The week that changed maths for ever
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What breakthrough did OpenAI achieve in solving a century‑old mathematics problem?
This is the Guardian.
Did you miss what could be the biggest science story of 2026? Last week, OpenAI announced that it had solved a major problem in mathematics, one that comes with a million dollar reward. The news was quickly buried under fears that AI will end humanity, but it's worth revisiting. The Navy Stokes problem stood for ninety years, but it took ten thousand AI agents just eighty-eight hours, that's less than four days, to reach their solution. It left mathematicians reeling. А содей the week that changed maths forever. From The Guardian, I mean sample of this is Science Weekly.
Professor Colveroni Dougle, you're head of pure mathematics at the University of St Andrews. First of all, what are the Millennium Prize problems and where do they fit into the work mathematicians do?
So the Millennium Prize problems are a collection of problems released by the Clay Maths Institute to celebrate the year 2000. And they were picked as a set of seven problems. They span mathematics. They're all very hard. They've all been open for a while. And the Clay thought that focusing attention on them would lead to the development of lots of interesting mathematics. So it's not just the problem itself, it's the sense that working towards that would result in lots of other useful things. Until two weeks ago, only one had been solved. Um now in the last few days, potentially two have been solved.
And why are the problems themselves important? I mean, do the solutions have practical value for society or what have you, or for mathematics?
So I think it varies from problem to problem. And I think it depends on what kind of solution is found. So for example, the Navier Stokes one, which has been in the news just recently, is somewhere in between. I mean it's It's about modeling fluid flow and and hence also airflow. And that's very important for all sorts of engineering applications. But it's a question about whether our current model ever breaks down. So it's not clear that having a setup where it breaks down immediately is going to result in anything very practical.
What are the Millennium Prize problems and why do they matter to mathematicians?
What was your reaction when you heard that OpenAI had had solved the Navier Stokes problem?
I was very, very, very surprised. I thought we were years away from AI being able to do that kind of thing. And so Yeah, I I got told it's standing in a common area just outside my office by a junior colleague and I was like, oh yeah, and then went home to read about it.
And what does that sort of trigger in your mind? I mean, are you wondering what's next? And and how are you feeling about the fact that this is, you know, this is an AI company that's done this with uh an in-house model?
I'm extremely unhappy that it's been sold for advertising purposes, to put it mildly. So, I mean, it's exciting that it's being this kind of progress is occurring. Um It's terrifying thinking how much this is gonna change how we day to day do our jobs, but at the moment we don't quite know how it's gonna change how we day to day do our jobs. So Um The sort of models one can play with for free on the internet are not solving these kind of problems. And you're not going to solve them with the kind of access you could get for just a few hundred dollars. We're talking millions of dollars, um, which most mathematicians don't have in their grants. We tend to work on problems for very long periods of time, so it's made planning extremely difficult.
I'm currently trying to finish a paper I've been working on for about six years, um, and that's not unusual. And so when I started it, ChatGPT had barely been bought.
How do we know that the AI's solution to that Navier Stokes problem is is correct? Does it matter how important is it for mathematicians to understand the solution that these AI agents have come up with?
My understanding is that they've released enough that some people are saying it's correct. It's really important that we understand why. So the question was, do these equations ever break down? And the answer seems to be yes, they can be made to break down in a particular situation.
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Chapters
7 chapters
1
What breakthrough did OpenAI achieve in solving a century‑old mathematics problem?
0:00–2:37
2
What are the Millennium Prize problems and why do they matter to mathematicians?
2:37–4:48
3
How did Professor Colva Roney‑Dougal react when she heard AI had solved Navier‑Stokes?
4:48–7:55
4
How can we verify that an AI‑generated Navier‑Stokes solution is correct?
7:55–10:14
5
Why is the AI breakthrough compared to Deep Blue’s chess victory and what does it mean for maths?
10:14–12:46
6
Why did 25 Fields Medalists sign an open letter warning about AI’s impact on mathematics?
12:46–15:29
7
What new norms and hurdles must the mathematical community address in the AI era?
15:29–15:39
Speakers
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