OpenAI Says Its AI Solved a 90‑Year‑Old Math Puzzle – But Fellow Researchers Question the Claim

In a statement that made headlines across tech and science circles, OpenAI said an internal, still‑under‑wraps model managed to produce a solution to the Navier‑Stokes existence and smoothness problem – one of the seven famed Millennium Prize challenges – in roughly 88 hours. The company portrayed the feat as a watershed moment for artificial intelligence, even though the proof has yet to be vetted by the Clay Mathematics Institute, the body that awards the $1 million prize.

Not everyone is buying the story at face value. Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, who works for OpenAI’s rival Anthropic, have publicly raised eyebrows. Both had been tinkering with the problem using OpenAI’s own Codex tool, and Buckmaster says he learned about OpenAI’s claim only after he and Alpöge had already shared some progress among themselves.

“We quietly chose to attack Navier‑Stokes using a method that stemmed from earlier academic work,” Buckmaster explained. “It’s not something a model can stumble upon in a couple of days just by being fed the problem statement.” He added that he had not yet examined OpenAI’s full proof but felt compelled to speak out “because letting a string of unverified announcements stand would be misleading.”

OpenAI, for its part, denies having accessed any of the researchers’ private work before it went public. The company insists it only saw Buckmaster and Alpöge’s findings after they were released openly and that no specific user data was harvested to crack Navier‑Stokes. Nonetheless, OpenAI concedes it cannot rule out the remote chance that anonymized interactions with its products nudged the model in the right direction.

Sam Altman, OpenAI’s chief executive, said the firm would have “greatly preferred coordination” with the external team. He claims OpenAI even offered to let Buckmaster take the lead on a joint rewrite of the proof and to step aside for the prize. The offer, according to Alpöge, fell flat because the terms were “pretty wacky, unstrategic and unnecessary.”

According to OpenAI’s timeline, the model’s training began in late August after the system displayed unusually strong math chops. By September 1, rumors of two Millennium problems being solved spurred the company to unleash thousands of AI agents across six challenges – Navier‑Stokes, the Riemann hypothesis, P vs NP, among others. After about 50 hours, the agents made notable headway on a Navier‑Stokes‑related sub‑task, prompting the team to double‑down and swell the swarm to roughly 10 000 agents.

The swarm reportedly exchanged nearly three million internal messages, generated around 130 billion tokens, and burned computing resources estimated at about $10 million. OpenAI says the work wrapped up on September 5 and was subsequently verified by computer checks, though human mathematicians have yet to certify the proof.

For context, the Navier‑Stokes equations govern fluid flow – think air over a wing, ocean currents, or blood through veins. The existence and smoothness problem asks whether solutions that start out smooth can develop singularities (blow‑ups) in three‑dimensional space. Solving it would unlock deeper understanding in physics, engineering, and beyond. So far, only the Poincaré conjecture, another Millennium problem, has been fully resolved.

OpenAI emphasizes that it is not chasing the prize money. “Our goal in releasing this result is to report on the substantial progress of our AI models,” a company spokesperson said. “We do not intend to claim the Millennium Prize for this result.” The proof will now undergo the usual scrutiny of the mathematical community before anyone can decide whether the claim holds water.