AI Is Breaking How We Teach | Terry Tao

Yeah, that's what Jim Simons told you.

Uh, when we look at uh the future of education, you're not only a Fields Medalist, a mathematician, and father of everything else that you do, but you're a teacher and you're educator. Um, talk

to me about your vision for the future.

What's your philosophy of teaching?

Yeah, so um it needs to evolve um quite a bit from for many reasons. Yeah, so

the world has become infinitely more complex and unstable and unpredictable.

Um and now they know and and and now with AI, you know, humans used to be sort of a a monopoly on cognitive tasks like um you know um and and now

AI so one of the problems with AI actually I mean the way the subject develops is is not so much that it will it will over take human um like research level mathematics or any other discipline in the near future, but

already undergraduate level um mathematics for instance um many of the homework assignments that we we teach we assign right now they can be done by by AI.

Yeah. So we have to reinvent uh the way we um uh we teach. So um

we teach. So um one thing that will become more important is um students will need to have much more training in how to validate um information that they see.

You know, so in the past we had like a small number of authoritative um uh source of information or textbooks and and your teacher or something and um and uh you know, we didn't have social media and and and the internet and all

kinds of information of now and now AI of all this information of really variable quality. On the other hand, the

variable quality. On the other hand, the um in the past um when you had information that was low quality content, it was also low quality in presentation. Now so you could tell that

presentation. Now so you could tell that like a really well-produced textbook would likely have more um accurate content than than you know, something written in crayon or something, but but now our our ability to produce

high-quality uh presentation has far outpaced our ability to produce high-quality content. So um you can now

high-quality content. So um you can now have have um you know, YouTube videos or or or or or textbooks that look flawless okay and now AI-generated output, but have got

lots of fundamental So um yeah, we we need to to encourage you critical thinking um I I already see teachers experimenting with things like you know, here's a a question that I would have assigned, uh

but I've given it to to chat GPT and this is this is the answer that they give. It's wrong. Please critique it and

give. It's wrong. Please critique it and and and correct it.

Interesting. And these are I think more the skills more interactive, you know, so not treating knowledge as as as a passive thing to be acquired by a authority, but something that you always have to question. And struggle with.

Interesting, you know, that kind of reminds me of John Preskill at Caltech uh 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 and um I wonder do will we throw more AIs at the problem? You know,

this kind of flipped it you threw natural you know, human brains at an AI to prove what's up, but will we be in a place where AI could police itself and so what what would it take to trust them? It's it's good to to to make them

them? It's it's good to to to make them more reliable, but I I think um well may maybe if if we use a very different architecture from the the current AIs uh become so by by

nature they are inherently unreliable, but we we have we have ways to use unreliable tools. Um you know, random

unreliable tools. Um you know, random number generators um are the the most unreliable um um device technology we have, but they're extremely useful for all kinds of things like cryptography. Yeah, that's I think

like cryptography. Yeah, that's I think as long as you pair these AIs with with good verification and and you and you only use the AIs to the extent that that you can verify the outputs and and and

no further um then they can be a great tool. Um I see them more as

tool. Um I see them more as complementing um human scientists and mathematicians. Um so um

mathematicians. Um so um because there are not there are so few human scientists in the world and and we don't only have so much time to to work on on research, we tend to focus on sort

of high-value you know, high-priority um isolated problems. Uh but in mathematics and the sciences there are millions and millions of there's a long tail of lots and lots of of less uh well-known

problems which should require some attention, but um and they're not the most difficult or important, but it would be good to have some someone else or something look at them.

And so I think AI actually their best use case is um not to to to um target them on on the most high-profile problems, but actually on the millions of medium difficulty problems um and you

know, they they may fail and they may only do they only solve 10% of these million problems, but that's 100,000 problems solved. So scale is is the big

problems solved. So scale is is the big advantage, you know, you cannot scale a graduate student.

You're right. I have it this way. Okay.

Um Not legally, yeah. No, not legally.

Uh yeah, or ethically. Okay. But uh but AI you know, I I think I that that's that's where the the big the the real value lies. What's your highest priority

value lies. What's your highest priority task right now? Well, uh research-wise uh what I'm interested in most nowadays is is new workflows to uh um

um modernize mathematics and make it more um more collaborative, more um more accessible to public uh and to integrate in these new tools like AI.

The way you that we've done mathematics has not changed fundamentally in centuries. Now we we you know, you can

centuries. Now we we you know, you can you see our blackboards uh in in my office, you know, we still work with pen and paper. We use computers a little bit

and paper. We use computers a little bit um um but not so much and our collaborations are still very small. We

work with two, three people, you know, in the sciences of course you know, with thousands thousands in large part because um we don't know how to incorporate contributions from the public. I mean there's a barrier to

public. I mean there's a barrier to entry first of all. A lot of what we do is very technical.

Um but in we need to synthesize proofs where every single step has to be verified. Um so if we had thousands

verified. Um so if we had thousands people you have to verify verify a thousand little components that it's it's it wasn't feasible until very recently. Also

because of all these factors it's uh we don't collaborate as much with the other sciences as as we ought to. Especially

the the the new sciences which are so data-driven um and uh and connected to the world in new ways, you know, uh you know, in with uh um you know, like social network analysis or whatever. So that that is I

think my the direction in which my research is going to it's it's it's almost more the sociology of mathematics actually than than the than the than the technique. And more recently I've been

technique. And more recently I've been I've been interested in trying to secure funding for for mathematical research that that has become very unstable in in recent years.

about that in a bit. So uh reach out friend Sergio Kleinerman asked me a question related to what you just brought up uh sociology of science and and he he wondered how was stressful for

you to be you know, reputed the the the best mathematician on Earth, the Fields Medalist, a very young and extremely successful um mathematician. Did that um did that affect you? Was that was that a

challenge for you with that mantle that that weight on your shoulders perhaps or maybe not? Okay, I I I do remember the

maybe not? Okay, I I I do remember the uh the year like it was like 2006. Uh my

life did change in many ways like uh so suddenly I got invitations like embassies and I would meet with people who I would not normally meet and um and I got asked to be on all these committees. You know, suddenly my

committees. You know, suddenly my opinion was was sought after. Um so that that was a sea change. Um I mean I was on some of these already, but um so that took some getting used to. But I think

one thing um that helps ground mathematicians a little bit is is that you know, I mean as a pure mathematician you know, your main task is you have these problems you want to solve and you you might prove theorems that that solve

these problems and your proof um has to be correct and every step has to be validated and doesn't matter how famous you are or how much of a reputation you have, you can't just say I've proven something, trust me. Okay.

You have to supply the detailed steps by the proof. And if you if you don't have

the proof. And if you if you don't have the proof, you don't have the proof. So

I think this naturally provides some check on on just sort of how high your ego can go uh that's from his words.

You know, I mean that's okay. There are

problems that I would love to solve um you know, the twin prime conjecture we talked about, but but the hundreds of problems that I would love to solve and I just know I don't know how to solve and so I know more problems that I can't solve than the problems I have solved.

Um so I think that uh that you know, so that keeps you somewhat honest. What

about the uh you know, the old trope that you know, mathematicians do their best work by age 30? Were you in your 50s now you and I? What what do you make of 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 your and he he did stop at age 30, but that's because he worked intensely for 10 years, not because he hit an arbitrary

age array. You've heard this trope. What

age array. You've heard this trope. What

do you make of it? Yeah, so um different mathematicians have had different career tracks. So I definitely was was very typical as I had um

I skipped it um I um I skipped a child at that accelerated um uh I skipped several grades um and so yeah, I I did well with my work when I was younger. Um but there are

other mathematicians who started quite late. Maybe they they didn't become

late. Maybe they they didn't become interested in mathematics until college or when they switched became quite good.

My advisor when I was at Princeton um my PhD advisor you know, I started um I would meet with him every week and I'd discuss the problems that he'd assign me to work on and I'd spend hours trying all kinds of crazy things and I'd report

all these things I tried didn't work. I

tried this it didn't work. This this I all this energy time and he would just sort of look at uh what I wrote on the blackboard and and just think for a block of a few seconds and say, you know, the difficulty you're having is exactly

the same difficulty that so-and-so had in this paper. So he'd go smiling cabinet and he'd push out this this one paper a preprint. Say, read this. This

will solve your problem. Um so yeah, there was was a different way of doing mathematics that I I I didn't uh I I couldn't see how he put because now I would go home and read it and it would solve my problem. I I would then hit

another up structure like for the next week, but but you know, I spent hours on these problems. Um and he just thought about it for for 10 10 seconds and he just knew from experience what to do.

It's the wisdom. Just wisdom. Yeah,

wisdom. So um I think as you get older you you approach uh you you you find different ways to do mathematics which um it it it may not be as flashy you know,

like in terms of more brute force it may not be as as as efficient, but it can be more it can be more um productive. I

mean, yeah. I can now pull the same trick on my own graduate students. So

and so it's like kind of satisfying cuz you see, a circle back. Okay, you could do second order, you could say when my advice are told me really.

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