Alex reports the Millennium Prize problem solved, and the cost of solving it

Okay. Navier-Stokes, one of the Clay Millennium Prize problems, a grand challenge in math. For those who watched our New Year's predictions episode at the end of 2025, one of my predictions for this year was that AI would solve one of these Clay Millennium Prize problems. And it appears in the past 24 hours — actually in the past 6 hours, as of time of this recording — it has happened. OpenAI has a team. There were several academic teams that also either achieved it or came close. And there's probably going to be a bit of a second day story about whether there was some foul play between OpenAI and some of the frontier teams, who scooped whom, blah blah blah.

Punchline: Navier-Stokes, which is this grand challenge in math that deals with, as I put it when last we were discussing this, whether in some sense whether there's a way to stir a glass of liquid or water in such a way that a singularity pops out. Basically, can you stir a cup of coffee in such a way that you get a black hole out of it? It looks like in the continuum limit the answer is yes. And the OpenAI team, using a version that's not GPT-6 Astra but an internal more advanced model — appears it, uh, and I think we'll know more in 24 or 48 hours — appears the answer is yes. There is a way to stir a cup of coffee, an idealized cup of coffee, to get a black hole out of it. And they did it.

I can just see the headlines now. [unclear] proclaims black hole in your cup of coffee.

Surprised there's a singularity in the singularity.

Wait, can you also — like, Navier-Stokes is incredibly important for aeronautics, for submarines, for hydro. It's like artificial — it's not just about black holes and coffee. Let's talk about the —

No, but — no, but this is the point. The point of the Navier-Stokes conjecture is it hinges on whether it's possible in finite time with continuous initial conditions to achieve a singularity in an idealized fluid, and of course in the real world we don't actually have idealized fluid. Will you actually be able to create black holes in cups of coffee using this? No. But it teaches us something.

Yeah. Don't worry about black holes in cups of coffee yet. But this is just the first of many grand challenges. Like, Peter, you and I wrote in Solve Everything — like, now is the moment. You — I, if you have to pick a moment, I maintain singularity is, you know, an interval in time. But if you want to pick any sort of moment when the loud noises start, now is as good a time as any.

OpenAI reportedly was able to do this with only 10,000 agents in 88 hours with 130 billion tokens and approximately $6.5 million. 10,000 agents, 88 hours, 130 billion tokens, approximately $6 and a half million dollars of inference time compute, by at least one estimate, was all it took to solve a grand challenge in, call it, mathematical physics. And this will not be the last one. The era of grand challenges getting bulk solved by AI is here. It's now and it's going to be very exciting.