Everything is cooked, price-performance, and Emad on how the solution came together

Yeah. Uh yeah, we've talked about cooking math, char-broiling math and physics. Everything is cooked at this point. Everything is cooked. It's just a matter of time.

Also, a lot of people are going to be intimidated by that $6 million number, but keep in mind that we're predicting 100x inference time — this is all inference time compute, not training time. And we're predicting 100x price-performance improvement between here and the end of the year. And it could be more like a million-x next year. So, take that — you know, it could be six bucks within a year and a half to do that exact same thing.

You want to talk about what Navier-Stokes means in real life to real people?

Yeah, I mean, kind of — Alex said, this is an idealized kind of scenario because it's not the full algebra as it were. So it's the idealized one where you go down and you drop a dimension from reality. Um, that causes a degenerate algebra which has things like commuting, time translations and others. But it's a very hard problem. It's one of the hardest of all time. Uh, Terence Tao, one of the top mathematicians, literally focused almost all his time on this.

Um, what happened is that there were rumors about a month — a week ago — that this had been solved and people [were asking], is it Anthropic, is it OpenAI and others. On August 28th, um, Noam Brown at OpenAI said in a reply to someone — they said, have you solved a Millennium Prize problem? He's like, no, we've thrown loads of compute at it, like nothing's happened. In the post today they said on August 28th we started training a new model that got really good at math, and then on September 1st they pointed it at this and then it solved it.

But more than that, I've been talking to buddies at OpenAI. This model has solved a lot more problems. It's solving problems quicker than anyone can ever see. Um, I think I shared a chart — again this is like live — that shows that on open math it literally doubles the solving rate, but it's figuring out things that nobody has seen before.

Anthropic and an independent mathematician, a professor at New York, I think, um, had a solution to a smaller problem, which is the Euler blowup, which is kind of a slightly easier problem. It's still very, very hard. Um, and OpenAI thought that it could have been that, and so they reached out, and I talked to like Sebastien Bubeck, who kind of leads this. There's a whole hoo-ha about attribution this morning that's now getting cleared up.

But then when OpenAI kind of looked at it, they were like, well, that's that solution, this is the Navier-Stokes solution, and it's bitter-lessoned. You used to be able to get AI better by applying more compute to it. Now it seems like you can do that for any verifiable domain. I think that's the headline with this new type of model that only started training 9 days ago. So they figured out a new type of post-training, it seems. And again, people inside OpenAI are like, oh my God, what's happening now? These things are falling one after the other. It's like when you reach that capability threshold of going from a crap website to a good website from your coding agent. It's that, but for math and physics.

And you know, we've been hearing about it for the last few days. Like, I put out one of my physics results, a very beautiful one about chirality and the standard model. It's like very nice, but I was like, eh, I'm going to get that first before everything gets solved. And I think that it won't be a question of 2 years now. It'll be a question of much shorter than that.

The other thing that I think is very interesting is there was actually one more solution of a Euler blowup by, I think it was — was it Princeton? — using physics-inspired neural networks. That probably has more practical use than this one. But this one's an example of just now problems that are really complicated and have troubled us for ages and now tractable just by applying more compute to what seems to be a new breakthrough in model capability.