Dwarkesh Patel: belief

Transcript context

…I agree. They excel at breadth, and humans excel at depth, human experts at least. I think they’re very complementary. But our current way of doing math and science is focused on depth because that’s where human expertise is, because humans can’t do breadth. We have to redesign the way we do science to take full advantage of this breadth capability that we now have. We should have a lot more effort in creating very broad classes of problems to work on rather than one or two really deep, important problems. We should still have the deep, important problems, and humans should still be working on them. But now we have this other way of doing science. We can explore entirely new fields of science by first getting these broad, moderately competent AIs to map it out and make all the easy observations. And then identify certain islands of difficulty, which human experts can then come and work on. I see very much a future of very complementary science. Eventually, you would hope to get both breadth and depth and somehow get the best of both worlds. But we need practice with the breadth side. It’s too new. We don’t even have the paradigms to really take full advantage of it. But we will, and then science will be unrecognizable after that, I think. To this point about complementarity, programmers have noticed that they’re way more productive as a result of these AI tools. I don’t know if you as a mathematician feel the same way, but it does seem like one big difference between vibe coding and vibe researching is that with software, the whole point is to have some effect on the world through your work. If it leads to you better understanding a problem or coming up with some clean abstraction to embody in your code, that is instrumental to the end goal. Whereas with research, the reason we care about solving the Millennium Prize Problems is that presumably that in the process of solving them, we discover new mathematical objects or new techniques that advance our civilization’s understanding of mathematics. So the proof is instrumental to the intermediate work. I don’t know if you agree with that dichotomy or if that in any way will explain the relative uplift we’ll see in software versus research. 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.…

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