OpenAI’s Navier–Stokes Claim: Is This What AGI Looks Like? with Emad Mostaque

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Brian Keating (1:30)

Welcome everybody. We have an emergency podcast. I don't do many of these. It's not entirely clickbait to say that we have an emergency situation going on.

Right now in the deep annals of mathematics, the foundations of mathematics, and there's no one I'd rather talk to about this than my friend, Emad Mostaque, who's joining us all the way from London. How are you, Emad, on this late evening for you or early afternoon for you? Whatever the case may be.

SPEAKER_1 (1:55)

I can't do the conversion too early for me.

Emad Mostaque (1:58)

Yeah, it's the mid-afternoon. I'm feeling a bit sleep deprived after the excitement of the last 24 hours or so.

Brian Keating (2:04)

Yeah, it hasn't even been 24 hours. It's been 21 hours. I looked at the timeline. I've looked at some of the constraints and the complaints and what people are saying about it. So this is exciting. So we're going to talk about OpenAI's claimed solution to one of the millennium problems, which has lasted since the, I would say, the early part of the previous millennium when the Clay Mathematics Institute has provided a gauntlet of challenges for mathematicians and other assorted geeks and dweebs and nerds to go through. Some of them impossible seeming, some of them quite possibly solved already. So today we're going to talk about the Navier-Stokes equation.

I should say, I put a link below to a video I did yesterday. I actually recorded it a long time ago with Terry Tao, his thoughts, some of his ideas that he had convinced me of about how AI would approach this very situation. This is one of his fields, he has many fields of expertise, but this is certainly one of them. And that was the blow up or singularity in a finite time of these very interesting equations that are governed by very simple laws of physics. And I thought we'd start off with what your take on the Navier-Stokes equation is, maybe some of the applications to it, although you are a much more theoretically inclined than certainly even I am, but maybe you can break it down. What is the Navier-Stokes equation? And what was your first reaction when you heard this yesterday? For me, it was like a Higgs boson like moment. I woke up the kids, I went into my research group meeting and all my students and post docs were so excited about it.

What does it mean to you and first off, what is it?

Emad Mostaque (3:43)

Yeah. So we have the Navier-Stokes Fluid equations governing fluid dynamics in the real world as it were, so kind of our De Sitter type world.

And this specific group of equations is compressible fluids in R3. So as you head towards the Galilean kind of more classical world, heading towards a continuous limit. Will fluids move normally or do you get blowups or singularities, where it can suddenly start accelerating and then you just have a cup of tea blowing up, shall we say?