YouSaid · the spoken record

Terence Tao

lines on the record: 252
first: 2025-06-15
most recent: 2025-06-15
sittings or episodes: 1
sources: podcast

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“When the infrastructure and the culture is healthy, the community of humans can be so much more intelligent and mature and rational than the individuals within”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, well, already plenty has happened. If you could go back in time and talk to you of your teenage self or something, you know what I mean? Just the internet and our AI. I mean, they're beginning to be internalized and say, yeah, of course an AI can understand our voice and give reasonable slightly incorrect answers to any question. But this was mind-blowing even two years ago.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I think the younger generation is always really creative and enthusiastic and inventive. It's a pleasure working with young students. The progress of science tells us that the problems that used to be really difficult can become extremely trivial to solve. Navigation, just knowing where you work on the planet was this horrendous problem where people died or lost fortunes because they couldn't navigate. And we have devices in our pockets that do us automatically for us. It's a completely solved problem. So things that are seem unfeasible for us now could be maybe just homework exercises for me.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so the mathematical community plural is incredibly super intelligent entity that no single human mathematician can come close to replicating. You see it a little bit on these question analysis sites. So this method of aflow, which is the math version of Stack Overflow. And sometimes you get this very quick responses to very difficult questions from the community. And it's a pleasure to watch actually as an expert.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, yeah, yes. So humanity plural has much more intelligence in principle on his good days. Than the individual humans put together. It can all have less.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, okay, I mean, how much augmentation are you willing? Like, for example, if I didn't even have pen and paper. If I had no technology whatsoever, okay, so I've not allowed Blackboard pen and paper.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, I guess a mathematician, I mean, it's originally, there must be a sufficiently large number that you can't understand. That was the first thing that came to mind.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, yeah. I mean, with anything, psychology is really important. You talk to athletes, like marathon runners and so forth. And they talk about what's the most important thing, the training regimen or the diet and so forth. So much of it is actually psychology, just tricking yourself to think that the form is feasible so that you can motivate to do it.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“So, you know, like the next step then is to try anything, like no matter how stupid. And in fact, almost the stupider the better, which a technique which is almost guaranteed to fail, but the way it fails is going to be instructive. It fails because you're not at all taken into account this hypothesis. Oh, this hypothesis must be useful. That's a clue.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, this is bystander effect everywhere. If no one says you should do X, everyone just will move around waiting for someone else to do something and nothing gets done. And one thing that actually you have to teach undergraduates in mathematics is that you should always try something. So you see a lot of paralysis in an undergraduate trying a math problem. If they recognize that there's a certain technique that can be applied, they will try it. But there are problems which they see none of their standard techniques obviously applies. And the common reaction is then just paralysis. I don't know what to do, or I think there's a quote from the Simpsons. I've tried nothing and I'm all out of ideas.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, Hilper Spaces. We have lots of things that are named after him, of course, just the arrangement of mathematics and just the introduction of certain concepts. I mean, 23 problems have been extremely influential.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, if you pull cumulatively over time, for example, Euclid is one of the leading contenders. And then maybe some unnamed anonymous messages before that whoever came up with the concept of numbers.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so it does keep us honest. I mean, you can still, 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.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I think mathematics inherently, I mean, mathematics is so huge these days that nobody knows all of modern mathematics. And inevitably, we make mistakes. You can't cover up your mistakes with just sort of bravado and... I mean, because people will ask for your proofs, and if you don't have the proofs, you don't have the proofs.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I don't work in machine learning and I don't work in true formalization. And there's a limit to how much I can just rely on authority and saying, oh, I'm a well-known mathematician. Just trust me when I say that this is going to change mathematics and I'm not doing it any when I don't do anyway myself. So I felt like I had to actually justify it. A lot of what I get into actually I don't quite see in advance as how much time I'm going to spend on it. And it's only after I'm sort of waist deep in a project that I realize by that point I'm committed.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“But there was even then there was one talk about language models and the potential capability of those in the future. So that got me excited about the subject. So I started giving talks about this is something we should more of us start looking at this conference. And then ChatGPT came out and suddenly AI was everywhere. And so I got interviewed a lot about this topic. And in particular, the interaction between AI and formal proof assistants. And I said, yeah, they should be combined. It's a perfect synergy to happen here. And at some point, I realized that I have to actually not just talk the talk, but walk the walk.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“About four or five years ago, I was on a committee where we had to ask for ideas for interesting workshops to run at a math institute. And at the time, Peter Schultzer had just formalized one of his new theorems. And there were some other developments in computer-assisted proof that look quite interesting. And I said, oh, we should run a workshop on this. It's a good idea. And I was a bit too enthusiastic about this idea. And so I got volunteered to actually run it. So I did with a bunch of other people, Kevin Bazer and Jordan Ellenberg and a bunch of other people. And it was a nice success we brought together a bunch of mathematicians and scientists and other people. And we got up speedless state of the art. And it was really interesting developments that most mathematicians didn't know was going on. That lots of nice proofs of concept. Just before.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“First of all, I've always been interested in new ways to do mathematics. I feel like a lot of the ways we do things right now are inefficient. Many of my colleagues who spend a lot of time doing very routine computations or doing things that other mathematicians would instantly know how to do. And we don't know how to do. And why can't we search and get a quick response and so on? So that's why I'm always interested in exploring new workflows.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“It's a tough, tough, tough question. Yeah. So there's a lot of certainty now in the world. There was this period after the war where, at least in the West, if you came from a good demographic, there was a very stable path to a good creator. You go to college, you get an education, you pick one profession and you stick to it. It's becoming much more a thing of the past. I think you just have to be adaptable and flexible. I think people have to get skills that are transferable. Like learning one specific programming language or one specific subject of mathematics or something, that itself is not a super transferable skill, but sort of knowing how to reason with abstract concepts or how to problem solve and things go wrong and so whatever, these are things which I think we will still need even as our tools get better and you'll be working with AIs.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“If programming was taught as an almost entirely theoretical subject, where you just talk the computer science, the theory of functions and routines and so forth, and outside of some very specialized homework assignments, you're not actually programmed on the weekend for fun. Or, yeah, they would be as considered as hard as math. So, as I said, there are communities of non mathematicians where they're deploying math for some very specific purpose, like optimizing their poker game. And for them, then math becomes fun for them.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“One thing about these formalization projects is that they are bringing together more, bringing in more people. So I'm sure there are high school students who have already contributed to some of these formalizing projects who contribute to Matholib. We don't need to be a PhD holder to just work on one atomic thing.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Chess and baseball. I mean, there's meth all over the place. And I'm hoping actually with these new sort of tools for lean and so forth, that actually we can incorporate a broader public into math research projects. This is almost, it doesn't happen at all currently. So in the sciences, there is some scope for citizen science. Astronomers, the amateurs who discover comets and there's biologists, there are people who identify butterflies and so forth. And in method, there are a small number of activities where amateur mathematicians can discover new primes and so forth. But previously, because we have to verify every single contribution, most mathematical research projects, it would not help to have input from the general public. In fact, it would just be time consuming because just error checking and everything.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah It's a tricky problem. One nice thing is that there are now lots of sources for my FICO enrichment outside the classroom. So in my day, already there are math competitions. And there are also popular math books in the library. But now you have YouTube. There are forums just devoted to solving math puzzles. And math shows up in other places. For example, there are... Hobbyists who play poker for fun. And there for very specific reasons are interested in very specific probability questions. And they actually this community of amateur probalists in poker.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Process they take different paths, they're very quick at things that I struggle with and vice versa, and yet they still get to the same goal. That's beautiful. But I mean, the way we educate, unless you have like a personalized tutor or something, I mean, education sort of just by nature of scale has to be mass-produced. You have to teach the 30 kids. If they have 30 different styles, you can't teach 30 different ways.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“To mathematics. Are other centers are sophisticated enough that different people we can repurpose other areas of our brain to do mathematics. So some people have figured out how to use the visual center to do mathematics. And so they think very visually when they do mathematics. Some people have repurposed their language center and they think very symbolically. Some people, like if they are very competitive and they're like gaming, there's this part of your brain that's very good at solving puzzles and games and that can be repurposed. But when I talk to other mathematicians, they don't quite think, I can tell that they're using somehow different styles of thinking than I am. I mean, not disjoint, but they may prefer visual. I don't actually prefer visual so much. I need lots of visual aids myself. My fact provides the common language that we can still talk to each other.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, it works for me. Yeah, I mean, also people who are very productive and they focus very deeply on. I think everyone has to find their own workflow. One thing which is a shame in mathematics is that we have mathematics, there's sort of a one size fits all approach to teaching mathematics. And so we have a certain curriculum and so forth. I mean, maybe if you do math competitions or something, you get a slightly different experience. I think many people, they don't find their native math language until very late or usually too late. So they stop doing mathematics and they have a bad experience with a teacher who's trying to teach them one way to do mathematics that they don't like it. My theory is that humans don't come evolution has not given us a math center of a brain directly. We have a vision center and a language center and some other centers which have evolutionist honed. But we don't have innate centers.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I like moving on from a problem if it's giving too much difficulty But you need the people who have the tenacity and the fearlessness. I've collaborated with people like that where I want to give up because the first approach that we tried didn't work and the second one didn't approach, but they're convinced and they have third, fourth, and the fifth approach works. And I have to use my words. Okay, I didn't think this was going to work, but yes, you were right along.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, that is a romantic, so it kind of fits with sort of the romantic image that I think people have of mathematicians to the extent that they think of thinking at all as these kind of eccentric wizards or something. So that certainly kind of accentuated that perspective. It is a great achievement. His style of solving forms is so different from my own, which is great. I mean, we need people like that.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“And functions and things that are within scope of a high school math education to at least define. But then this is very advanced algebraic side of number theory where people have been building structures on structures for quite a while. And it's a very sturdy structure. It's been very at the base at least it's extremely well developed in the textbooks and so forth. It does get to the point where if you haven't taken these years of study and you want to ask about what is going on at like level six of this tower, you have to spend quite a bit of time before they can even get to the point where you can see something you recognize.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I guess you're right. The objects that they use, you can define them. So they've been defined in lean. So just defining what they are. Can be done. That's a really non trivial, but it's been done. But there's a lot of really basic facts about these objects that have taken decades to prove that all these different math papers. And so lots of these have to be formalized as well. Kevin Buzzard's goal, actually, he has a five-year grant to formalize Fermosthore. And his aim is that he doesn't think he will be able to get all the way down to the basic axioms, but he wants to formalize it to the point where the only things that he needs to rely on is black boxes are things that were known by 1980 to number theories at the time and then some other person or some other work, what have you done to get from there. So it's a different area of mathematics than the type of mathematics I'm used to. In analysis, which is kind of my area, the objects we study are kind of much closer to the ground. I study things like prime numbers and”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah. You know, so yeah, we all talked about it at tea and so forth. I mean, we didn't understand, most of us didn't understand the proof. We understand sort of high-level details. Like there's an ongoing project to formalize it in Lean. Kevin Buzzard is actually.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so I was a graduate student at the time. I mean, I vaguely remember there was press attention and we all had the same, we hold pigeonholes in the same mail room, so we all pick out mail and suddenly Andrew Wiles' mailbox exploded to be overflowing.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“But that's a story that's difficult to tell if you're not an expert because it's easier to just say one person did this one thing. It makes a much simpler history.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Representative people of the 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. The very accelerated education, I skipped a lot of classes. I think I had very fortunate mentoring opportunities. And I think I was at the right place at the right time. Just because someone doesn't have my trajectory doesn't mean that they can't be good mathematicians. I mean, in a very different style, and we need people with different style. And sometimes too much focus is given on the person who does the last step to complete a project in mathematics or elsewhere that's really taken centuries or decades with lots and lots of building on lots of previous work.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“And so we have to simplify the POMA 99.9% of humanity becomes the other. And often these models are incorrect and this causes all kinds of problems. So to humanize a subject, if you identify a small number of people and say, you know, these are...”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Some recognition is necessarily important, but yeah, it's Also important to note that these things take over your life And only be concerned about getting the next big award or whatever. I mean, yeah, so again, you see these people try to only solve like a really big math problems and not work on things that are less sexy, if you wish. but actually still interesting and is instructive. As you say, the way the human right works, we understand things better when they're attached to humans. And also, if they're attached to a small number of humans, the way our humans is wired, we can comprehend the relationship between 10 or 20 people. But once you get beyond 100 people, there's a limit. I think there's a name for it beyond which it just becomes the other.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“It's always an option. But there are things that like. I mean, so I don't spend as much time as I do as a postdoc, you know, just working on one pop at a time or fooling around. I still do that a little bit. But yeah, as you're advancing your career, the more soft skills, so math somehow front loads all the technical skills to the early stages of your career. So as a postdoc, it's published or perish, you're incentivized to basically focus on proving very technical theorems to sort of prove yourself, as well as prove the theorems. But then as you get more senior, you have to start mentoring and giving interviews and trying to shape directional fields, both research-wise and sometimes you have to do very administrative things. And it's kind of the right social contract because you need to work in the trenches to see what can help mathematicians”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I have a lot less free time than I had previously. I mean, mostly by choice. I always say I have the option to sort of decline. So I decline a lot of things. I could decline even more. Or I could acquire a repetition of being so unreliable that people don't even ask anymore.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Most mathematicians, uh, there's just career mathematicians, you know, you just focus on public paper, maybe getting one promoter, one rank and starting a few projects, maybe taking some students or something. But then suddenly people want your opinion on things. And you have to think a little bit about things that you might just foolishly say because you know no one's going to listen to you. It's more important now.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“I mean, that's another sort of flip side. I mean, we're not a lot of problems that we solve, you know, some of them do have practical application, and that's great. But if you stop thinking about a problem, so he hasn't published since in this field, but that's fine. There's many, many other people who've done so as well. Yeah, so I guess one thing I didn't realize initially with the Fields Metal is that it sort of makes you part of the establishment.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, no, he's somewhat of an outlier, even among mathematicians who tend to have somewhat idealistic views. I've never met him. I think I'd be interested to meet him one day, but I never had the chance. I know people who've met him. He's always had strong views about certain things. I mean, it's not like he was completely isolated from the math community. I mean, he would give talks and write papers and so forth. But at some point, he just decided not to engage with the rest of the community. He was disillusioned or something. I don't know. And he decided to peace out and collect mushrooms in St. Petersburg or something. And that's fine. You can do that.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Certainly more on the node than on the yes. The funny thing about Picosapi is that we have also a lot more obstructions than we do for almost any other problem. So while there's evidence, we also have a lot of results ruling out many, many types of approaches to the problem. This is the one thing that the computer scientists have actually been very good at. It's actually saying that certain approaches cannot work, no-go theorems. It could be undecidable. We don't know.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Is possible. I mean, there's this various scenarios. I mean, there's one way it is technically possible, but in practice never actually implementable. The evidence is sort of slightly pushing in favor of no, that probably P is not a good NP.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Wanted to be randomly. So, more broadly, I'm just looking for more tools, more ways to show that Things are valuable. How do you prove a conspiracy doesn't happen?”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“We believe to be almost impossible to crack, at least mathematically. But if something has caught our belief as human hypothesis is wrong, it means that there are actual patterns of the primes that we're not aware of. And if there's one, there's probably going more. And suddenly a lot of our crypto systems are in doubt.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. If the Riemann hypothesis is disproven, that would be a big mental shock to the number theorists, but it would have follow-on effects for cryptography. Because a lot of cryptography uses number theory constructions involving primes and so forth. And it relies very much on the intuition that number theories are built over many, many years of what operations involving primes behave randomly and what ones don't. And in particular, encryption methods are designed to turn text-written information on it into text which is indistinguishable from random noise. Hence,”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“It's up there. P equals NP is a good one because that's a meta problem. If you solve that in the positive sense that you can find in PCOSMP algorithm, then potentially this solves a lot of other problems as well.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, if you want to do it not statistically, but you really want 100% of all inputs to for the Earth. So what might be feasible is assisting 99%. But everything. That looks hard.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“So, Conway, so similar, in fact, that was more inspirations for that project. Conway studied generalizations of the collapse problem, where instead of Moscow 3 and adding one or dividing by two, you have more complicated branching words. But instead of having two cases, maybe you have 17 cases and you go up and down. And he showed that once your iteration gets complicated enough, you can actually encode Turing machines and you can actually make these problems undecidable and do things like this. In fact, he invented a programming language for these kind of fractional linear transformations. He called a fact track as a play on Fortrad. And he showed that you could program, it was too incomplete. You could make a program that if your number you inserted in was encoded as a prime, it would sync to zero. It would go down. Otherwise, it would go up and things like that. So the general class of problems is really...”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source
“In fact, there's some mathematicians, Alex Kontovich, who've proposed that actually these collateral iterations are like these cellular automator. If you look at what happened in binary, they do actually look a little bit like these game of life type patterns And in an analogy to how the game of life can create these massive self applicating objects and so forth, possibly you could create some sort of heavier than air flying machine, a number which is actually encoding this machine, which is just whose job it is to encode, is to create a version of itself which is larger.”
2025-06-15 · Lex Fridman Podcast · #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI · IDENTIFIED FROM THE TRANSCRIPT · source