Turbulence is one of those things everyone has watched — smoke curling off a candle, rapids crashing over rocks — and yet, mathematically, nobody has ever fully explained. That gap has stood since the 1930s. This week, OpenAI claimed it made real progress toward closing it, using a swarm of AI agents. The announcement landed with excitement, and almost immediately, with controversy.
What OpenAI Claims
According to OpenAI, the company built a new internal AI model at the end of August that showed unusual aptitude for mathematics. Curious what it could do with real unsolved problems, researchers set roughly 10,000 AI agents loose on some of the most famous open questions in math, including several tied to the Millennium Prize Problems — a set of seven problems, each carrying a $1 million reward from the Clay Mathematics Institute for a verified solution.
One target was the Navier–Stokes existence and smoothness problem, part of the equations that describe how fluids move. In roughly 88 hours, OpenAI says its agents produced a proof addressing two of the four statements the Millennium Prize requires to be resolved. That’s a partial result, not a full solution — and OpenAI has been explicit that it is not attempting to claim the prize.
The scale of the effort was enormous: OpenAI says the agents exchanged nearly 3 million messages and generated 130 billion output tokens working on this problem alone, at a compute cost the company estimates around $10 million.
Why This Is a Big Deal (If It Holds Up)
The Navier–Stokes equations sit at the center of fluid dynamics — used everywhere from weather forecasting to aircraft design — yet no one has proven whether smooth, well-behaved solutions to these equations always exist, or whether they can spiral into singularities. Even chipping away at part of that problem would be a notable mathematical achievement, and OpenAI is framing the episode less as “we solved a Millennium Problem” and more as a demonstration of how fast frontier AI reasoning is improving.
Crucially, the proof has not been independently verified, and the Clay Mathematics Institute hasn’t weighed in. In pure mathematics, a claimed proof isn’t considered established until other experts have scrutinized it line by line — a process that can take months or years.
The Backlash
The announcement didn’t sit well with everyone. Tristan Buckmaster, a mathematics professor at NYU, says he and Levent Alpöge — a mathematician working at OpenAI’s rival Anthropic — had independently been chipping away at the very same problem, using OpenAI’s coding tool Codex along the way.
Buckmaster’s complaint isn’t just about timing. He says that details of their progress reached OpenAI before OpenAI’s own effort began, and that he only learned of this after OpenAI’s announcement had already gone out. He shared correspondence with OpenAI raising questions about the sequence of events, saying he felt he had to speak up rather than let a version of events he believes is inaccurate stand uncontested.
OpenAI’s response, published the same day, praised Buckmaster and Alpöge’s “concurrent work” as remarkable, and said it never accessed their work through any channel before it was made public. The company did leave a narrow door open, however, acknowledging that anonymized data from their use of OpenAI’s products might — though it considers this unlikely — have influenced its models indirectly. OpenAI also emphasized that its proof and Buckmaster and Alpöge’s differ, including in the specific results each establishes.
The Bigger Picture
Strip away the dispute over credit and timing, and what’s left is a genuinely interesting data point about where AI reasoning stands. Whether or not this particular proof survives peer scrutiny, the fact that a company could point 10,000 AI agents at an untouched piece of a 90-year-old problem and get something publishable in under four days says a lot about where things are headed.
At the same time, the controversy is a reminder that AI-assisted mathematics research raises real questions about attribution, data provenance, and trust — especially as AI labs compete to be first to claim breakthroughs. As independent mathematicians begin reviewing OpenAI’s work, and as the dispute with Buckmaster and Alpöge plays out, this story is likely far from over.