Has AI cracked a $1m maths problem?

The artificial intelligence company OpenAI announced yesterday that one of their systems solved one of the most famous problem in maths. It concerns the Navier-Stokes equations, which describe the behaviour of liquids and gases. The equations are used in many real-world applications, for example in weather forecasting and designing airplanes.

To use the equations in such applications, you need to solve them. And the mathematical question was whether physically meaningful solutions to the equation always exist. The problem was deemed so important that the Clay Mathematics Institute offered $1 million for a solution.

OpenAI claims their system showed that "the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time". This means the equations predict that certain quantities involved in the fluid's motion can become infinite at particular points in space and time. And infinity isn't physically meaningful. So in some sense, the result claimed by OpenAI implies that the equations can "break".

The announcement comes at a time where the impact of AI in mathematics is hotly debated. If AI can solve long-standing, and very hard, maths problems where does that leave the field? You can read more about this debate on Plus, for example in our article from the International Congress of Mathematicians 2026, or in this recent article featuring expert in the field, Geordie Williamson. There's also been some friction surrounding the announcement and the relative contributions of AI and human mathematicians— here is a statement by the mathematician Tristan Buckmaster, who is intimately involved with the relevant mathematics. You may also want to read this statement from one of our partners, the Isaac Newton Institute for Mathematical Sciences.

While the world of mathematics checks, digests, and discusses this latest development, we asked our colleague, the well-known mathematician and broadcaster Hannah Fry, for her take on the topic. After all, Hannah worked on the Navier-Stokes equations for her PhD and is also an expert on AI. She chose to focus on what the result means for the equations:

"I know everyone is getting all excited about the proof and the scandal and the prize and the credit and the solution. But personally I'm taking a moment to mourn the equations. God, how I loved them."

We will continue to follow the developments regarding mathematics and AI closely. In the meantime, a word of reassurance. The fact that the Navier-Stokes equations can break doesn't mean that planes will fall out for the sky and weather forecasts become meaningless. The contexts in which the equations are used in practice are not affected by the result and mathematicians and engineers have found ways of dealing with the fact that they are hard to solve. So in that sense, we're safe.