OpenAI says its AI agents solved the Navier-Stokes problem, a $1 million prize question about fluid flow

What happened

• OpenAI announced, on September 8, 2026, that a swarm of roughly 10,000 coordinating agents, running an unreleased internal model over 88 hours, had produced a solution to the Navier-Stokes Millennium Prize Problem, which it described as verified in Lean.
• According to Fortune, the claimed result goes the "blow up" way: it says there are conditions under which the equations break down, rather than proving that they always stay well behaved. Neither report gives the exact mathematical setting.
• The Navier-Stokes equations describe how fluids move, and are used for everything from weather forecasting to aircraft design. The open problem asks whether they can break down under certain conditions. It is one of seven Millennium Prize problems chosen in 2000 by the Clay Mathematics Institute, which offers $1 million for the first correct solution to each. Only one, the Poincaré conjecture, has been officially solved. OpenAI said it does not intend to claim the prize.
• OpenAI published its Lean proof alongside the announcement. Lean is a programming language for proofs. If a Lean file compiles with no `sorry` placeholders and no extra axioms, a computer has checked every step of the proof, but only of the statement and definitions as written in Lean. Neither the CNN nor the Fortune report, as of its date, says that anyone outside OpenAI had checked the Lean files, or that the Clay Institute had reviewed or accepted the proof.
• Terence Tao, a UCLA mathematician widely considered one of the greatest living mathematicians, commented to CNN and on social media. His remarks, quoted below, are about how AI is being used in mathematics in general. He is also a member of the advisory group on mathematics and AI that OpenAI formed in September (see the entry on the 722 manuscripts).
• A separate dispute is running alongside the announcement. NYU mathematician Tristan Buckmaster had been working on the same problem with Levent Alpöge, a researcher at Anthropic, a rival AI company. Building on an approach by the mathematicians Diego Cordoba and Luis Martinez-Zoroa, they used AI models including Anthropic’s Claude and Codex, OpenAI’s coding tool, according to Fortune. Buckmaster alleges that after rumors circulated of their private effort, OpenAI (led on this effort by Sebastien Bubeck) produced a solution within about a week, using what he says was the same line of attack he and Alpöge had developed.
• Buckmaster also alleges he was offered a choice: publish partial results with OpenAI credited for the full solution, or claim the prize himself only if Alpöge’s name was removed, citing Alpöge’s Anthropic affiliation. He says he declined and said he would go public if OpenAI published that way, and that Bubeck then asked him, "Why would you ruin your career?" These are Buckmaster’s allegations, reported by Fortune, and they are unresolved.
• The other side, as reported: Bubeck wrote on X that "A series of false and inflammatory allegations against me are currently circulating on social channels." According to CNN, OpenAI said its work began on September 1, after hearing what it called a rumor of another Millennium Prize problem being resolved, and that it "did not see any of their work through any means until they released it publicly." In his own statement, Buckmaster wrote that he had not seen OpenAI’s proof and did not know whether their data was used: "I am not accusing anyone of anything." His allegations above, as Fortune reports them, are about credit and how he was treated.

What people said