Math proofs fall fastest where the whole test loop runs in software

Transcript

Transcribed by machine (Whisper) from the episode’s audio, so a word may be off here and there.

1. 39:25

   confidently say it's probably the biggest day of discovery in human history with the amount of knowledge that was revealed. In math history or human history? Human history because the implications that flow from all of these math probes are pretty significant. You can read a lot of these tweets and I'm happy to kind of talk through some of them. I'm not going to pretend to be an expert on any of these individual proofs. But many folks who are have started to kind of highlight what some of the implications are, they span everything from electronics, quantum computing, building systems for airplanes, building more sensitive diagnostics equipment for medical applications, and on and on and on. But I think what's really profound about this is how it was done. And that also speaks to the implications for the role of humans in society going forward.

2. 40:21

   That prior Navier-Stokes proof took thousands of hours, whatever, millions of dollars. The report is that each one of these proofs took less than three hours of compute time. And that's the equivalent of hundreds or perhaps thousands of years of human labor being reduced down to three hours on a computer for each one of these major discoveries. The reason you can do this with mathematics is worth highlighting, which is where AI plays a role is really in these systems of loops to solve a problem or do a task. A loop is a postulation or an idea, then you test the idea, you get the result, and then you change your postulation and you run that recursive loop over and over and over again. The real question for AI is where can you apply that loop model in a way that you can make a better prediction or better idea, each loop, where you can parallelize

3. 41:16

   loops, and where you can shorten the loop cycle. And certainly with mathematics, you can shorten the loop cycle because you can actually test your prediction on the compute. You don't have to go do anything in the physical world. So you can say, hey, here's an idea for a proof, test it, see if it works, and then see if it does or doesn't work, reason, come up with a new idea and do that over and over again. And you can do it all in silico. So you know, the results of some of these papers, the proofs, a lot of mathematicians have been talking about them, they call it like an alien intelligence, they don't really understand how the AI connected many different dots, different ideas, different concepts, different approaches to solving problems together to actually solve them, that it's very hard for humans to even comprehend how this was done. But that's one of the benefits

4. 42:03

   of running parallelized loops, many loops at the same time, each loop can connect dots that humans otherwise might spend many days or years trying to find research papers or come up with new theory. And then it can test itself in the compute and come up with the next idea and do it over and over and over again, such that in three hours, the computer can do the work of hundreds or thousands of years of humans. Now, this is an incredible breakthrough. It's amazing. It's going to change the world in many different ways. And it's only the beginning. But it begs the question that I think I need to talk about. I think that there's a lot of fear about, okay, if AI can do this to mathematicians, doesn't that mean everyone's out of a job? And the answer is no, because what was very unique about mathematics is that the entire test cycle, the entire loop

5. 42:49

   cycle can be done in silico. If you want to come up with a new drug discovery idea or a new protein folding model, or, you know, solve a problem in chemistry and material science, the loop has a physical component, there's a human in the loop, where you actually have to go and test it in a lab. And so there's a slow part of that loop cycle, you can certainly parallelize it, you can come up with better ideas. But the testing the actual speed of the loop is actually gated primarily by the physical world step. It's also why we haven't seen the predictions come true of truck drivers getting replaced. Everyone is like, oh, all the truck drivers are going to get replaced by 2025.

6. 43:26

   And none have been replaced by AI. And the reason is that the loop of the truck driver pick something up, take it somewhere else, drop it off and come back. The AI doesn't actually shorten the loop, you can't parallelize the loop, maybe you could do it a little bit better with an AI driver. But the AI actually doesn't make the economic efficiency of that particular loop any better. Whereas the loops of mathematics, where you come up with an idea, you test it, you realize you're wrong, you test a new idea, which is what mathematicians do as a job is they're running