OpenAI's AI Cracks a Math Puzzle That Stumped Scientists for 90 Years

In the early hours of Wednesday, OpenAI published a paper claiming to have solved one of the seven Millennium Prize Problems — the set of mathematical challenges for which the Clay Mathematics Institute offers a one-million-dollar reward for an official solution. The problem in question involves the Navier-Stokes equations, which describe the motion of fluids and gases and had puzzled scientists for roughly 90 years.

The mathematical community still needs to formally verify whether the result meets all the criteria for the problem to be considered solved, but initial reactions from experts suggest the puzzle may indeed have been cracked.

What the puzzle is actually about

The Navier-Stokes equations describe what happens to a fluid or gas once it starts moving — say, the air flowing around an airplane, water running through a pipe, or atmospheric phenomena. The equations themselves have long been a standard tool for scientists and hold no mystery on their own.

The real puzzle runs deeper: mathematicians wanted to know whether a smooth flow of fluid in three-dimensional space always stays smooth forever, or whether it can abruptly "break down" and produce what's known as a singularity — a point where some physical quantity grows without bound. Picture a vortex that keeps twisting tighter and tighter, its structure squeezing into an ever-smaller volume, until the mathematical description simply stops working.

According to OpenAI, the answer is yes — such a breakdown is possible. The system found a construction in which a singularity emerges in finite time from a perfectly smooth starting state. The company compared the result to a vortex that spirals inward and stretches out like spaghetti. One important caveat: this doesn't mean ordinary water in a glass could suddenly start accelerating forever on its own — in the solved version of the problem, the fluid is acted upon by an external smooth force, as allowed for in the official statement of the problem.

Not one chatbot, but 10,000 agents at work

What sets this work apart is that it wasn't tackled by a single chatbot but, according to OpenAI, by roughly 10,000 AI agents working simultaneously. Different groups tried different approaches and then shared their most promising ideas with one another — the company used its Codex tool to coordinate the effort.

The search for a solution took about 88 hours in total. Because a complex mathematical proof can look convincing while still containing an error, OpenAI ran the result through Lean, a formal verification system that machine-checks every step of a proof against precisely defined rules. Verifying the analytical proof took another 17 hours.

Over the course of the work, the AI agents exchanged 2.7 million messages and generated roughly 130 billion tokens of text — a scale that resembles a vast digital research lab far more than an ordinary chatbot conversation.

Around Prague, based on reporting by novinky.cz