Terence Tao: prediction

Transcript context

…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. 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?…

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