OpenAI Said its AI Cracked a $1 Million Math Problem. A Dispute Erupted
By Cris Tolomia
The lab used roughly 10,000 AI agents to crack the Navier-Stokes problem, but rivals contested OpenAI’s account of events before the proof was published.
OpenAI published a claimed solution on Tuesday to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems — a set of mathematical questions that carry a $1 million award each. The proof was produced by an internal AI model, not human mathematicians.
Only one Millennium Prize Problem had previously been solved. The Navier-Stokes problem, which has gone unresolved for roughly 90 years, asks whether smooth three-dimensional fluid motion can break down under the equations that govern how liquids and gases move. OpenAI’s model found that it can, describing a configuration in which a vortex tightens and spins ever faster — a phenomenon mathematicians refer to as finite-time blowup — while the fluid’s energy stays bounded throughout.
According to the Wall Street Journal, OpenAI said the system deployed up to 10,000 AI agents in parallel over approximately 88 hours, with computing costs running into the millions of dollars. The company released a 165-page proof and a Lean formalization — Lean being a programming language that checks each step of a mathematical argument for logical validity. OpenAI said it does not intend to claim the $1 million prize.
Before Tuesday’s announcement, competing researchers challenged OpenAI’s account of how the work unfolded. OpenAI said its effort began September 1 after it heard a rumor, which it later connected to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After completing its own proof and Lean verification on September 6, OpenAI said it contacted the two researchers to offer a joint announcement, at which point it learned their work addressed a related but distinct problem — the forced Euler equations, not Navier-Stokes. OpenAI said it recognizes the priority of their work on that problem.
OpenAI said the AI agents did not access the researchers’ work through any means before it was released publicly, though the company said it could not rule out that de-identified data from their use of OpenAI products may have contributed to model training.
Timothy Gowers, a Fields Medal recipient who said he had not yet read the proof, told the Wall Street Journal that the result was “undeniably a big moment.”
The development follows a period of rapid AI progress in mathematics. OpenAI’s Astra model generated solutions to 10 longstanding problems across mathematics and theoretical computer science — each unsolved for at least a decade — with Lean-verified proofs. The company said the internal model used for the Navier-Stokes result is more capable than GPT-6 Astra, and that its training remains ongoing.
OpenAI said it does not view the result as a culmination but as a marker of where AI development stands at this moment.
