YouSaid · the spoken record

Edward Frenkel

lines on the record: 257
first: 2023-04-10
most recent: 2023-04-10
sittings or episodes: 1
sources: podcast

Every line below is reproduced as it was said and linked to the record it came from. Nothing here is summarised or generated. Directory · Search · Corrections

“Because it's so easy, so tell me it's so easy to formulate. So, in fact, I think Ferma proved the case of cubes. I think he did actually prove some elsewhere the case of cubes. But so it remained like forced. There are infinitely many cases, right? You have to, even if you prove it for cubes and for fourth power and fifth, then still there are six, sevenths, and so on. There are infinitely many cases in which it has to be proved. And so, you see, the separately simple result took 350 years to prove And in a sense, it's like mathematicians, you would think mathematics is such a sterile profession. Everybody's so serious, you know, almost like we're all wearing lab coats. Like, take an elevator to the However, look at all this drama. Look at all this dramas. We also like drama. We also have narratives. We also have our myth”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So that was the statement. So, the theorem says that the equation x cubed plus y cube equals e c Has no solutions in natural numbers. Remember, natural means positive whole numbers. So, of course, there is a trivial solution 0, 0, 0. So this works. But you need all of them to be positive. x to the fourth plus y to the fourth equals z to the fourth also has no solution X to the fifth plus y to the fifth equals e to the fifth. No solutions. So you kind of see the trend. x to the n plus y to the n plus z to the n. If n is greater than 2 No solutions in natural numbers. That is a statement of Ferma's Deceptively simple as far as famous theorems are concerned. You don't need to know anything beyond standard arith Addition and multiplication of natural numbers. That's why a lot of people, both specialists and amateurs To prove it”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“One, two, three, four, five, six, and so on. Now, what's Ferma's last theorem? Ferma asked, what about what will happen if we replace squares by cubes, for example? So x cube plus y cube equals z Are there any solutions in what do you call natural numbers? Turns out the What about force Again”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So that's the equation, or x squared plus y squared equals z squared. And it turns out that this equation has solutions in natural numbers, actually infinitely many solutions in natural numbers. For example, if x is, you take x equals 3. y equals 4 and z equals 5. Solve this equation because 3 squared is 9. Squared 16. Nine plus 1625, and that's five squ So x squared plus y squared equals z squared is solved by x equals 3, y equals 4, z equals 5. And there are many other solutions of that nature.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“This is what happened here was Fermas last theorem, B was Shimurtaniamwe conjecture, and that's what Andrew Wiles and Richard Taylor really proved. So it requires to get to Fermat's last theorem, it requires that bridge, which was established by my colleague Ken Ribbitt at UC Berkeley. So now what is the statement of Ferma's last theorem? Let me start with Pythagoreas since we already talked about it. Let me start with Pythagoras theorem, which describes the right triangles. So what is the right triangle? It's a triangle in which one of the angles is 90 degrees. This so it has three sides. The longer side is called hypotenuse and then there's two other sides. So if we denote the length of hypotenuse by Z and the two other sides x and y, then z squared is equal to x squared plus y squared.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Now, what he proved actually was not Fermat's theorem itself But a certain statement which is called Shimura Taniama Wei conjecture named after three mathematicians, two Japanese mathematicians and one French-born mathematician who worked also at the Institute for Advanced Study in Princeton. And it was my colleague at UC Berkeley, Ken Ribbitt, who in the 80s connected the two problems. So this is how it often works in mathematics. You want to prove statement A. Instead, you prove that A is equivalent to B. So after that, if you can prove B, this would automatically imply that A is correct”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“This nullifies the whole thing. Even though, well, you could say there are some interesting ideas, but it's not the same as actually having a proof. So he apparently was really frustrated and he was really, a lot of people thought that it's going to be another hundred years or whatever. And then luckily he was able to enlist with the help, assistance of his former student, also great number theorist Richard Taylor. They were able to do that 1%, so to speak. Well, some people might say maybe not one, but 5% or whatever. But it definitely was an important ingredient, but it was not, he had sort of like a big new set of ideas and this one thing didn't pan out. They were able to close it with Taylor. And it finally was published and I think was accepted and refereed in 1995 and is believed to be correct.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So, this was 17th century Twitter style proof. But a lot of mathematicians took it seriously because he had great credibility, did make some major contributions. And the search was on. So for 350 years, about 350 years, it remained unproved with many people trying and failing until in 1994. In 1993, Andrew Wiles announced a mathematician from Princeton University announced the proof and it was very exciting because he was one of the top number theorists in the world. And unfortunately about a year later a gap was found. So this is exactly what we were talking about earlier. You have 99% of the proof. There's one little thing does not quite connect.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“At some point, I was giving a public talk about this and I made it as a joke. I made a tweet. In which I wrote that I have proved this theorem, but 280 characters are not enough and kind of cuts me in mid sentence.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Beautiful story, also behind it Pierre Ferma, a great French mathematician who lived in the beginning of mostly worked at the beginning of 17th century. And he actually has to his credit a number of important contributions. But the most famous is called Ferma's Last Theorem, or Fermas' great theorem. And the reason why it became so famous is in part because he actually claimed to have proved it himself. And he did it on the margin of a book that he was reading, which was actually an important book by Diafantos about equations with coefficients and whole numbers. And he wrote on the margin literally. This equation, you know, this problem, which I will explain in a moment, I have solved it, I have found a proof, but this margin is too small to contain it.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Sure, it's easy to do. I'm an optimist. I'm an optimist. I think I always think that everything can be explained Even though I say that not everything can be explained. But in mathematics within this particular framework, I think that I always feel optimistic when people ask me to explain something. I always start with the assumption that they will understand. So let's try. One of the jewels sort of of mathematics of all time.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“You feel it 99% is done. There is this one stubborn thing which just does not compute, you know, doesn't happen. And you're trying to find that push for this last link. And it could take, and nobody knows how long it's going to take.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Get to the point where there is this much you need to prove, and it just wouldn't come to you. And you just don't see it. And it can go on for months. Super frustrating.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes or no, because there is just a different. Instance, there is a different criterion for what constitutes progress. For instance, physics, Of arguments they make, they are not triggers from a mathematical perspective. It is kind of an intuitive argument. We think it is like this. And this is acceptable in the subject for a good reason. So there is some play. It's more like human activity day-to-day activity. For instance, you and I discuss something, you have an idea and I have an idea and we argue about it. And something seems more plausible. Something seems less plausible. And so we made decide to take this point of view or that point of view as a provisional sort of like point of view and go with it. In my mind, it doesn't work this way. You either prove it or you don't. And oftentimes”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“They say you can't do it by will. You cannot make it happen. If anything, you have to relax to let it come to you. It's kind of like that. It's kind of like that. I think that what matters, but you say how to think the point is that we're talking about such an esoteric area. Mathematics is really esoteric area. It's a really strange subject where you try to fit everything in this very, very stringent set of rules. Those”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“There is a famous story about Einstein that he used to go think, think, think, and then go for a walk. And he would whistle sometimes. So I remember the first time I heard this story. I thought, how interesting, what a coincidence that this came to him when he was whistling. But in fact, it's not. This is how it works in some sense, that you have to prepare for it, but then the moment it happens when you stop thinking, actually. So the moment of discovery is the moment when thinking stops. And you kind of almost become that truth that you're seeking. But you cannot do it by will in some sense. It's kind of like, you know how in Eastern tradition they have this concept of satori, like in Buddhism, in then Buddhism, Satori, which is enlightenment. And so the various reports of Buddhist monks or Buddhist masters who have had experience”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“No, it's deliberate because, you know, First of all, my first years as a mathematician, you know. I worked every day, weekends, holidays, doesn't matter. Didn't even question that, so I would feel something's missing if I took a day off. You know, so it was just a kind of a sustained effort. The point is that still the process is nonlinear to go back to what we discussed earlier, that in other words, the way I see it is you just, you are making an effort to bring all the information into focus, what you believe is correct. And you're playing with different. Ways of connecting things, but it is a total miracle when suddenly there is inside strikes. Is not something that, in my experience, could be predicted or even anticipated or brought closer.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And concentration actually doing mathematics at the top level these days requires because we're not talking about something that is more or less good. It is something which is unassailable. It's finding this treasure at the bottom of the ocean without the acolong without oxygen. That's why it's not people go crazy sometimes, you know, there is a reason for that.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“But I have to say to these days has become so much faster. It's really hard to do it being outside. Now, Eric is unique in this way, even though he did go to great undergraduate and graduate schools. And then worked for a while in academia. There are very few examples like that. There is Yutang Zhang who proved an important conjecture in number theory about 10 years ago and is now a professor at UC Santa Barbara. He worked outside of Actemia and was able to make. Tremendous advance on his own. This case is exceedingly rare. In part, because academia is trying to protect its turf and it's kind of creating the sort of prohibitive cost of an outsider. That is true. But there is also something about how much concentration in mathematics are not in the field understand what kind of focus.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“On the one hand, we are also supposed to be the truth seekers, but in reality, of course, it is a human activity and it is a human community with all kinds of good, bad, and ugly things that happen, a lot of them under the radar screen, so to speak. And so, but maybe there is something to it. There is definitely, there are definitely people who are upholding kind of old tradition, definitely. And that is inspiring. And I aspire to be, you know, one of those, do my best. So whether this is a system that will stay or should stay, I don't know. I really don't know.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Which comes with its own downside too, because you kind of get a little disconnected from the real world because you get tenure, so you feel financially secure. They don't pay you that much, so to speak, relatively speaking, it's comfortable, but it's not that much. But you can't be fired. So there is something about this, which I definitely have benefited from it, you know. And it does People are not even aware what it's like to live outside of where you don't have this type of security. On the other hand, that also means that we're lacking certain skills, that sort of real people in the real world have developed out of necessity to deal with that sort of insecurity. So it kind of always cuts both ways. One hand it gives, and with the other hand it takes away. And it's a very interesting setup.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“But I think you gave a very good description. I'm not sure I can on it because I don't have an overarching theory of. Academia. Definitely have been part of it, and I'm grateful because it gives you great sense of security.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And it may well be that you will answer in a way that I will just burst out laughing. It's like, how could we not see it? See, so that I totally see, but I don't see one equation governing them all.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, there are such equations. Let's say Interesting particular question, right? In the language program. So moving away from physics, let's talk about math. So in the context of language program. Have recently developed with my co authors Ettingoff and Cash Dan a kind of a new strand, a new flavor of the Langless program, if you will. So far, it's a vision, it's a set of conjectures, which we have proved in some cases, but not in full generality. So yes, I would like to use your framework for me the creator. Ask her. What is the explanation of this?”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“From it and confirm them to great accuracy. But the underpinnings doesn't have the real Gregor's foundation, from mathematical perspective. So in that sense, even if In that framework, a new theory could Lead to an explanation of some new explanation of some phenomena. It would still be incomplete in a sense because it wouldn't be mathematically rigorous, you see what I mean. Because the whole framework is not yet on a firm foundation.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“There are a lot of elements. It's a huge enterprise to have a theory because you have, just to describe the fields sort of the building blocks of the theory, it's already tremendous undertaking. And he's trying to do it for curved spaces and great generality, which is what makes it so unique and so beautiful. But then on top of that, there are this issue of quantization, of actually describing them as quantum field theory. And the quantum field theory, even as a language, as a framework is currently incomplete in my opinion, and not only my opinion, it's like everybody's agrees on that, that it's a... A collection of tricks, it's a collection of tools, it's a toolbox, but it is not a consistent rigorous theory like number theory. In mathematics, physicists have still been able to derive predictions.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Think it's important to realize that, in my opinion, that's not productive and it's not feasible anyway. So having said that, there are some theories are better than others, obviously. So for instance, Eric's theory has, as far as I understand, does have a certain way of producing some of the elementary particles that we see, and as well as force of gravity. So it does have that promise. I feel that at least from the place where I had seen it about 10 years ago, it still required a lot of work to get to the point of actually saying that it does work because”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, so it's a huge motivating factor. I don't deny that, but I feel that there are better ways to motivate people than like that, than this way. Okay, so I would say, for instance, if one, because then it's not a game of winner takes all in some sense. And in fairness, when physicists say theory of everything, grand unified theory, they mean something very specific, which is unifying the standard model and Einstein's relativity theory, which is the theory of gravity. So they don't necessarily, Klorophysis may say these words, but they don't really mean them.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Now, physicists, on the other hand, have been brought up, educated for decades with this idea. And to me, and I'm not sure I should say that, but I feel like it's kind of an ultimate ego trip so that I have come up with a unified. I have found Unthere of everything. It's me. And my name will be on it. I think a lot of physicists get educated this way, especially men. Take it seriously. I've seen that happen, and I think it is counterproductive. I think that a lot of people agree that this debate is kind of, I feel like it's kind of settled. I hear it less and less. I disagree with the whole premise.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Connecting connecting, but connecting doesn't mean that it covers everything, right? So you could connect two things and then you have a Infinitely many other things which are outside of the purview of this connection. That's how it is in mathematics. I feel. And I would venture to say that most mathematicians look at it this way. Like there is no idea that somehow, I think it's actually impossible because we're not talking about such a thing as one universe. We're talking about all possible universes of all possible dimensions and so on. It is just not feasible to have a unified everything in one equation.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And I think it's really not offend anybody, but it's ultimately a fault of education system of physicists. Like in mathematics, we're not brought up. We're not educated as mathematicians with the idea that one day we will come up with the theory of everything. Even though as a joke, I said that Langland's program is a mathematical theory of everything. But I meant it's a kind of a tongue in cheek.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“He shared with me some of it when I was in New York at Columbia 11 years ago. We actually spent a lot of time where he explained to me and I found it beautiful. He has a very original idea at the core of it where you have this instead of four-dimensional, instead of 10-dimensional, he has 14-dimensional space. And I thought it was really original. And this is exactly goes to the point I made earlier that we need new ideas. I feel that without some fundamentally new idea, we won't be able to get closer to understanding our universe. Now, I have a problem with the whole idea of theory of everything. I don't believe that one exists, nor that we should... Aim to construct one.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, in the form that it is now, that seems unlikely, but it could well be that based on these ideas with some modifications, with some essential new elements, it could work out. So I would say right now it doesn't look so good, like from the point of view from what we know. But maybe somebody will come into juice like square root of negative number I mean, they already introduced, but I mean, kind of like as a metaphor Maybe somebody will come and say, What if we do this? It looks crazy. You know, speaking of Niels Bohr, he had this famous quote that he said to somebody. There is no doubt that your theory is crazy. The question is whether it's crazy enough to describe reality. So that's where we are, kind of, you know.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“That's kind of like great luck, you know, we would say. In science, this happens sometimes that you have this theory which is not supposed to work because there are so many seemingly contradictory demands on it. And yet there is a sweet spot where they balance each other. So string theory is kind of like this. The unfortunate aspect of it is that it balances itself in 10 dimensions and not in four. So maybe there is another universe somewhere. But see, as a mathematician, for me, all spaces are created equal. So, mathematicians love string theory because it has given us so much food for thought.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Also, just the mathematical things that come out of it, the kind of it looks impossible to satisfy various constraints and then that is sort of like a unique way to do it. So that's sort of every time that happens when you have some system over determined system. Let's suppose. Have to do like five interviews in one day And you wake up in the morning and you're like, that's impossible. Because then so many things have to align. For instance, let's suppose you have to go from one place to another. Then you have a commute, and then who knows maybe there is a traffic jam and stuff like that. And now suppose that it all works seamlessly and there were like a bunch of places where it could have gone hopelessly wrong. And then in the evening, you're like wow, it worked. That's beautiful, right?”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, first of all, remember we talked about Pythagoreans and how for Pythagoreans, the whole world was the symphony where you have this different vibrations of all the humans. Every human is a vibration. Every animal, every being, every tree, and every celestial body and so on. So strength theory is kind of like that because string theory there is this fundamental object which is a vibrating string. And all particles are, in a sense, supposed to be different modulations or vibrations of that string. So that by itself is already interesting, that you kind of Describe this diversity of various particles and interactions between them using one guiding principle in some sense.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Standard model describing the three known forces of nature electromagnetic, strong and weak with great accuracy. And Einstein's relativity, which describes the fourth called gravity. Everybody above a certain age knows that one. So these two theories are in contradiction at the moment. And string theory was one of the promise of string theory was that it would unify those two. And so far it has not happened. So we are kind of at a very interesting place right now. And I think that new ideas perhaps are needed and I wouldn't be surprised if Whiton is one of those people who come up with those ideas.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Now, of course, the thing is that the theory is that physics, one could say, is in a sort of a crisis in some sense because of a current gap between the sophisticated theories which came from applying sophisticated mathematics and the actual universe. So we have theories which describe 10-dimensional worlds, 10-dimensional spacetime coming from string theory and things like that. But we don't know yet how to apply it to understanding our universe. Lot of progress has been made, but it's kind of a kind of impasse right now. And at the same time, our most realistic theories, most advanced theories of the four-dimensional universe are in contradiction with each other.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Groups of mathematicians trying to prove his conjectures and his ideas, and he would always be proven right. So in other words, being able to glean some mathematical truths from physical theories, that's one side. On the other hand, conversely, applying sophisticated mathematics is probably... Physical kind of good Lord and mathematics the fastest, I don't think some younger physicists maybe could come close, but it's still for them a long way to go to get to be comparable to Witten. Take some of the most sophisticated mathematics And don't learn it to the point where it becomes Then use it to gain some new insights on the physics side.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“He has had this unique vision of the subject. He was able to connect different things. Especially find connections between quantum physics and mathematics. Almost unparalleled. I don't think anyone comes close in some sense in the last. 50 years to him in terms of finding just consistently time after time, breaking new ground, new ground. So he would basically, one way one could describe it is. Would take some idea in physics. Find an interpretation of it in mathematics and then say distill it, present it in mathematical terms and tell mathematicians this should be like that, you know, kind of like 1 plus 2 plus 3 plus 4 is minus 1 over 12. And mathematics should be like, no way. And then it would pan out, and mathematicians would then whole industry would be created”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, fascinating. I enjoyed it very much. I also felt they have to keep up, you know. And so we wrote this long paper in 2007 and we collaborated for about a year. I have known him before and we talked before and I've seen him since and we talked, but it's very different to just meet somebody at conferences and have a conversation. Opposed to actually working on the project together. So he's very, very, very serious, very focused. This is one thing which I have to say. I was really struck by this”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“It means that what we believe are the fundamental elements of mathematics are not something beyond. It's like we previously thought that atoms are indivisible. Then we found out that there is a nucleus and electrons and the nucleus consists of protons and neutrons. Then we thought, okay, protons and neutrons must be elementary. Now we know they consist of quarks. So it's about kind of finding the quirks of mathematics”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So there is this one thing which has different projections, except it's not just a table and a wall, but there are many different walls, if you will.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Would say what it suggests is that there is some hidden principles which we still don't understand. My view is that we still don't know why, that we can prove some instances of this correspondences and connections. We still don't know the real underlying reasons, which means that there is a certain layer. Beneath the surface that we see now. It is like, so the way I see it now is like this, that there is something three-dimensional like this bottle, but what we are seeing is this projection onto the table and the projection to wall. And then we can map things from one projection to another and you say, oh my God, that's incredible. But the real explanation is that both of them are projections of the same thing. And that we haven't found yet. But that's what I want to find. So that's what motivates me, I would say.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Go out and explain to them to the different sites what this is all about so that more people are aware of this hidden structure, so this hidden parallels, if you will. So that has been sort of a theme in my research. And so I guess now I kind of understand more why it's kind of a balance, you know, like what we talked about earlier.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Bridging the gap between these patterns in quantum physics and in geometry, finding kind of a substruct, a kind of a superstratum, if you will, a kind of a way to connect these two things, kind of a bridge between these two fields. So I subsequently collaborate with Whitton on this, and this has been one of the major themes of my research. It's sort of, I always found it interesting. To connect things, to unite things Was younger, I couldn't understand why, but I was always interested in When not working in specific field, but kind of cutting across fields. And then we discovered that, for instance, I took some people who know what happens in this field but don't know what happens in their field. Or conversely. And then I would find it imperative.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So, what Langlands found is that some really difficult questions in number theory could be translated into much more easily tractable questions in harmonic analysis. That was his initial idea. But what happened next surprised everybody that the kind of patterns that he was able to observe, the kind of regularities that he was able to observe, which were quite surprising, were subsequently found in other areas of mathematics. Example, in geometry. And eventually in quantum physics So, in fact, Ed Whitton, who is kind of a dean of modern theoretical physicists, a professor at the Institute for Advanced Study as well, got interested in this subject. I describe in my book how it happened. And he was instrumental in...”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Any music lover can appreciate because the sound of a symphony can be kind of decomposed into sounds of different instruments and each of those sounds can be represented by a wave like this like a sine function. Those are the harmonics. The period of a harmonic periods of different nodes are different. They correspond to different nodes and different instruments, different semitons, if you will. But they all combine together into something special, which is not cannot be reduced to any one of those. So it's mathematically it's the idea that you can decompose a signal as a collection, as a simultaneous oscillation of several elementary signals. That's gold harmonic analysis.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Sure Is a mathematician, it's a name of a mathematician, a Robert Langlens. have worked. In fact, he used to occupy the office of Albert Einstein at the Institute for Advanced So he in the late 60s. He came up with a set of ideas which captivated a lot of mathematicians, several generations of mathematicians by now, which came to be known as the Langlands program. What it is about is connecting different fields of mathematics, which seem to be far away from each other. For example, number theory, which, as the name suggests, deals with numbers, and various equations with, you know, like x squared plus y squared equals 1. And on the other side, harmonic analysis. Something that”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Become widely available, or at least people will know where to find them, and they will not be afraid of going there and looking. And I think this will help because, like I said, for one thing, it gives you a sense of belonging. It gives you, it kind of is an antidote to the kind of alienation and separation that we feel today oftentimes because of ideological divide, sectarian strife and all kinds of things like that. Because then you will, once you see, there's like a critical mass of this beauty that kind of like dawns on you. It's like my God, this is what we all have in common.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source