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I recently read some exciting news: OpenAI says its AI system has solved the famous Navier–Stokes existence and smoothness problem, one of the hardest questions in mathematics.

So, what are the Navier–Stokes equations? In simple words, they describe how fluids move. They help scientists study air around airplanes, water in oceans, weather systems, and even blood moving through our bodies.

The problem is difficult because fluids can behave in incredibly complicated ways. A smooth flow can suddenly form a tiny, violent swirl called a singularity. Mathematicians have spent about 90 years trying to prove whether this can happen in three-dimensional fluids. Even viscosity, which normally makes fluid motion smoother, does not make the mathematics easy.

This problem is one of the seven Millennium Prize Problems. The Clay Mathematics Institute offered a prize of $1 million for a correct solution. However, it is important to clarify one common misunderstanding: there is no Nobel Prize for solving this problem. Nobel Prizes are awarded in areas such as physics, chemistry, and medicine, while this is a mathematics prize.

According to OpenAI, its internal AI system used around 10,000 cooperating AI agents. They explored many possible approaches, shared useful ideas, and eventually produced both a written proof and a computer-checked version written in Lean. OpenAI says the proof shows that a smooth fluid can develop a singularity in a finite amount of time. The key idea is a vortex that spirals inward and stretches like spaghetti while its speed grows dramatically.

One surprising fact is that the AI reportedly found the result in about 88 hours, with another 17 hours used for verification. The agents exchanged about 2.7 million messages and produced around 130 billion tokens.

This does not mean that computers have replaced mathematicians. The result still needs careful review by independent experts. But if the proof is confirmed, it could become an important moment in the history of mathematics—and a fascinating example of how AI may help humans explore problems that once seemed impossible.

Source: OpenAI’s announcement
Source: Wikipedia: Navier–Stokes equations