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Lex Fridman Podcast / episode intelligence

#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI

15 Jun 2025 35 published claims 2 attributable people

Speakers in the public record

Claim mix

belief 16evaluation 6commitment 4preference 4uncertainty 3observation 1prediction 1

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Every row below preserves an exact excerpt. Identified speakers are linked; unresolved voices are labeled and excluded from people counts.

Claim ledger

The useful parts, with receipts.

35 published records

01 / belief

Maybe if you do math competitions or something, you get a slightly different experience. But I think many people, they don’t find their native math language until very late or usually too late.

“Maybe if you do math competitions or something, you get a slightly different experience. But I think many people, they don’t find their native math language until very late or usually too late.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

03 / evaluation

I mean, you can ask some cheater if there’s a specific thing that’s blocking you that some bad case keeps showing up, that for which your tool doesn’t work.

“I mean, you can ask some cheater if there’s a specific thing that’s blocking you that some bad case keeps showing up, that for which your tool doesn’t work.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

04 / observation

You talk to athletes like marathon runners and so forth and they talk about what’s the most important thing, is it the training regimen or the diet and so forth? So much of it is psychology, just tricking yourself to think that the problem is feasible so that you’re motivated to do it.

“You talk to athletes like marathon runners and so forth and they talk about what’s the most important thing, is it the training regimen or the diet and so forth? So much of it is psychology, just tricking yourself to think that the problem is feasible so that you’re motivated to do it.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

05 / belief

Let’s step back and maybe look at a bit of a romanticized version of mathematics. So I think you’ve said that early on in your life, math was more like a puzzle-solving activity when you were young.

“Let’s step back and maybe look at a bit of a romanticized version of mathematics. So I think you’ve said that early on in your life, math was more like a puzzle-solving activity when you were young.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

07 / belief

I think the theories that work well, that explain the universe, tend to also involve the same mathematical objects that work well to solve mathematical problems.

“I think the theories that work well, that explain the universe, tend to also involve the same mathematical objects that work well to solve mathematical problems.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

08 / commitment

One of the things I find really sad about the finiteness of life is that I won’t get to see all the cool things we create as a civilization because in the next 100 years, 200 years, just imagine showing up in 200 years.

“One of the things I find really sad about the finiteness of life is that I won’t get to see all the cool things we create as a civilization because in the next 100 years, 200 years, just imagine showing up in 200 years.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

09 / belief

Yeah, I think mathematics inherently, mathematics is so huge these days that nobody knows all of modern mathematics. And inevitably, we make mistakes and you can’t cover up your mistakes with just bravado because people will ask for your proofs, and if you don’t have the proofs, you don’t have the proofs.

“Yeah, I think mathematics inherently, mathematics is so huge these days that nobody knows all of modern mathematics. And inevitably, we make mistakes and you can’t cover up your mistakes with just bravado because people will ask for your proofs, and if you don’t have the proofs, you don’t have the proofs.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

10 / belief

I think on the whole, it is a hugely positive thing. To talk about Steve Jobs as a representative of Apple, when I personally know and of course everybody knows the incredible design, the incredible engineering teams, just the individual humans on those teams.

“I think on the whole, it is a hugely positive thing. To talk about Steve Jobs as a representative of Apple, when I personally know and of course everybody knows the incredible design, the incredible engineering teams, just the individual humans on those teams.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

12 / belief

I think you also suggested somewhere this fascinating approach, which really stuck with me as they’re using it, and it really works, I think you said it’s called structured procrastination.

“I think you also suggested somewhere this fascinating approach, which really stuck with me as they’re using it, and it really works, I think you said it’s called structured procrastination.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

15 / belief

I would definitely not want this to become part of your tenure review or something. But I mean, I think already in enterprise computing, people do use some of these metrics as part of the assessment of performance of an employee.

“I would definitely not want this to become part of your tenure review or something. But I mean, I think already in enterprise computing, people do use some of these metrics as part of the assessment of performance of an employee.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

16 / uncertainty

There’s a kind of emergence that happens with these cellular automata local rules… maybe it’s similar to fluids, I don’t know, but local rules operating at scale can create these incredibly complex dynamic structures.

“There’s a kind of emergence that happens with these cellular automata local rules… maybe it’s similar to fluids, I don’t know, but local rules operating at scale can create these incredibly complex dynamic structures.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

17 / belief

Yeah, so it does keep us honest. It’s not a perfect panacea, but I think we do have more of a culture of admitting error because we’re forced to all the time.

“Yeah, so it does keep us honest. It’s not a perfect panacea, but I think we do have more of a culture of admitting error because we’re forced to all the time.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

18 / belief

New concepts, new ways of thinking, also sucking at a thing that others… I think in that talk, you could be a Fields Medal-winning mathematician and an undergrad knows something better than you.

“New concepts, new ways of thinking, also sucking at a thing that others… I think in that talk, you could be a Fields Medal-winning mathematician and an undergrad knows something better than you.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

20 / commitment

There are simpler versions of the conjecture where we are getting really close. So I think in 10 years we will have many more much closer results, we may not have the whole thing.

“There are simpler versions of the conjecture where we are getting really close. So I think in 10 years we will have many more much closer results, we may not have the whole thing.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

22 / uncertainty

I don’t know how to completely power down the big machine, so it doesn’t interfere the writing of the smaller machine, but everything in principle can happen.

“I don’t know how to completely power down the big machine, so it doesn’t interfere the writing of the smaller machine, but everything in principle can happen.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

23 / uncertainty

If they recognize that there’s a certain technique that can be applied, they will try it. But there are problems which they see and none of their standard techniques obviously applies and the common reaction is than just paralysis, I don’t know what to do.

“If they recognize that there’s a certain technique that can be applied, they will try it. But there are problems which they see and none of their standard techniques obviously applies and the common reaction is than just paralysis, I don’t know what to do.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

24 / belief

I think the way of colleague might put it is that if you are on the streets of New York and you’re put in a blindfold and you’re put in a car and after some hours the blindfold is off and then you’re in Beijing.

“I think the way of colleague might put it is that if you are on the streets of New York and you’re put in a blindfold and you’re put in a car and after some hours the blindfold is off and then you’re in Beijing.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

25 / belief

We believe the primes behave like a random set. And so the reason why we care about the twin prime conjecture is a test case for whether we can genuinely confidently say with 0% chance of error that the primes behave like a random set.

“We believe the primes behave like a random set. And so the reason why we care about the twin prime conjecture is a test case for whether we can genuinely confidently say with 0% chance of error that the primes behave like a random set.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

26 / evaluation

Often these models are incorrect, and this causes all kinds of problems. So yeah, to humanize a subject, if you identify a small number of people and say these are representative people of a subject, role models, for example, that has some role, but it can also be too much of it can be harmful because I’ll be the first to say that my own career path is not that of a typical mathematician.

“Often these models are incorrect, and this causes all kinds of problems. So yeah, to humanize a subject, if you identify a small number of people and say these are representative people of a subject, role models, for example, that has some role, but it can also be too much of it can be harmful because I’ll be the first to say that my own career path is not that of a typical mathematician.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

27 / preference

” Like you mentioned, coding as an analogy is interesting, because there’s also this activity called the code golf, which I also find beautiful and fun, where people use different programming languages to try to write the shortest possible program that accomplishes a particular task, and I believe there’s even competitions on this, and it’s also a nice way to stress test not just the programs, or in this case, the proofs, but also the different languages.

“” Like you mentioned, coding as an analogy is interesting, because there’s also this activity called the code golf, which I also find beautiful and fun, where people use different programming languages to try to write the shortest possible program that accomplishes a particular task, and I believe there’s even competitions on this, and it’s also a nice way to stress test not just the programs, or in this case, the proofs, but also the different languages.”
Speaker
Lex Fridman
Publisher
Lex Fridman Podcast

28 / evaluation

If viscosity was all there was, then nothing bad would ever happen, but there’s also transport that energy from… in one location of space can get transported because the fluid is in motion to other locations.

“If viscosity was all there was, then nothing bad would ever happen, but there’s also transport that energy from… in one location of space can get transported because the fluid is in motion to other locations.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

29 / preference

If I take a set of odd numbers and I flip a coin for each number, and I only keep the numbers for which I got a heads… So I just flip coins, I just randomly take out half the numbers, I keep one half.

“If I take a set of odd numbers and I flip a coin for each number, and I only keep the numbers for which I got a heads… So I just flip coins, I just randomly take out half the numbers, I keep one half.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

30 / preference

I spend a lot of time… If there’s a result, I see it in one field, and I like the result, it’s a cool result, but I don’t like the proof, it uses types of mathematics that I’m not super familiar with, I often try to re-prove it myself using the tools that I favor.

“I spend a lot of time… If there’s a result, I see it in one field, and I like the result, it’s a cool result, but I don’t like the proof, it uses types of mathematics that I’m not super familiar with, I often try to re-prove it myself using the tools that I favor.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

31 / evaluation

Now I think there’s some more awareness that this systemic risk is actually a much bigger issue, and just because the model is pretty and nice, it may not match reality.

“Now I think there’s some more awareness that this systemic risk is actually a much bigger issue, and just because the model is pretty and nice, it may not match reality.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

32 / prediction

There’s no reason why they should un-mix. But in principle, because of all the collisions between them, there could be some sort of weird conspiracy that maybe there’s a microscopic demon called Maxwell’s Demon that will… every time an oxygen and nitrogen atom collide, they’ll bounce off in such a way that the oxygen sort of drifts onto one side and then nitrogen goes to the other.

“There’s no reason why they should un-mix. But in principle, because of all the collisions between them, there could be some sort of weird conspiracy that maybe there’s a microscopic demon called Maxwell’s Demon that will… every time an oxygen and nitrogen atom collide, they’ll bounce off in such a way that the oxygen sort of drifts onto one side and then nitrogen goes to the other.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast

35 / evaluation

I think hedgehogs and fox… A fox knows many things a little bit, but a hedgehog knows one thing very, very well, and in mathematics, there’s definitely both hedgehogs and foxes, and then there’s people who can play both roles, and I think ideal collaboration, British mathematicians involves very… You need some diversity, like a fox working with many hedgehogs or vice versa, but I identify mostly as a fox, certainly.

“I think hedgehogs and fox… A fox knows many things a little bit, but a hedgehog knows one thing very, very well, and in mathematics, there’s definitely both hedgehogs and foxes, and then there’s people who can play both roles, and I think ideal collaboration, British mathematicians involves very… You need some diversity, like a fox working with many hedgehogs or vice versa, but I identify mostly as a fox, certainly.”
Speaker
Terence Tao
Publisher
Lex Fridman Podcast
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