AI Is Breaking How We Teach | Terry Tao

Yeah, that's what Jim Simons told me. When we look at the future of education, you're not only a fields mentalist, an athletician, a father, and everything else that you do, but you're a teacher and you're an educator. Talk to me about your vision for the future. What's your philosophy of teaching? Yeah, so it needs to evolve quite a bit for many reasons. So the world has become infinitely more complex and unstable and unpredictable. Now with AI, humans used to have a monopoly on cognitive tasks. So one of the problems of AI, actually, I mean, the way the subject develops, it's not so much that it will overtake human research-level mathematics or any other discipline in the near future, but already undergraduate-level mathematics, for instance, many of the homework assignments that we assign right now, they can be done by AI. So we have to reinvent the way we teach. One thing that will become more important is students will need to have much more training in how to validate information that they see. So in the past, we had a small number of authoritative sources of information, or textbooks, and your teacher or something, and we didn't have social media and the internet and all kinds of information, now AI, of really variable quality. On the other hand, in the past, when you had information that was low-quality in content, it was also low-quality in presentation. You could tell that a really well-produced textbook would likely have more accurate content than something written in crayon or something. But now our ability to produce high-quality presentation has far outpaced our ability to produce high-quality content. So you cannot have YouTube videos or textbooks that look flawless, and now AI-generated output, but have got lots of fundamental mistakes. So yeah, we need to encourage critical thinking. I already see teachers experimenting with things like, here is a question that I would have assigned, but I've given it to ChatTPT, and this is the answer that they give. It's wrong. Please critique it and correct it. Interesting. And these are, I think, more of the skills. More interactive. So not treating knowledge as a passive thing to be acquired by an authority, but something that you always have to question. And struggle with. Interesting. That kind of reminds me of John Preskill at Caltech, talking about quantum computing and quantum supremacy and so forth. And one of the ways to overcome some of the issues with error correction in quantum computing is to throw more qubits at the problem. I wonder, will we throw more AIs at the problem? This kind of flipped it through natural human brains and AI to prove where it's wrong. But will we be in a place where AI could police itself? And so what would it take to trust them? It's good to make them more reliable. But I think, well, maybe if we use a very different architecture from the current AIs. So by nature, they are inherently unreliable. But we have ways to use unreliable tools. Random number generators are the most unreliable device technology we have, but they're extremely useful for all kinds of things, like cryptography. I think as long as you pair these AIs with good verification, and you only use the AIs to the extent that you can verify the outputs, and no further, then they can be a great tool. I see them more as complementing human scientists and mathematicians. Because there are so few human scientists in the world, and we only have so much time to work on research, we tend to focus on high-value, high-priority, isolated problems. But in mathematics and the sciences, there are millions and millions. There's a long tail of lots and lots of less well-known problems, which should require some attention. And they're not the most difficult or important, but it'll be good to have someone or something look at them. And so I think AI, actually, their best use case is not to target them on the most high-profile problems, but actually on the millions of medium-difficulty problems. And they may fail, and they may only solve 10% of these million problems, but that's 100,000 problems solved. So scale is their big advantage. You cannot scale a graduate student this way. Not legally. No, not legally or ethically. But AI, I think that's where the real value lies. What's your highest-priority task right now? Well, research-wise, what I'm interested in most nowadays is new workflows to modernize mathematics and make it more collaborative, more accessible to the public, and to integrate in these new tools like AI. The way we've done mathematics has not changed fundamentally in centuries. You can see I have blackboards in my office. We still work with pen and paper. We use computers a little bit, but not so much. And our collaborations are still very small. We work with two or three people. In the sciences, of course, we have thousands. In large part because we don't know how to incorporate contributions to the general public. There's a barrier to entry, first of all. A lot of what we do is very technical. But we need to synthesize proofs where every single step has to be verified. So if we had thousands of people, if we had to verify a thousand little components, it wasn't feasible until very recently. Also, because of all these factors, we don't collaborate as much with the other sciences as we ought to, especially the new sciences, which are so data-driven and connect the real world in new ways, like social network analysis or whatever. So that is, I think, the direction in which my research is going. It's almost more the sociology of mathematics, actually, than the technique. And more recently, I've been interested in trying to secure funding for mathematical research that has become very unstable in recent years. We'll talk about that in a bit. So, a mutual friend, Sergio Kleinerman, asked me a question related to what you just brought up, sociology of science. And he wondered how it was stressful for you to be reputed the best mathematician on Earth, the Fields Medalist, a very young and extremely successful mathematician. Did that affect you? Was that a challenge for you, with that mantle, that weight on your shoulders, perhaps? Or maybe not. Okay, I do remember the year. I think it was about 2006. My life did change in many ways. So suddenly I got invitations to embassies, and I would meet with people who I would not normally meet. And I got asked to be on all these committees. Suddenly my opinion was sought after. So that was a sea change. I mean, I was on some of these already, so that took some getting used to. But I think one thing that helps ground mathematicians a little bit is that, I mean, as a pure mathematician, your main task is, you have these problems you want to solve, and you need proof theorems that solve these problems. And your proof has to be correct, and every step has to be validated. And it doesn't matter how famous you are or how much reputation you have. You can't just say, I've proven something, trust me. Okay, you have to supply the details, you have to supply the proofs. And if you don't have the proof, you don't have the proof. So I think this naturally provides some check on just sort of how high your ego can go just from these awards. Because, you know, I mean, there are countless problems that I would love to solve. You know, the Trunheim conjecture we talked about, the hundreds of problems that I would love to solve. And I just know I don't know how to solve them. And so I know more problems I can't solve than the problems I have solved. So I think that keeps you somewhat honest. What about the, you know, the old trope that mathematicians do their best work by age 30, we're in our 50s now, you and I. What do you make of that statement? Jim Simons used to tell me, he didn't really believe it. He thought that actually a clock starts, you know, at a certain moment, and then you have 10 years or 20 years to do it. And he did stop at age 30, but that was because he worked at Pensley for 10 years, not because he hit an arbitrary age. You've heard this trope. What do you make of it? Yeah, so different mathematicians have had different career effects. So I definitely was stereotypical. And I had skipped a childhood, I excelled, I skipped several grades. And so, yeah, I did all of my work when I was younger. But there are other mathematicians who started quite late. They didn't become interested in mathematics until college, when they switched, it became quite good. My advisor, when I was in Princeton, my PhD advisor Elias Stein, I would meet with him every week and I would discuss the problems that he'd assigned me to work on. And I'd spent hours trying all kinds of crazy things and I'll report all these things I tried didn't work, I tried this, it didn't work, just like all this energy and time. And he would just sort of look at what I wrote in Blackboard and just think for a few seconds. He said, you know, the difficulty you're having is exactly the same difficulty that so-and-so had in this paper. So he'd go to a filing cabinet and he'd push out this one paper, a preprint. He said, read this, this will solve your problem. So yeah, there was a different way of doing mathematics and I couldn't see how he put, because I would go home and read it and it would solve my problem. I would then hit another old fracture the next week. But no, I spent hours on these problems and he just thought about it for 10 seconds. I mean, he just knew from experience what to do. It's the wisdom, just wisdom. So I think as you get older, you approach, you find different ways to do mathematics, which it may not be as flashy, I think it does have more brute force than it probably does as a first, but it can be more productive, I mean. Yeah, I can now pull the same trick off my own graduate students, okay. And so it's like kind of satisfying to see the full circle of it. Okay. You can do second order. You can say what my advisor told me.