Dwarkesh Patel: belief

Transcript context

…Certainly in math, the process is often more important than the problem itself. The problem is kind of a proxy for measuring progress. I think even in software, there are different types of software tasks. If you just create a webpage that does the same thing that a thousand other webpages do, there’s no skill to be learned. Well, there is still some skill maybe that the individual programmer could pick up. But for boilerplate-type code, it’s something that you should definitely offload to AI. Sometimes once you make the code, you still have to maintain it. There are issues with upgrading it and making it compatible with other things. I’ve heard programmers report that even if an AI can create the first prototype of a tool, making it mesh with everything else and making it interact with the real world in the way they want is an ongoing process. If you don’t have the skills that you pick up from writing the code, that may impact your ability to maintain it down the road. So yes, certainly mathematicians, we’ve used problems to build intuition and to train people to have a good idea of what’s true, what to expect, what is provable, and what is difficult. Just getting the answers right away may actually inhibit that process. I made a distinction between theory and experiment before. In most sciences, there’s an equal division between the theoretical side and the experimental side. Math has been unique in that it’s almost entirely theoretical. We place a premium on trying to have coherent, clean theories of why things are true and false. We haven’t done many experiments as to, if we have two different ways to solve a problem, which is more effective. We have some intuition, but we haven’t done large-scale studies where we take a thousand problems and just test them. But we can do that now. I think AI-type tools will actually revolutionize the experimental side of math, where you don’t care so much about individual problems and the process of solving them, but you want to gather large-scale data about what things work and what things don’t. The same way that if you’re a software company and you want to roll out a thousand pieces of software, you don’t really want to handcraft each one and learn lessons from each. You just want to find what workflows let you scale. The idea of doing mathematics at scale is at its infancy. But that’s where AI is really going to revolutionize the subject. I feel like a big crux in these conversations about how good AI will be for science is, I think you said this, that they’re using existing techniques and modifying them. It would be interesting to understand how much progress one can make simply from using existing techniques. If I looked at the top math journals, how many of the papers are coming up with a new technique, whatever that means, versus using existing techniques on new problems? What is the overhang? If you just applied every known technique to every open problem, would that constitute a humongous uplift in our civilization’s knowledge, or would that not be that impressive and useful? This is a great question, and we don’t have the data to fully answer it yet. Certainly, a lot of work that human mathematicians do… When you take a new problem, one of the first things we do is we look at all the standard things that have worked on similar problems in the past, and we try them one by one. Sometimes that works, and that’s still worth publishing because the question was important. Sometimes they almost work, and you have to add one more wrinkle to it, and that’s also interesting. But the papers that go into the top journals are usually ones where the existing methods can kind of solve 80% of the problem, but then there is this 20% which is resistant and a new technique has to be invented to fill in the gaps. It’s very rare now that a problem gets solved with no reliance on past literature, where all the ideas come out of nowhere. That was more common in the past, but math is so mature now that it’s just so much of a handicap to not use the literature first. AI tools are getting really good at the first part of that, just trying all the standard techniques on a problem, often making fewer mistakes in applying them than humans. They still make mistakes, but I’ve tested these tools on little tasks that I can do, and sometimes they pick up errors that I make. Sometimes I pick up errors that they make. It’s about a tie right now. But I haven’t yet seen them take the next step. When there are holes in the argument where none of the things are working, then what do you do? They can suggest random things, but often I find that trying to chase them down to make them work, and finding they don’t work, wastes more time than it saves. I think some fraction of problems that we currently think are hard will fall from this method, especially the ones that haven’t received enough attention. With the Erdős problems, almost all of the 50 problems that were solved by AIs were ones for which there was basically no literature. Erdős posed the problem once or twice. Maybe some people tried it casually and couldn’t do it, but they never wrote up anything. But it turned out that there was a solution, and it was just combining this one obscure technique that not many people know about with some other result in the literature. That’s the median level of what AI can accomplish, and that’s really great. It clears out 50 of these problems. So I think you will see some isolated successes. But what we found… Some people have done large-scale sweeps of these Erdős problems. If you only focus on the success stories, the ones that get broadcast on social media, it looks amazing. All these problems that haven’t been solved for decades, now they’re falling. But whenever we do a systematic study, on any given problem an AI tool has a success rate of maybe 1% or 2%. It’s just that they can buy scale, and you just pick the winners. It looks great. I think there’ll be a similar thing happening with the hundreds of really prestigious, difficult math problems out there.…

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