the possibility of human error in the verification process. The computation cost several million dollars.

The solution is rigorous by formal verification standards. But rigor is not the same as authorship, and that distinction is where the story becomes contested. The analytical techniques at the core of the proof were developed not by an AI but by Diego Córdoba, a mathematician at the Institute of Mathematical Sciences in Madrid, and Luis Martínez-Zoroa, a recent doctoral graduate working in Córdoba’s group. Charles Fefferman of Princeton, one of the world’s leading experts on the problem, said plainly that the true intellectual heroes of the breakthrough are those two researchers. Tristan Buckmaster, a mathematician at New York University who led a competing team that reached similar conclusions on related problems, argued that Martínez-Zoroa deserves a Fields Medal — the highest honor in mathematics — for the underlying creative work.

What OpenAI’s agents did was take those human-developed ideas and execute the formal verification at a scale and speed no human team could match. Whether that constitutes solving the problem depends on what solving means. The headline version — AI defeats a nearly two-century-old mathematical mystery — is not wrong. It does leave out the people who generated the core insight. OpenAI’s announcement credited the AI agents prominently; Córdoba and Martínez-Zoroa received a footnote. That asymmetry has generated significant pushback from the mathematical community.

It is also worth noting what the result does not change in practice. The singularities identified in the proof exist in an idealized mathematical world where fluids are continuous. Real fluids consist of discrete molecules; the equations are an approximation of physical reality, not a direct description of it. Finding a mathematical blow-up does not mean that any real fluid anywhere will suddenly accelerate to infinite speed. The engineering models that pilots, meteorologists, and cardiologists rely on are unaffected.

The Clay Mathematics Institute has not yet officially awarded the $1 million prize. A formal human review — verifying that what was proven is precisely what the problem asked — remains pending. The institute applies rigorous criteria; the previous Millennium Problem to be resolved, the Poincaré conjecture, required three years of community review before any prize was confirmed. Whether Córdoba and Martínez-Zoroa receive formal recognition, and how the $1 million might be distributed between a corporation and the humans whose mathematical ideas made the proof possible, are questions the institute has yet to answer.

Tags: artificial intelligence, OpenAI, mathematics, Clay Mathematics Institute, Millennium Prize, Navier-Stokes