Grant Sanderson: prediction

Transcript context

…Can I ask you about that? Obviously, one question for AI for math is not only can it do it, but is it any good? Or is it good for anything? You were describing all the ways in which, with group theory, we’re trying to figure out random facts about the roots of different kinds of functions, and now there are all these different applications that are practical across many different fields. Do you have some sense of whether, if we just totally get to a place where the field of human mathematics is accelerated 10X or 100X and some crazy shit happens, or are we just going to be bottlenecked by other fields? I think there are some fields that probably will. It’s super spiky. With progress in algebraic number theory, it feels unlikely that that then unlocks something. But I remember talking to this mathematician who does more dynamics and PDE-solving type stuff. He was referencing that his group had some ideas. Let me see if I summarize this right. It’s like the way Boeing would make planes is that they’d make it, do a bunch of tests, and they had to disassemble it and reassemble it based on those tests. His group essentially had some insights on how to do more in simulation such that you don’t have to deconstruct and rebuild it. It saved Boeing billions of dollars or something, and then they just started funding that group. That’s much more obviously application-adjacent, because PDEs just are that. Progress in that domain, you would imagine actually does unlock some things. I don’t know if it’s these step changes, but maybe it’s more on the side of engine design becoming a little bit more fluid, or coming up with the right wing shape instead of running a whole bunch of complicated CFD. Maybe you’re able to speed up your CFD simulations because certain pure math insights make those more efficient. I bet you’d just see a lot of great incremental improvement there. It seems less likely that the massive breakthroughs in math immediately turn into this massive economic breakthrough, like you solve the Navier-Stokes problems, and then that unlocks an ability to simulate more things. But you probably will see, at those fringes, some meaningful leakage out of the pure math insights into other things. There’s a ton of people working on things like AI engineering, physical engineering, and material science. You have to imagine they’d be in a good position to look at the AI math insights and decide whether they’re relevant in some way or not. It’s another one of these things where I’m not going to sit here and put a flag in the sand predicting that there will be. But it’d be a little bit disappointing and a little bit surprising if there weren’t, over the next five years, economically valuable improvements made that were directly referable to the AI progress in math. It would just be disappointing if it was just taking down a bunch of Erdős problems and none of them were doing any of the math that actually directly touches the physical world. To your point about how a lot of the history of mathematics was about building up these piles of concepts and connections. Sometimes the piles connect with each other, or you discover an application somewhere else. At the very least, you just build up this huge pile. Then as broader progress in society happens during the singularity, when we get to the industrial part of the singularity, you just have all these different ideas that hopefully are useful in other parts of the world.…

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