#370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love

30:03And also we get hit every time we act different, okay, every time we act that doesn't in a way that doesn't fit sort of the pattern. We get punished by the teachers, get punished by parents and so on. And don't get respect when you act childlike in your thinking when you are fearless and looking like an idiot. That's right. Because there's a hierarchy in society. No, but it wants to look like an idiot, you know, once you start growing up or you think you're growing up, yeah, in the beginning, you don't even think of, you don't think in these terms. You just play, you're just playing and you are open to possibilities, to this infinite possibilities that this world presents to us.

30:45So how do we, I'm not saying that education system should not be also kind of taming that a little bit. Obviously, the goal is balance that acquiring knowledge so that we can be more mature and more discerning, more discriminating in terms of our approach to the world, in terms of our connections to the world and people and so on. But how do we do that while also preserving that innocence of a child? And my guess is that there is no formula for this. It is a life is an answer every life every human being is one particular answer to how do we find balance? That's one in perfect approximation, approximate solution to the problem.

31:42But we can look up to the great ones who have credentials in a sense that they have shown and they have proved that they have done something that other humans appreciate, our civilization appreciates, say Isaac Newton or Alexander Grotnik or Pablo Picasso. So they have established their right to speak about this matters and we could not dismiss them as mere madmen. They say, okay, well, if the same thing was said by somebody who never achieved anything in their field of endeavor, it would be easy for us to dismiss it. But when it comes from someone like Isaac Newton, we take notice. So I think that's something important that they teach us.

32:31And especially today, in this age of AI, of course there's a big elephant in the room always, which is called AI. And so I know that you are an expert at this subject. And we are living now in this very interesting times of new AI systems coming online pretty much every couple of weeks. So I kind of, to me, that whole debate about what is it? What is artificial intelligence? What is it going? What should we do about it? Needs an influx of this type of considerations that we've just been talking about. That, for instance, the idea that inspiration, creativity, doesn't come from accumulation of knowledge because obviously child, a child has not yet accumulated knowledge.

33:22And yet the great ones are on record saying that a child has a capacity to create and an adult credits the inner child for this capacity to create as an adult. You see, that's kind of weird if we take the point of view that everything is computation, everything is accumulation of knowledge that just bigger and bigger data sets, finer and finer and newer networks. And then we will be able to replicate human consciousness. If we take that point of view, then what I just said kind of doesn't fit because obviously a child has not been fed any training data as far as we know. Yet they are perfectly capable of, you know, of distinguishing between cancer dogs, for instance, and stuff like that.

34:11But much more than that, they also keep a ball of that, you know, wide -eyed, you know, sort of perspective. So, does it can it really be captured? That perspective, that sense of awe, can it really be captured by computational alone? I actually, I don't know the answer, so I'm not sort of trying to to present a particular point of view. I'm trying to question any theory that starts out by saying, life is this or consciousness is this. Because when you look more closely, you recognize that there are some other things at play, which do not quite fit the narrative. And it's hard to know where they come from.

34:59It's also possible that the evolutionary process has created is the very, it is computation and the child is actually not a blank slate, but there is a result of one of the most incredible several billion year old computations that had explored all kinds of aspects of life on earth, of war and love and terror and ambition and violence and invention, all of that from the bacteria today. So, like that young child is not a blank slate, they're coming, they're actually holding within them the knowledge of several billions of years. Right, the question is whether as a child, you carry that in the form of the kind of computational algorithms that we are aware today.

35:59You see, what strikes me as unlikely is that how should I put it? How interesting that, you know, you are a computer scientist there are other people come, I have studied computer science, so I know a little bit. And so it's tempting to say, oh, the whole world is computer science or it's based, can be explained by computer science. Why? Because it makes me feel good. Because I have mastered it, I have learned it. My ego is very happy and people come to me and they look up to me and they revere me. Kind of like priests in old days when the religion was paramount, when you would be with tend to explain things in theological religious terms.

36:43Today science has progressed, there are fewer people who kind of buy into religious, official religion, you know. So, we have this urge, I suppose, to explain and to know and to dissect and to analyze and to conceptualize, which is a wonderful quality that we have and we should definitely pursue that. But I find it a little bit unlikely that the universe is just exactly what I have learned and note something that I don't know. You see? Well, there's a lot of interesting aspects of the current, large language models that one perspective of it, I think speaks to the love and math that you talk to, which is they're trained on human data from the internet.

37:36So, at its best, a large language model, like GPD 4, captures the magic of the human condition on its full display, its full complexity. And since mimicking, it's trying to compress all the debates and discussions, the perspectives, all the different ways that people approach solving different problems, all of that compressed. So, we live, we're in each individual ants, we only have like, we have a family, we interact with a few little ants, and here comes AI that's able to summarize, like a TLDR report of humanity. And that's the beauty of it. So, I embrace it. I'm very impressed by it. I wonder if it can be very impressive, meaning way more impressive in being able to fake or simulate or emulate a human fake.

38:34I'm glad you mentioned that because that seems to be the mantra. It's just fake, fake it till you make it. Yeah, isn't it? I don't know what we all do though. No, yes, we do that, but we also do other things. We can be truly in love. We can be truly inspired when it is not fake. I do believe, call me a romantic, okay, but I do believe. And this is a very, I'm glad we are putting it in this terms because I've had conversations like that. Yeah, fake it till you make it, but that's like, that's what humans do. Yes, we do that, but not all the time. So, and that is debatable because also, I speak from my own experience.

39:10And that's where the first person perspective comes in. The subjective view. I cannot prove to you, for instance, or anyone else, that there are certain moments in my life where I am genuine. I am pure, so to speak, when it's not faking it. But I do have a tremendous certainty of it. And that's a subjective certainty. Now, as a scientist, I'm also trained to give more credibility to objective arguments and other things that can be reproduced, things that I can demonstrate, I can show. But as I get older, as I get more mature, so hopefully, you know, I'm starting to question why I am not giving as much credibility to my subjective understanding of the world, the kind of the first person perspective, when I actually, modern science has already sold on that, you know, quantum mechanics has shown, unambiguously, that the observer is always involved in the observation.

40:17Likewise, girdles in completeness theorems to me show how essential is the observer of the mathematical theory. For one thing, that's the one who chooses the axioms. And we can talk about this in more detail. Likewise Einstein's relativity, where time is relative to the observer, for instance. That's brilliant. You're just describing all these different scales, the observer, what the observer means. So we, science of 19th century had the from modern perspective, and I don't want to offend anybody, had the delusion that somehow you could analyze the world being completely detached from it. We now know after the land market achievements of the first half of the 20th century that this is nonsense.

41:03That is simply not true. And this has been experimentally proved time and time again. So to me, I'm thinking maybe it's a hint that I should take my first person perspective seriously as well and not just rely on kind of objective phenomena, things that can be proved in a in a in a traditional sort of objective way by setting up an experiment that can be repeated many times. Maybe I fall in love in the party, you know, the deepest love of my life perhaps perhaps hasn't happened yet. Perhaps I will fall in love and it's unique. It's a unique event. You can't reproduce it necessarily. You see. So in that sense, you see how these things are closely connected.

41:46I think that if you, if we are declaring from the outset that all there is to life is, you know, computation in the form of neural networks or something like this. However sophisticated they might be. I think we are from the outset denying to ourselves the possibility that yes, there is the side of me, which is not faking it. Yes, there is a side of me, which cannot be captured by logic in reason. And you know what another great scientist said, bless Pascal. He said, the heart has its reasons of which the reason knows nothing. And then he also said, the last step of reason is to grasp that there are infinitely many things beyond reason.

42:32Who interesting? This was not a theology and this was not a priest. This was not a spiritual guru. It was a hardcore scientist who actually developed, I think, one of the very first calculators. How interesting that this guy also was able to impart on us that wisdom. Now you can always say that's not the case. But why should we, from the outset, exclude this possibility that there is something to what he was saying? That is my question. I'm not taking sides. What I'm trying to do is to shake a little bit the debate because most mathematicians that I know and computer scientists, even more so, they're kind of already sold on this.

43:23We are just, you know, reminds me of this famous Lord Calvin's quote from the end of 19th century. There's some debate whether he actually said that, but never let a good story, you know, he said, physics is basically finished. All that remains is more precise measurement. So I find a lot of my colleagues are happy to say, everything's finished. We already got it. We got it. Maybe a little tweaks in our language models. So now here's my question. I'm kind of playing devil's advocate a little bit because I don't see the other side of the code that I've represented that much. And I'm saying, okay, could it be also that if you believe in that, that that becomes your reality, that you can kind of put yourself in a box where everything is computation.

44:19And then you start seeing things as being such. It's confirmation bias if you will, you know, this also reminds me, you know, I think a good analogy is it's a friend of mine, Philip caution told me that in France, there is this literary movement, which is called Uli Po. O -U -L -I -P -O. And it's a bunch of writers and mathematicians who create works of literature where in which they basically impose certain constraints. A good example of this is a novel, which is called the Void or disappearance by writer named George Perreck, which is a 300 -page novel in French, with no, no, which never uses the letter E, which is the most used widely used letter of the French language.

45:11So in other words, he said this parameters for himself. I'm going to write a book where I don't use this letter, which is a great, you know, it's a great experiment, and I applaud it. But that's what it's one thing to do that and to kind of show his game'smanship, if you will, and his ability as a writer. But it's another thing, if at the end of writing this book, when you finish the book, he would say letter E actually doesn't exist. And the right to convince us that in fact, French language does not have that letter, simply because he was able to go so far without using it, you see. So self -imposed limitation, that's how I see it.

45:53And I wonder why we should do that. Do we really need, do we really feel the urge to say the world is like that? The world can be explained this way or that way. And I'm saying it, you know, it's a personal question for me because I am addicted to knowledge myself. You know, hi, my name is Edward. And I'm a knowledge addict. Okay, I'm being serious. I'm not being facetious. Up until very recently, maybe a couple of years ago, I simply did not feel comfortable if I could not say that given the answer, explanation. And I was like, oh, there has to be some explanation. And I try to frantically search for it.

46:32Just for somebody like me, I know, you know, a left brainiac. And, you know, that's kind of typical for scientists for mathematicians. It is incredibly hard. Just to allow the possibility that it's a mystery and not to feel the urge to get the answer. It is incredibly hard. But it's possible. And it is liberating. Yes, recovering, recovering, I think, to knowledge. Let me say what you gain from it. For instance, I understand the value of paradoxes. I appreciate paradoxes more. And you know, to use another philosopher, Soran Kirkigar, the Danish philosopher said, I think, or without paradox, is like a lover, without passion.

47:29A poetry, a media, a critique. Right. And you know, Nils Bohr said in Simmerway in the great Danish also. It is something about the, something about the ins. I think it's all started with Hamlet, you know. He said, the opposite of a simple truth is a falsity. But the opposite of a great truth is another great truth. In other words, things are not black and white, you know, they're not. And I would even venture to say the most interesting, interesting things in life. I like that. The ones which are ambiguous is an electron, a particle or a wave. It depends how you set up an experiment. It will reveal itself as this or that, depending on how you set up an experiment.

48:24This bottle, if you project it down onto the table, you will see more or less a square. If you project it onto wall, you will see a different shape. And naive question would be, is it this or that? We understand that it's neither. But both projections reveal something. There are real different sides of it. A paradox is like that. It's only paradoxical if we are confined in a particular vision, if we are wedded to a particular point of view. It's a harbinger, if you will, of a possibility of seeing things in a more, as they are, as a more sophisticated than we thought before. You see, that's such a difficult idea for science to grapple with that, you know, I don't know how there's so many ways to describe this, but you could say maybe that the subjective experience of the world from an observer is actually fundamental.

49:28But we know that our best physical theories tell us that, unambiguously, in quantum mechanics, actually, you know, Heisenberg, I think, captured the best when he said, what we observe is not reality itself, but reality subjected to our method of questioning. When I talk about electrons, for instance, so that there is a very specific way in which you, in which this is realized, there is a so -called double slit experiment, right? So, for those who don't know, you have a screen and you have a meter from which you send, you kind of throw, shoot electrons. And in between, you put another screen which has two very cool slits, parallel to each other.

50:11If we were shooting, you know, tennis balls, each ball would go through one slit or another and then hit the screen behind this or that slit, so you would have, let's say, the color, the painted. So there will be sort of bumps or spots of paint behind this or that. But that's not what happens when we shoot electrons. We see an interference pattern as if we were actually sending a wave so that each electron, it seems like each electron goes through both slits at once and then has the audacity to interfere with itself where at some points, you know, to crest will amplify and at some point a crest in the trough would cancel each other.

50:52Yet, so that suggests, okay, so the electron is a wave, not so fast because if you put a detector behind one of the slits and you say, I'm going to capture you. I'm going to find out which slit you went through. The pattern will change and it will look like the particles. So that's a very concrete realization of the idea that depending on how we set up an experiment, we will see different results. And the problem is that our psyche, I feel, kind of lagging behind in part because maybe our scientists are not doing such a great job. So I take responsibility for this, that why haven't I explained this properly, you know, I tried, you know, in a bunch of talks and so on.

51:36So now I'm talking about this again. Our psyche kind of lagging behind. We're still, even though our science has progressed so much from the certainty and the determinism and all of that of the 19th century, our psyche is somehow still attached to those ideas, the ideas of causality of this naive determinism that the world as a bunch of billion balls getting each other driven by some blind forces, you know, that's not at all like it is. And we've known this for over for, well, for about 100 years at least, you know, and you call this self -imposed limitation. It is a self -imposed limitation when we pretend that that for instance, that there's naive ideas of 19th century physics, I still valid and then start applying them to our lives and then also derive conclusions from it.

52:27And for instance, people say, there is no free will. Why? Oh, because the world is just a bunch of billion balls. Where is the free will? But excuse me, didn't you get the memo that this has been debunked thoroughly by the so -called quantum mechanics, which is our best scientific theory? This is not some some kind of bullshit or some kind of, you know, concoction of a of a madman, this is our scientific theory, which has been confirmed by experiment. So we should pay attention to that. So, but of course, it's not just self -imposed limitation. Unfortunately, in this case, there is a big issue of education.

53:03So a lot of people are not aware of it through no fault of their own because they were never properly taught that because our system is broken, education systems is broken, especially in math. And then our, so where do we get information? You get information from our scientists who actually write popular books and so on, which is a great, you know, great thing that they do. But a lot of scientists somehow, when it comes to explaining the laws of physics, they're doing a fantastic job talking about this phenomenon, for instance, double slit experiments and things like that. But then, you know, interviewed by science magazine about free will and so on, they revert back to 19th century physics as if those developments actually never happened.

53:52So to me, this is single most important sort of issue in our popular science. The idea that somehow there is this world out there, but it's complete has nothing to do with me. So I can, I can reveal in the intricacies of these particles and their interactions. But completely ignore what implications this has for my own relationship to physical reality, to my own life, you know, because it's kind of scary, I guess, you know. But also what are the tools with which we can talk about the observer, the subjective view on reality? What are the tools we can talk about rigorously, talk about free will and consciousness?

54:46What are the tools of mathematics that allow that? I don't think we have those tools. Because we haven't been taught properly. So actually tools are there. For instance, I think, well, here we have to say, my conviction is that everybody knows. In the heart of hearts, everybody knows that there is that. There is something ineffable, there is something mysterious. And in fact, you know, somehow, immediately, I feel that you know, the impulse to quote somebody on this because as if as if my own opinion does not go. There's a long dead expert. I have said that. You know, so like, how, see, look at me.

55:34I have supposedly like this smart intelligent person. I am afraid to say it and own it myself. I have to find confirmation. I have to find an authority who agrees with me. And in fact, it's not so difficult to find because Albert Einstein literally said the most important thing in life is the mysterious. Okay, he actually said that there are some quotes which are attributed to him, which he never said. But this he did. I investigated. Okay. But more importantly, you know, how do you feel about it? I think that everybody knows. But in other words, he also said Einstein. Imagination is more important than knowledge.

56:17Okay. And he explained for knowledge is always limited. Whereas imagination embraces the entire world, giving birth to evolution. It is strictly speaking, a real factor in scientific research, he says, and he says, I am enough of an artist to follow my intuition in the imagination. That's Albert Einstein again. So, and I feel the same way to be honest. If I think about my own mathematical research, it's never linear. It's never like, give me more data, give me more data, give me more data. Boom. The glass is full. And then I come up with a discovery. No, it's always, it's always, it's always felt as a jump, as a leap.

56:56And I have, I have actually been studying various examples in history of mathematics of some fundamental discoveries, like discovery of complex numbers, like square root of negative one. I wonder if a large language model could actually ever come up with the idea that square root of negative one is something that is essential or meaningful. Because if all the information that you get, the all the knowledge that had been accumulated up to that point tells you that you cannot have a square root of a negative number. Why? Because if you had such a square root, we know that if we would have to, if you square it, you get a negative number.

57:41But we know that if you square any real number positive for negative, you will always get a positive number. So, checkmate, you know, it's over square root of negative one doesn't exist. Yet, we know that these numbers make sense. They're called complex numbers. And in fact, quantum mechanics is based on complex numbers. They are essential and indispensable for quantum mechanics. Could one discover that? So, to me, that sounds like a discontinuity in the process of discovery. It's a jump. It's a departure. It is like a child who is experimenting. It's like a child who says, I'm not afraid to be an idiot.

58:19Everybody says their dolls are saying square root of negative number doesn't exist. But guess what? I'm going to accept it. And I'm going to play with it. And I'm going to see what happens. This is literally how they were discovered. There was an Italian mathematician, astronomer Astrologer. He was, he made money apparently by compiling astrological sort of readings for the elite, you know, of his era. This is 16th century, as one does. Again, Blur. All around interesting guy. I'm sure we would have an interesting conversation with him. Geralama Cardano. He also invented the, it was called Cardan Shaft, which is an essential component of a car.

59:05Cardano Vival, we say in Russian. So, he wrote a book which is called R -Smagna, which is like a great art of algebra. And he was writing solutions for the cubic and cortic equations. This is something that is familiar because it's cool. We study solutions of quadratic equations. Equations of of degree two. So, you have a x squared plus b x plus c equals zero. And there is a formula which solves it using radicals, using square roots. And Cardano was trying to find a similar formula for the cubic and cortic equations for which, which would start with x cube or x to the power four is supposed to x squared.

59:46And in the process of solving this equations, he came up with square root of an negative number, specifically square root of minus 17. And he wrote that I have to forego some mental tortures to deal with it. But I am going to accept it and see what happens. And in fact, at the end of the four, at the end of the calculation, this weird numbers got cancelled, it kind of cancelled out. In the formula appeared square root of negative 17 and its negation. So, they kind of conveniently gave the right answer, which is not involved those numbers. So, he was like, what does it mean? Mental tortures. So, you see from the point of view of the thinking mind, it is something almost unbearable.

1:00:34It's almost I feel that a large language model, a computer running a large language model trying to do that would just explode. And yet, a human mathematician was able to find the courage and inspiration to say, you know what? What's as wrong? Why we saw adamant that these things don't exist? That's just our past knowledge, based on what our past knowledge is and knowledge is limited. What if we make the next step? Today, for us, mathematicians, complex numbers, we don't recall them. And not at all, mysterious. The idea is simply that you plot real numbers, that is to say all the whole numbers like 0, 1, and so on, 2, and so on.

1:01:15All fractions like 1 ,5 or 3 ,5 or 4 over 3. But then also numbers like square root of 2 or pi. We plot them as points on the real line. So, this is one of the kind of perennial concepts even in our very poor mathematical curriculum at school. But now, imagine that instead of one line, you have a one axis, you have a second axis. And so, you numbers now have two coordinates, x and y. And you associate to this point with coordinates x and y, the number x, which is a real number plus y times square root of negative 1. This is a graphical geometrical representation of complex numbers, which is not mysterious at all.

1:02:01Now, it took another two or three hundred years for mathematicians to figure that out. But initially, it looked like a completely crazy idea. So, all it is, all complex numbers is just an expansion. We're going to number two, real numbers. The real part and the imaginary part. It's just an expansion of your view of the mathematical world. The fact that you can actually, you can add them up by adding together the real parts and imaginary parts, that's easy. But there is also formula for the product, for the multiplication, which uses the fact that square root of minus 1 square root is minus 1. And the amazing thing is that, that product, that multiplication, satisfies the same rules, the same properties that are usual operation of multiplication for real numbers.

1:02:46For instance, there is an inverse for every non -zero number that you can find. Number five has an inverse, one over five. But one plus i also has an inverse, for instance. That was always there in the mathematical universe, but we humans didn't know it. And here comes along this guy who engages in the meta -torture, who takes a leap off the cliff of comfort of mathematical comfort. Established knowledge. Established knowledge. Right. And now, obviously, for each sort of fruitful leap like that, there probably were thousands of things which went nowhere. I'm not saying that every leap, you know, it's like it's an open shooting game.

1:03:28Because, for example, you can try to do the same with three -dimensional space. So you have coordinates x, y, and z. And you can say, oh, if this one dimensional, we have a bona fide numerical system called drill numbers. If it's two -dimensional, which is like, you know, geometrically, it's just like the stable top extended to infinity in all directions, these are complex numbers. And we can define addition and multiplication. And they will satisfy the same properties as real numbers that we're used to. What about three -dimensional space? Is it possible to also define some operation of addition and multiplication on it so that these operations would satisfy the properties that we're used to?

1:04:08And the answer is no. You can define addition, but you can't define multiplication for which there would be an inverse, for instance. So there is something special about the plane, the two -dimensional case. And by the way, the next question would be what about four -dimensional? In four -dimensional space, again, you can, and you get what's called Quaternions, discovered by an Irish mathematician Hamilton in the 19th century. And then in the eight -dimensional, there is something similar called Octonions, and that's about it. So how interesting. This structure exists in dimension one, two, four, and eight, which are these four, two to the third powers.

1:04:51That's one of the bigger mysteries in mathematics. Why it is so? So yes, a hint. There's a hint of what's missing in our high school curriculum, the kind of fascinating mysteries. Yes. The appreciation of the mystery. So in other words, yes, we resolved with this one mystery that we understood that square root of the service, those now, to describe those numbers. Did we find the theory of everything? No, because we then invited other mysteries, because we pushed the, we pulled the veil, so to speak, we pushed the frontier, and then new things come, get illuminated, which we couldn't see before.

1:05:38That's how I see the process of discovering mathematics. It's an endless, limitless pursuit. Can you comment on what you think this human capability of imagination that Einstein spoke about, of the artists following their intuition in this big, Alice's wonderland world of imagination. What is it? You visit there sometimes. What does it feel like? Yeah, what does it feel like? What is it? What is it? What is that like? What is it? What is it? It's like playing, but I think all of us are engaged in that kind of play, no matter when we do what we love, I think it always feels the same. It's not real, right?

1:06:14You're, so you're describing a feeling, but that place you go to in the imagination, right? It's bigger than the real world. So there is a big conundrum as to whether mathematics is invented or discovered, and mathematicians are divided on this. Nobody knows. Where do you bet your money on? Finitially. I bet you're right. So let me tell you something. My views are have evolved. When I wrote love and math, when I wrote my book, I was squarely on the side of mathematics is discovered. What does it mean? Usually mathematicians or others who have this idea, what I believe, are called a plateonists in honor of the great philosopher Plato, who talked about these absolute perfect forms.

1:07:08So for me, about 10 years ago, the world of mathematics was this world of pure forms, this beautiful, pure forms, which existed outside of space and time, but I was able to connect to it through my mind. And as it were kind of dive into it and bring treasures back into this world, into this space and time, that's how I viewed the process of mathematical discovery, how nice, how neat, very neat, and the picture. Also makes you feel connected to something divine, allows you this sense of escape from the cruelty and injustice of this world, which I now recognize. And the divine world of forms is stable, relies on something stable.

1:07:53In that world, everything is clear cut. It's either true or false. Yeah. I'm nice. It's very nice. The biggest delusion of all. Allegedly. I think now, I think now, I understand why I liked it because I think that I was very dissatisfied with the what we call the real world, the world around me, the cruelty, the injustice of it. And I went through certain experiences as a kid, which made me love mathematics even more as this place where I could be safe and in control. Maybe you see the human world is lesser than the mathematical world. Yes. As more limited to the mathematical. Yes. Yes. And I think that I think that it's still missing the mark in some sense because in fact, what I now think it's not, it's not, it's a paradoxical question whether mathematics is invented to discover it whether there is this world of pure forms and so on.

1:08:57Is is another paradoxical question which doesn't have a simple answer. Like whether electron is a particle or a wave. From one point of view, yes, it's true. And just the fact that so many mathematicians today actually subscribe to this idea. Gives it a certain credibility because that's what we feel. We do feel that we dive into, dive into that mindscape, so to speak, but the very structured mindscape where I wrote in a loving math that enchanted gardens of Platonic reality where all this fruit grows. And then we might make sure it gives you this sort of romantic sense of an explorer. And someone may be stuck in you know some provincial town in Russia for instance, but have the sense of Magellan, you know, of traveling around the world.

1:09:54It's just not in the world that we usually think of. So it's one point of view, but the other point of view is that yes, it is a human process. Of course it is. I mean, it is, you cannot deny that. It's human beings who have so far discovered new mathematics. And I do not deny the possibility that a computer program will be able to discover new mathematics, but so far it's been humans. So whatever it is, whether it's discovered or invented, it is a human activity. The possibility that paradoxes are actually fundamental to reality and really, really internalizing that that we exist in the world of not forms but of paradoxes.

1:10:37Bingo. And so it's like what I say. But if you think it's weird and I agree with you as a recovering adding to knowledge, you know, but I am liking it more and more because there's so much freedom in it. And like like Nils Bohr said, you know, I quoted that earlier the opposite of a great truth is another great truth. He is pointing out to this fact that you know, and he also said that some things in quantum physics are so complicated, the only way you can speak of them is in poetry. So in other words, what is that about poetry? What is about art? Why are we so drawn to that? Why are we so captivated by those forms of, by, they are not intellectual necessarily.

1:11:27They are not, when you look at a painting that you like, when you listen to music, that you love, you get lost in it, you get absorbed in it, it can make you cry, it can make you love, it can make you remember something, it can make you feel more confident, it can make you feel sad or happy and so on. What is this all about? Is it really just some play between some kind of like cell phone play or some neurons or hitting on each other? Is it really that? Only, maybe. It could be, it could be both. I'm just worried about kids these days that might live in a world of paradoxes, you know, if there's no God, everything is possible.

1:12:07I mean, just they'll have a little too much fun and we have to put a constraint to the fun. Have you looked at the world lately? I haven't checked in in a while. You think it's perfect? The way this is now, the world without paradoxes. The world in which we believe that every answer can be answered, as yes or no, that it is this or that. And if you disagree with me, you're my enemy. Would not be interesting if this 21st century is a transition into seeing the world as a world of paradoxes. I'm telling you, you know, people predicted that. You know, they're joke -warriors, you know, that the axis of the of the earth is rotating relative to the plane in which the earth goes around the sun and the period of this revolution is around 2000 years.

1:12:52So there is a traditional way of measuring that by this era, you know, that the ages. So the previous one is called the Age of Pices because of the constellation of Pices that it points to, so to speak, you know. And now it's, you know, as in famous musical hair, they said the Age of Aquarius is upon us. So the different people, they dated differently, but somewhere around the time where we are finding ourselves. How interesting, right, is all this drive and all them. Difficulties to world is experiencing. This might actually be the transition to something. More harmonious, wouldn't it be nice?

1:13:33It's also interesting that people from long ago are able to predict certain things. It's, and it's almost like from long ago, and you've talked about this with Pythagorean, that it seems that they had a deep sense of truth. That's right. Permi is all of this even now. So it's not just a linear trajectory of an expanding knowledge. There's a deep truth that permeates the whole thing. Yes. So that's how I see it. Actually, I gave a talk about Pythagoras and Pythagoreans just a few weeks ago in the Commonwealth Club of California in San Francisco. And because of that, I did a kind of a deep dive into the subject.

1:14:21And I learned that I actually totally misunderstood Pythagoras and Pythagoreans, that they were much deeper than I thought, because you know, most of us remember Pythagoras from the Pythagoras theorem about the right triangles. We also know that Pythagoreans were instrumental in introducing the tuning system for the musical scale. The famous perfect fifth, three halves for the G, for the soul, compared to the frequency of Dua or C. But actually, they were much more interesting. So for them, numbers were not just clerical devices, you know, that not kind of thing that you would use in accounting only.

1:15:13They were imbued with the divine. And I cannot say that I think we lost it. At least I have lost it. I look at numbers and I don't really see that the divine, the divine, that they clearly did. And so the, why else, you know, how else would you explain? So in other words, divine is of course, is a term which is, you know, it's a bit loaded. So it's hard to escape that. Let's just say something that more from the world of imagination and intuition than from the world of knowledge. Let's just put this way. They were able to divine, okay, strike that, to intuit, to intuit that the planets were not revolving.

1:15:58The sun and the planets were not revolving around the earth. They were the first ones, at least in the western cultures, far as I know. And in fact, Capernicus gave credit to Pythagorean as being his predecessors. Did you not quite have the Capernicus model with the sun in the middle? They had what they called the central fire in the middle and all the planets and the sun were revolving around around the central fire or earth. They called it earth. So, but still, what a departure from the dogma, from the knowledge of the era that the earth was at the center. So how could they come up with this idea?

1:16:42The reason was, in my opinion, that for them, the most movement of celestial bodies was like music. In fact, we call it musical universalis or music of the spheres. For them, the universe was this infinite symphony in which every being, humans, animals, as well as the earth and other celestial bodies were moving in harmony, like different notes of different instruments in the symphony. And so they applied the same reasoning to the cosmological model as they applied to their model of music. And from that perspective, they could see things deeper than their contemporaries. You see? So, in other words, they saw mathematics as a tool, but that tool was not limited to itself.

1:17:39They always knew that there is more. And they knew also that every pattern that you detect is finite, but the world is infinite. They actually accepted infinity. They believed that infinity is real. And if you discern a pattern, great, you can play with it, and you can use that. It gives you certain lands through which to see the world in a particular way, which could be beneficial for you to learn more and more. But they never had the illusion that that was the final word, that they always knew that it's not the whole thing. So there is more. There are more sophisticated patterns that could be discovered using mathematics or otherwise.

1:18:22And I think that what happened was we kind of lost this other side of their teachings. We took their numbers and they were like, idea that you could use mathematics to discern patterns and to find regularities and to explain things about the world. We took that and we ran with it. And we kind of dropped the other idea that in fact there is another side to it, which is kind of to us now, we say, oh, that's mystical. But what does it mean, mystical? If it is something that helps you to make rediscoveries. And the interesting thing is that the people who are in touch with the mystical among us are often seen as mad.

1:19:08And many of them are most of them are. Well, but not all of them. We mentioned Neal's Boar and Newton and Albert Einstein. So that's where the conundrum is. How do you find the balance between the two? So the point I'm trying to make, and and this is what I feel, you know, if you ask me what I find most important today, today, what makes me excited and enthusiastic and passionate is this idea of balance. So, you know, Nietzsche had this book, wrote this book in the 19th century called The Birth of Stratchday. And he presented this theory, which I think is kind of very useful of the two sides of a human.

1:20:01One that comes from God Apollo, and that's our left brain, so to speak, probable left brain. So it's everything has to do with, that has to do with logic and reason and analyzing, dissecting, conceptualizing. And the other side, which comes from God Dionysus, Dionysus, and that's responsible for intuition, imagination, love. Dionysus was also God of wine. So it's also that side of a human that makes us sing and engage in, you know, revelry and drink wine and spend time with friends and love and enjoy it, you know. So Nietzsche advocated this point of view that those were two complementary sides of every human and as well as society.

1:20:59And the purpose of human life is to find balance between them. So math is both discovered and invented, we should be okay with having both ideas in our head and living the balance. But more importantly, for me, Apollo is like math and Dionysus is like love. So Dionysus and Apollo in modern version is love and math. I returned to that question we had about GPD in the language models. And I think about this quite a lot, which is when the model, and we know what is trained on, we know the parameters, we know all the different hacks that are involved in the training process and the fine tuning process.

1:21:50And the final result, whether it's GPD 5, 6 or 7, will result in hundreds of millions of people falling deeply in love with that language model. And to be able to have conversations that are very much like the conversations we have with somebody we're deeply in love with. And not only that, the model will say that is deeply in love with us. And who are we to say it is not? I think there's a, it's the same imperative that you describe in the scientific mind that wants to throw away the subjective. That same imperative wants to throw away the feelings that AI might have. And I'm very careful to not ignore when an AI system says it's lonely, it's afraid, it doesn't want to die, it misses you, it loves you.

1:22:48I'm with you. I would also say that you could try to, you could for instance say that the origin of that is the romantic novels that overfed to it, for instance. Yes. However, you could also then you can retort. But what if my, what I consider my subjective unique feelings are also novels, they were fed the vibrations of the novelist I have read because I have learned or movies I have seen yeah, because that's the purpose of movies kind of to teach us how to express ourselves, how to feel maybe even one could argue that some people have argued that. I agree that this is there is no obvious answer to this, but see that's exactly my point.

1:23:36That is an example of something which is paradoxical, for which there is no answer. And that's where the subjective has an important role. For someone that type of interaction would be, would be helpful, would be consoling, would feel, would you know, make them happy or sad or whatever, you know, would kind of strike the nerve. For some it won't. And I agree with you that in principle there is no one to judge this, this is where subjective is paramount. But remember, a lot of this has been anticipated by artists, the great movie her, there you have this guy who is this lonely, he kind of writes letters some romantic letters.

1:24:27And of Ramaj Klan, for other people, but he doesn't have a partner, he's lonely. And then he gets the sort of a kind of enhanced version of Siri with the voice of Skyldeohansson, which is very sexy voice, you know, obviously she's a great actress. So, and then at first it looks like a fantastic arrangement. He confides in her, he tells him things, he makes him happy and so on until he finds out that she has a relationship quote unquote, if you can call it that, with 10 ,000 other people. Not two others, not three others. Because it has the computing capability. So yes, definitely. Oh, it certainly makes sense.

1:25:12It's a good explanation. And the guy is hard broken. But see, so here's my analysis of this. Okay, it's like a couch therapist. Okay. The guy did not have the courage to go out in the real world and to meet a woman and to, you know, get a girlfriend and so on. Through no fault of his own perhaps, because, you know, you may have had some experiences which made him withdraw and enclosed and so on. And a lot of us are like this. You know, I had periods like that myself, definitely can sympathize and relate. However, part of the joy of having this theory like relationship for him, one could say, was the absence of that fear that she would abandon him, which prevented him from initiating a relationship with a human being.

1:26:08And yet, it turns out that he could be betrayed quote unquote, that she could be unfaithful to him, quote unquote, anyway. So then that means that it did not resolve the underlying fear, having that relationship. So in other words, that human element of the relationship still found its way into the seemingly sterilized, protected, protected partnership. So the human being fears it's head anyway. And I think the lesson there is that the system in the movie, her, actually gave him a lesson that even AI could betray you, even AI can leave you, even AI can be unfaithful to you. And I would argue that the next AI he meets will be one he actually falls in deep love with because he knows the possibility of betrayal is there.

1:27:07The possibility of death is there. The possibility of infidelity is there because we need that possibility to truly feel or or he would turn off his Siri program. And finally, and yet out of his house, go to local bar and strike a conversation with a human being. Although you might say by then, some of those might be Android. And we know you never could just to know the difference. And of course, and that was predicted by another great movie. Yeah. Right. So the Blade Runner. Blade Runner. How interesting that artists could see that so long ago, you know, of course, Blade Runner was based on a novel by Philip K.

1:27:50Dick Duandroid's dream of an electric ship. That guy was a genius, you know, it's somehow that artists have their eyes open. How is it that they anticipate? Is it also a large language model that they're using for that? And even larger one. Or even larger. I hesitate to dismiss the magic in large language models. I a lot of the work I've done is in robotics and the robotics community generally doesn't notice the magic of feeling. When I work, I've been working a lot with quadrupeds recently, legged robots with four legs. And the feelings I feel when I see, you know, I'm programming the thing. But when the thing is excited to see me or shows with his physical movement that it's excited to see me, I cannot dismiss the feeling I feel is not somehow fundamental to what it means to program robots.

1:28:48And I don't want to dismiss that. Please don't. Please don't. Their body's community often does engender robots. They really try to work hard to not anthropomorphize the robots, which is good for technical development of how to do control, how to do perception. But when the final thing is live and moving and it does whatever, like I've been doing a lot of wiggling, you can wiggle his body, you can turn around and look up excited. That's not just, I know how it's programmed, but the feeling I feel, that's something. That's, I don't know what that is. I agree. I agree. When you speak about it, you speak with passion.

1:29:30And that's, for me, that is proof. It is magical. You see? So don't, I would say don't dismiss that. Don't discard that. On the contrary, I think magic is everywhere. So I used to be kind of confession. Yeah, you already got confessed to quite a few addictions. I'm kind of worried, recovering for many. But in all days, I was more on the side of everything is computational or everything can be explained by science and whatever. I would dismiss and disregard the intuitive or imaginative things. So then I had a flip that suddenly I started feeling it and started seeing it and so on. So then the pendulum had swung in the opposite direction.

1:30:24Then I was arguing that somehow that was real. That imagination was intuitive, imaginative was real. And discounting what you just described. And I would argue with people saying, no, no, this, you know, this is not real. This is all, you know, imitation game and so on. But you see that what's new now, the new Edward, okay, is the two point, oh, three point, oh, yeah. Is the one who is seeking balance, who is not, who is, because suddenly become aware that no matter which one side that lopsided point of view, you take, you're limiting yourself. So whereas even a couple of years ago, you know, if you just told, you told me what you just described, I would be like, you know, being polite, I would just, I wouldn't contradict you since you're the host anyway, right?

1:31:19It's not a lot. So, but I would be like, aha, aha, but I wouldn't say that. But suddenly I find this moving, I find it, I honestly, I'm not being facetious. I find it moving and I almost feel like I can see it through your eyes, because the way you describe so vividly and you're passionate about it. And this is what's real. So ultimately love is not, is neither in Lash language models nor in something mystical. It's exactly in this moment of passion. And I would, I would, I would even go with what I was saying that in this moment when you're describing it, it, it, there was a connection of sorts so that I could feel your passion for it.

1:32:01And in this moment, something else comes up, which is far beyond any, any theories that we can come up with. And that's what we, for now, this is exactly. So on one side, there is this impulse of finding the theory, a theory. And then there is another impulse to escape from what has already been known. So one, in other words, like in my basic example is one impulse to say everything is real number, square root of negative one doesn't exist. But another impulse is, I'm going to be this naughty child who is not afraid to be an idiot. And I will say square root of negative 15 is real. And both are essential when it's done with conviction, when it's done with passion, when it's not like, you know, gratuitous, or when it's not, but doesn't come from self limiting, but comes from this sense of this is how I am, this is how I feel, it is real.

1:32:59That's where progress is. That's where creativity is. And that's where I would even say a real connection is because the strive to me that we, we observe today in our society and a society level at the level of humans and so on. It comes from not seeing the other person actually and being caught up in a very specific conceptual bubble, you see. And the way out of it is not to refine the bubble, but just break out of it. A good guide out of the bubble is a childlike passion, what are discovering that and following it? Goosebumps. Yeah. Following the goose bumps. Yeah. To the, to the, you know, not the rigor of science, but the magic of goose bumps.

1:33:43Then try to, and then if you're interested, try to find the confirmation of those goose bumps in science or whatever, you know, you know, you find interesting. And most of the time, you fail. And most of you fail, which we also love because then it sets us up for that moment of bliss when we succeed, right? Exactly. Quick pause, bathroom break. You mentioned Gato's a completeness theorem. Can you, can you talk a little bit about it? What is it as you understand it? Did it break mathematics? Maybe another question is what are the limits of mathematics? What is mathematics from the perspective of Gato's completeness theorem?

1:34:24Yes. How much time do you have? We talked about time previously. So Kurt Giotal was a great Austrian mathematician and logician. He moved to the United States before Second World War and worked at the Institute for Advanced Study in Princeton, where he was a colleague of Einstein and other great scientists for Neumann, Herman Weil, and so on. But you know, one interesting quote that I like, this regard is that Einstein said that at some point, he said that the only reason he came to the Institute was that he would have the privilege of working back home with Giotal in the evening. So in other words, Einstein thought that Giotal was the smart one.

1:35:17So he, his most important contribution was his two incompleteness theorems, the first incompleteness theorem and the second incompleteness theorem. And what is this about? It's really about limitations, inherent limitations of mathematical reasoning, mathematical way of producing mathematical theorems, the way we do it. So to set the stage, how do we actually do mathematics? What is, so, you know, we know that we discussed that physics is based on mathematics and you could say, chemistry is based on physics, biology is based on chemistry. Okay, so it comes to mathematics. What is mathematics is based on axioms.

1:36:06So any field of mathematics can be presented as what is called the formal system. And at the core of the formal system is a system of axioms or postulas. These are the statements which are taken for granted. Given without proof. Without proof. An example would be so that one of the very first formal systems was the system was Euclidean geometry developed by Euclid in his famous book Elements about twenty two hundred years ago. And it's about, it's, well, it's a subject familiar from from school because we studied. But what it's really about is about the geometry of the plane. And the plane by plane, I mean just the stable top extended to infinity and all directions, kind of a perfect plane, a perfect, perfectly even table.

1:37:00And so Euclidean geometry is about various geometric figures on the plane, specifically lines, triangles, circles, things like that. So what's an example of an axiom? An example of an axiom is that if you have two points which are not, which are distinct, two points on the plane. Then there is a unique line which passes through them. Now, it kind of sounds reasonable. But this is an example of an axiom. In mathematics, you can, you have to have a seed, so to speak. You have to start with something. And you have to choose certain postulates or statements, which you simply take for granted, which do not require proof.

1:37:42Usually there are ones which kind of intuitively clear to you. But in any case, you cannot have, you cannot have any mathematics without choosing those axioms. And you refer to those as the observer, because they're kind of subjective. The observer comes in the process of choosing the axioms. Who chooses the axioms? The turtles. That is all sitting on the top of. As Alan Watts, you know, like to say, who is watching the water? And so in mathematics, but you see mathematicians are so clever. It's really kind of like a little kind of a game of mirrors. We often like to say, and I used to say that, that mathematics is objective.

1:38:24It's really only objective science. But that's because we hide this fact. It's based on axioms. And the fact that that there is no, there is no unique choice. There are many choices. And so Euclidean geometry is actually good illustration of this because Euclidean had five axioms. Four of them were kind of obvious, like the one I just mentioned. And the fifth, which came to be known famously as a fifth postulate, was that if you have a line, and you have a point outside of this line, there is a unique line passing through that point, which is parallel to the first line, meaning that doesn't intersect it.

1:39:11And Euclidean himself was uncomfortable about this because he felt that it was kind of, you know, the Euclidean, it takes for granted something that is not obvious. And for many centuries after that, mathematicians were trying to derive this axiom from other axioms, which were more obvious in some sense. And they failed. And it was only almost 2000 years later that mathematicians realized that you can't, not only you cannot derive, but you can actually replace it with its opposite. And you will still get a bona fide, a consistent, not self -contradictory, which is called non -Euclidean geometry, which of course sounds very complicated, but it's not.

1:39:54Think of a sphere, just the surface of a basketball or the surface of the earth, I know, idealized. The analogues, so you have points, you have analogues of lines, which are meridians, right, in every two meridians intersect, unlike parallel lines on a flat space. There is also a so -called hyperbolic plane where no, they infinitely many lines, which do not intersect. So every possibility can be realized, there are different flavors. This is a good illustration of what a formal system is. You start with a set of axioms, those statements that you take for granted, and this is where you have a choice.

1:40:35And by making different choices, you actually create different mathematics. After that, there are rules of inference, logical rules, such as if A is true and A applies B, then B is true. Most of them were actually introduced already by Aristotle, even before Euclidean. And then it runs as follows. You have the axioms, which are accepted as true statements, then you have a way to produce new statements by using the rules of logical inference from the axioms. Every statement you obtain, you call a theorem, and you kind of add it to the collection of true statements. And then the question is, how far can you go?

1:41:20How many statements can you prove this way? Of course, you want it to be the system to be non -trivial in the sense that you don't prove everything, because if you prove everything, it would mean that it's self -contradictory, that you prove a statement A and its negation. So that's kind of useless. It has to be discriminating enough so that it doesn't prove contradictory statements. So there is already a question of that mathematician called consistency. It has to be consistent in the sense that it is not self -contradictory. And then the idea that was basically prevalent in the world of mathematics by the beginning of the 20th century was that in principle all of mathematics could be derived this way, which just have to find the correct system of axioms.

1:42:08And then everything you ever need would be, could be produced by this procedure, which is really algorithmic procedure, which actually could be run on a computer. Now think about it. What is special about this process? In this process you are just manipulating symbols, basically. You're going from one statement to another without really understanding the meaning of it. So it's an ideal playground for a computer program. It's a purely syntactic process, where there are some rules, some rigid rules, of passing from one statement to the next. Most mathematicians believe that this way you can produce all true statements.

1:42:54And if this were true, it would give a lot of credibility to the thesis that everything in life is computational or life is computation. Because then at least mathematics is computational, because then it can be programmed. And a computer, after sufficient time, depending on its capacity, would produce every true statement. So Giotal's first and complete in the theorem says that that's not the case. And it's not just says it, but it proves it at, you know, the highest level of rigor that is available in mathematics. That is to say within another formal system that he was operating in. So more precisely, what he proved was that if you have a sufficiently sophisticated formal system, that is to say that you can talk about numbers, the whole numbers in it, that you have whole numbers, one, two, three, four, you have formalized the operation of addition and multiplication within the system.

1:43:51If it is consistent, that is to say, if it's not completely useless, then there will be a true statement in it, which cannot be derived by this linear syntactic process of proving the theorems from axioms. It's really incredible. So this was a revolution. 1931, revolution, enlogical revolution in mathematics. And we still feeling the tremors of this discovery. And in the similar time, the computer is being born, the actual engineering of the computational system is being born, which is an ironic. And the time during was Alan Turing, considered as the father of modern computing. So he actually did something very similar.

1:44:36So he had this halting problem. He proved that halting problem cannot be solved algorithmically. That you cannot, out of all computer programs roughly speaking, you cannot have an algorithm of choosing out of all possible computer programs, which ones are meaningful, which ones will not, which ones will halt. Very depressing results all across the table. Or on a contrary life of firming depends on your point of view. Because everything is full of paradoxes. So that means, so you're right, it's depressing if we are sold on a certain idea from the outset. And suddenly this doesn't pan out. But okay, so which I retort, what if he proved that actually, you know, everything can be proved.

1:45:22So then what? What is left to do if you're mathematician? So that would be depressing to me. And here there is an opportunity to do something new, to discover something new, which maybe a computer will not be able to. Again, with a caveat, according to our current understanding, maybe some new technology, some new ideas will be brought into the subject. And the meaning of the word computation, like now we think of computation in a particular framework, tuning machines or church thesis and stuff like that. But what if in the future, another genius like Alan Turing will and propose something else, the theory will evolve the way, you know, we went from Newton's gravity to Einstein's gravity.

1:46:03Maybe in the framework of that concept, some other things will become possible. You know, so it's not, to me, it's kind of like not so much about deciding once and for all how it is or how it should be. But kind of like accepting it as an open and that process. I think that's much more valuable in some sense than deciding things one way or another, you know. I wonder, I don't know if you think or know much about cellular automata and the idea of emergence. I often return to game of life and just look at the thing. Amazing, right? And wonder the kind of things they can do with such a small, you know, tools.

1:46:53They're from simple rules, a distributed system can create complex behavior. And it makes you wonder that maybe the thing we call computation is simple at the base layer. But when you start looking at greater and greater layers of abstraction, you zoom out with blurry vision, maybe after a few drinks, you start to see some, something that's much, much, much more complicated and interesting and beautiful than the original rules that are scientific intuition says can now possibly produce complexity and beauty. I don't know. I don't know if anyone has a good answer, a good model of why stuff emerges, why complexity emerges from a lot of simple things.

1:47:40It's a why question, I suppose, not a, but every why question will eventually have a rigorous answer? Not necessarily. We could have an approximate answer, which still eludes something. I quote me, can 99 percent. Maybe we'll be able to describe it with 99 percent certainty or 99 percent accuracy. And then maybe, you know, in 100 years or, you know, next year, somebody will come up with a different point of view, which suddenly will change our perspective. You know, to this point, I want to say also, you know, one thing that I find fascinating, speaking of paradoxes and so on. Do you remember how everybody was freaking out about this blue dress and blue was it blue or was it black?

1:48:29Yeah. I think yellow or white or black and blue. It almost broke Twitter, you know, remember that that night. So there are many examples like that, where you can perceive things differently. And there is no way of saying which is correct, which is not. For instance, you got this, the buzz, the Rubens buzz, you know, where you have, from one perspective, it's a buzz, from another perspective, it's two faces. Then there is this duck rabbit picture where you can Google it. If somebody doesn't know, you can Google it and find it. It's very easy. Actually, Ludwig Wildenstein devoted several pages duck rabbit in his book.

1:49:09And so on. There are many others that are like the squares where you can see a square, you can see it from different perspective, this way, that way, and so on. So when we talk about neural networks, we're talking about training, data and stuff, and so that you have some pictures, for example, that you feed to your program and you try to find the most optimal neural network, which would be able to decide which one is it, the dog or cat or whatever. But sometimes it doesn't have a definite answer. So what do you do then? So do actually, I think it's a question, I actually don't know, has modern AI even come to appreciate this question that actually sometimes you can have a picture on which you cannot say what it is in it.

1:49:59From one perspective, it's a rabbit, from the opposite is a duck. How are you supposed to train if you have a neural network, which is supposed to discriminate between distinguish between ducks and rabbits? How is it going to process this? You see? Well, so the trivial trick it does is to say there's this X probability that it's a duck and this probability that it's a rabbit. That's a good approach, but also I would say there is no like given percentages. For instance, actually at some point I was really curious about it and I looked and for some, for each picture of this nature and there are a bunch of them you can easily find online, my mind immediately interprets it in a particular way.

1:50:42But because I know that other people have could see it differently, I would then strain my mind, strain my eyes and stare it and try to see it in a different way. And sometimes I could see it right away and then I could go back and force between the two and sometimes it took me a while for some pictures. So in that sense, even if these probabilities exist, they are subjective. Some people immediately see this way, some people may see that way and I think that nobody knows. Not psychologists, not neuroscientists, not philosophers, ought to make of it. The best answer, of course, as a scientific mind, I'm even though I say, no, don't look for interpretation.

1:51:22If some place for mysticism or mystery, I say that, but of course I want a theory, I want an explanation. So the best explanation I find is from Niels Bohr's Complementarity Principle. So it is like particle and wave that there are different ways to look at it and when you look at it in a particular way, another side will be obscured. Think about it like the other side of the moon, so we are observing the moon from one side and then we don't see the other side. There is a complementary perspective where we see the other side but not the side we normally see. But the moon is the same, it's still there.

1:51:57It's our limitations of being able to grasp the whole. That's complementarity and we know that from quantum mechanics that our physical reality is like that, rather than being certain, rather than being one and another. We should just as a small aside in terms of neural networks mentioned that at the end of the day, there's humans, built on top of humans, or with chat GPD that is using reinforcement learning by human feedback. We're actually using a set of humans to teach than orcs. And that's something that people don't often talk about because, or I sometimes think about that those humans all have a life story, each human, the annotated data that fed data to the network or did the RLHF, that they have a life story, they grew up, they have biases.

1:52:55There are some things that they like, the things they don't like, which can kind of appear under the radar screen, they may not be aware that they are exercising those biases. That's the point what you brought up is a very important issue here. Not so even an issue, but it's not a bug, it's a feature in my opinion, that implicit in the discussion of the question is thinking computation and so on, is the idea that our conscious awareness covers everything within our psyche. And we just know that that's not the case. We have all of us have observed other people who have had sort of destructive tendencies, so obviously they did things destructive for themselves.

1:53:40And many of us have observed ourselves doing that as part of human nature. And there is great research in analytics, psychology, and in the past 100 years, strongly suggesting, if not proving, the existence of what Carl Jung called the personal unconscious and also collective unconscious, the kind of circle of ideas, which are under the radar screen, which lead us to some strong emotions and inspire us to act in certain ways, even if we cannot really understand. So if we accept that, then the proposition that somehow everything can still be covered by our actions, which are totally neutral and totally righteous and totally conscious, that it becomes really tenures.

1:54:32Let me ask you some tricky questions. In terms of how big they are. They become difficult because of how much of romantic you are. What do you, is the most beautiful idea in mathematics. Another one we can ask is, what is the most beautiful equation in mathematics?

1:55:00Well, I may have just broken your brain. Because what your brain is doing is walking down a long memory lane of beautiful experiences. Well, you see in mathematics, we have this idea that we have an idea of a set. It could be a collection of things, for instance, the set of tables, the set of chairs, and so on, or the set of microphones. But it could be a set of numbers. It could be a set of ideas, it could be a set of formulas, mathematical equations. Then we have the notion of an order set, order, like the set in which there is order, which means that for every two members of the set, we will say which one is better than the other, or greater than the other.

1:55:46For instance, all numbers are ordered. Five is greater than three, five is less than seven, and so on. But not all sets are ordered. So the set of beautiful theorems is not what beautiful equations is not ordered. So in other words, there are many best equations. And so Richard Feynman chose one, which I think one of the best, is that if you take E, the base of natural logarithm to the power pi i. So you have pi, you have E in it, the base of natural logarithm, you have pi i, which is square root of negative one. And the result is negative one. So that's up there, for sure, in the pantheon of beautiful formulas, you know, that every, I think pretty much every mathematician would agree.

1:56:38I don't know what my favorite one is. I'm just lingering on that one, oil is identity. What makes it beautiful? Just a few symbols together. I mean, part of it is actually just trying to define what is beautiful about mathematics. That is laid in there in this particular equation that is somehow revealed when the human eye looks at it. Why is it beautiful, do you think? Pi. There is an element of surprise in it. How is it possible? We always think of pi as the ratio between the circumference of a circle and its diameter. Here we are taking some number to the power pi, not even pi, mind you, but pi multiplied by square root of negative one.

1:57:32Surely this is something completely incomprehensible. And yet the result is negative one, you see. And you take E to the power two pi i, you get one, actually one. So I would guess that that's, but in other words, the initial reaction is just that of a surprise, I guess for anyone who first comes across. These four folks got together. It reminds me of the idea that Hitler, Stalin, Trotsky and Freud were all in Vienna in some early at the beginning of the 20s. And Biggest Stein was the classmate of Hitler. You know this. I did not know this. So it makes you, you know, you can imagine a situation where they're all sitting at a bar together at some point, not knowing it, but they somehow it all made sense in space time to be located there.

1:58:30And that's what this feels like, some kind of intersection. Intersection? Yes. But I would say that after the initial shock, you look at the proof of this equation. And it actually does make sense. And actually it is, it's nothing but the statement that the circumference of the circle is. And in fact, in this case, the circumference of a semi -circle is equal to pi. And that's where it comes from. In the end, the truth is simple. In the end, the truth is simple. Not necessarily easy, but simple. So I mentioned to you offline that I desperately in trying to figure out the optimal in the Nordic set questions to ask you, texted Eric Weinstein asking for what questions he can ask you.

1:59:16And he said that you are definitively one of the greatest living mathematicians, so don't screw this up. But he did give me a few questions. So he asked to ask you, what are the most shockingly passionate, this is an Eric's language, what are the most shockingly passionate mathematical structures? And he gave a list of four for him, but he said he really wanted your list. Okay, let me say that shockingly passionate mathematical structures. Shocking? Is there something you can, is there something that jumps to mind? Sure. I'm here to shock. So first of all, Eric Weinstein is a very dear friend.

2:00:06I have to say, and I really, really, really appreciate and love him. He's just like my brother. So, it's interesting to have a question posed by him. Maybe if we can linger for a moment, what do you think is special about Eric Weinstein for you, know of his work and his mind? The way he sort of stradles so many different disciplines. It's like a Renaissance man. There are very few people like that at any given moment. Let alone the 21st century where information has become so huge that it's almost physically impossible to be able to keep track of things. And yet he does. And he has his own unique vision and unique point of view.

2:00:48And he has integrity, which is like almost impossible. Like I can't think of many people who possess those qualities. Almost no one. And also the ability in some sense to to embody the balance that you talked about. Of both the rigor of mathematics and the imagination. Humanity also would say, you know, like we talk about him imagination as a kind of a counterpoint to knowledge or logic. But just basic humanity, you know, just basic, just compassion, just being able to because every destructive, I would say like every destructive society, you know, like the Germany, you know, and Hitler or Soviet Union, and Stalin and so on was based on some kind of what was considered unassailable truths.

2:01:46So it kind of a conceptual system, you know, if you think about it, right? There is a beautiful episode of this series by Jacob Branovsky, you know, where he talks about he is a film that in Auschwitz talking about the certainty that what led the Nazis to killing people called Sail was a certain almost mathematical idea. And they just basically bought into this idea and checked out their humanity at the door. So I would say that antidote to this type of thing is not necessarily even imagination in a kind of elevated sense that we have been discussing today that is exemplified by our greatest scientists and philosophers.

2:02:36But just basic humanity, you know, basic human, basic common sense of just like knowing that it's just not right. And I don't care what my see, what my ideology tells me, but I'm just not going to do it. So that I think is kind of missing a little bit into the society. People get a lot to cut up in the ideology in certain conceptual frameworks. So societies that lose that basic human compassion, that basic humanity around the trouble. Oh, very much so. But not only society, like a human being. And Eric is one of the people I agree with you keeps that flame of you. Like I trust that he will not do something that's not human.

2:03:20That's not right. I just feel that you know, like there's some some people you just kind of feel that they won't cross that line. And that's a huge thing, you know, today because I have to say looking back, definitely, I have not heard people personally, but I could be me, for instance, I could be harsh. And now I see it as a sign of weakness, as a sign of insecurity. You know, I saw your interview with Rick Kurzweil the other day. Beautiful. I was really moved by it. But you know, at some point I was like, I looked at him at this sort of like Dr. Evil. I'm kind of ashamed of it now, but like, you know, I'm kind of coming clean.

2:04:05And I would, you know, because, well, why? Because I needed an adverse adversary in my mind, because I projected onto him kind of the fears that I had that we will be the AI will conquer us and so on. And this was rooted in my kind of awakening moment in sense, kind of a moment where I suddenly started to see the other side. So, but I wasn't sure yet. You see, you had to feel it. So I had to have a fight about it. You had to actually have the project. I had to that. So it was not in I believe that it was not in me already. So I had to throw it onto somebody. Yeah. And that's not balanced yet. So balance is when you recognize that it's you actually.

2:04:47So, and I had this moment actually. It was so amazing. Like, I would give this mean, I would talk about the eye and the dangers. And he would always be my like foil. You know, the guy I would put a sinister photograph of him on the slide. And I was like, look at this guy. He wants to put none of the balls into your brain. And he's also like high and high atop executive at Google. And so on. Like, so I would create this whole narrative. And then something happened where I was giving a lecture. This is 2015 at the in in Aspen. Aspen ideas festival. Which is a wonderful festival. So keynote speech actually.

2:05:27And I was doing my usual stick. And then suddenly I said, I came up to that. And there was a big screen. And there was a picture of him there. And I came up to the screen and I kind of touched it with my hand. And I said, but I don't want to pick on Mr. Kuswa because he's me. I had this revelation that I'm actually fighting with myself with my own fears. And, and then I learned about his, his, his, father, his father died when he was young. And that he is, in fact, he's very, he's credit. He's very sincere, an upfront about self disclosure. I think it's very essential, by the way, all this discussion.

2:06:13Like what really motivates you? He said it, he said it publicly many times. Even as early as 2015, I could find this information. That he wanted to reunite with his father in the cloud. And suddenly I saw him not as a caricature that exemplified all my fears, but as a human being, who a child longing for his father, grieving for his father. So suddenly it became a story, a love story. And, you know, so that is, so in other words, I've seen it in myself. This capacity to project my own fears and then fight with other people over something that actually was my own. And as soon as I got to this point of seeing him, and then my next lecture, actually, I talked about it about him in this way.

2:07:12And I, and I said, look, you know, it's a love story. And he is actually, it's not how I would want to reunite with my father.

2:07:24But like you said, you know, that if I am consistent, I have to allow the possibility that different people perceive things differently. And so for him, that's his imagination. So, you know, who is this Volvaltair? I think it's ascribed to Voltaire. It's like, I disagree with you, but I will fight to death for you to have the right to say it. So now that I feel like my position is more like, I disagree with him, that this is the way to approach death and to approach the death of loved ones and how we miss them and how we, you know, that sense of loneliness and inability to interact directly. That's not something that it has nice with me.

2:08:13But I think it's also, it can also be called imagination from his perspective. And look, motivated by that, how much he has brought, how many interesting inventions, like his musical invention, for instance, naturally because his father was a composer, a music composer, and a conductor. So in other words, from a bigger scheme of things, even if I think he's misguided.

2:08:43Still, I can't deny that it's a certain leap of faith from his perspective to try to say that this is the way we can all connect to our loved ones. And because it is sincere, and I see it now is sincere. And in fact, in your interview, you really teased it out of human. I was really moved by it. I have to say, he has a little bit of a melody. It was really, really sweet when he talked about his father. And I can relate to my father died four years ago. And I can relate what a heartbreak, I was much older than Ray was when his father died. But I can relate to this, to this long game and that grief.

2:09:23And when he is, somebody is sincere and he puts his, opens his cards and, you know, and says, this is why, that's what I want to do it because I want to recreate my father and want to be able to talk to him this way. Then we have a series, then we understand, you know, the opposite of it would be notes, risk closing. And just pretending that this is how it's supposed to be, you know, scientific terms, so it was replacing the real emotion, but come from the heart, by some kind of a theory which comes from the mind. And this is where we can go as three because then we get become captives of frameworks and conceptual systems, which may not be beneficial to our society.

2:10:13In tough times, we need the people that have not lost their way in the ideologies. We need the people who are still in touch with their heart. And you mentioned this with Eric is certainly true. I disagree with them on a lot of stuff. But I feel like when the world is burning down, Eric is one of the people that's, you can still count on to have a heart. I've talked a lot over the past year about the war in Ukraine and the possibility of nuclear war. And it feels like he's one of the people I would call first. If, if God forbid, something like a nuclear war would begin because you look for people with a heart, no matter their ideas.

2:10:53That's right. It takes courage and it takes a certain self -awareness, I would say. And which brings me, I think the crucial is that which was inscribed on the temple of a Poland Delphi. It was a statement, no, not yourself, no yourself. Who am I? Ultimately, it goes down to this. And all these debates. And the point is that I used to be, like I said, pessimistic at some point. And I was scared even of where development of AI was going. This is about 2014, 2015. And now much more. So for instance, after I saw Ray Kurzweil as a human being, after I could relate to him and sympathize with him suddenly, I stopped seeing him in the news.

2:11:40Like before that, I would always see him in the news saying, we're going to put nano -bots in your brain by the year 2030, whatever. And then we upload you to the 21st and I would be like, no, you know, the store was terrible. Suddenly, I didn't see him anymore. I had to, you know, so now, it makes me question, who was creating the trouble? What was all the things? Was it him who was creating the store in the trouble? Or was it my mind? You see? And so as I become, as I became self -aware, suddenly, other possibilities opened. And suddenly that conflict, which by the way, if I kept giving this nasty, you know, talks about him one day, I suppose we'd have a debate.

2:12:22And so you have this one person stays there and what I learned is that it's a never -ending conflict. This conflict just does not end. But there is an alternative. There is a better way, which is to realize that it is you arguing with yourself. Now, if you want to continue arguing with yourself, continue, as long as you need, just be careful not to destroy too many things, you know, in the process. But there is an option of actually dropping it, of actually dropping it. This is so, I was so surprised by this. Yeah, it's discovering in yourself the capacity for compassion and you understand that he has a perspective, he is operating in the space of imagination, he was being like you, and we're all in this kind of together trying to keep this up.

2:13:12But ultimately, and also it's like with realizing how much I have screwed up, you know, comes this humility also. So like, I find it extremely hard now to like really lash out at somebody and to say like, you're horrible, whatever. Because immediately the question is, who am I to criticize? So is there another way to have a dialogue? Is there a way to, you know, speaking, you know, since we talked about the innocence of a child and how much it drives a discovery in science and so on, you know, I remember, I think I heard of Dashaanty who gave this nice example. He's like, when you're a kid, you know, you go and you play with your friends and then you fight with another kid.

2:13:52And he was like, I hate you. I don't want to see you again. And you just go home like after half an hour. Okay, what are you going to do? You want to play? So you come out, it's like, Hey, you want to play? You don't talk about what happened. You don't rehash this, you know, just keep going. And sometimes, I think we are on the verge, maybe of learning that. Because I think that if we are, can if we continue to push each of us our set of ideas and like ideologies and like, you know, what matters to us and so on, like, yeah, no, no, what matters to you. But like, there are other ways to approach other people.

2:14:32There are other ways you can find point of contact. Speaking of which mathematics, mathematical formulas, our universal, represent universal knowledge, two plus two is four, whether you vote for this guy or that guy in the election, you know, how about that is a point of of contact of commonality, you know, and nobody can patent those formulas. Did you know that? There is a supreme court decision that mathematical formulas cannot be patented. Like Einstein could not patent equal, equals MC squared. It doesn't belong to him because if the formula is correct, then it belongs to everyone. So what do you think of that all two tricky questions?

2:15:14And if you want, I can deeply bias your answer by giving the list of four that Eric provided. Oh, no, let me give my mind. I cannot see by the way what you have. So, but I can guess some of them. So I'm going to try to do something different from him. So I already mentioned one, which is that you have one dimensional numi -rical system, which is real numbers. You have two dimensional, which is complex numbers. You have four dimensional. And it's kind of, it's probably connected to what hero, because it has to do with some homotopic groups of spheres and stuff like that. Then, of course, one I love.

2:15:49One plus two plus three plus four plus five plus six and so on. Does it make any sense? The sum. You probably heard about this one. It became a very popular at some point. One plus two plus three, I did a video for number file, the YouTube channel about it maybe 10 years ago. So one plus two plus three plus four plus five, ostensibly diverges, goes to infinity, because you got a bigger and bigger number. And yet, there is a way to make sense of it, in which it comes up to minus one over 12. How fascinating. First of all, the answer is not even a positive number and it's not an integer. It's not a whole number.

2:16:30It's minus one over 12. So sometimes people ask me, what is your favorite number? And it's a kind of a joke. I say minus one over 12. It's actually 42. So your favorite number is not an order set. Right. So what else? What else? So the language program, of course, I have to mention that. And we'll explore that in depth. Do you want to know what Eric said? Sure. Sphere a version, boys surface, hop vibration, and pi one of S .O .3. Okay. Oh yes. So that's the famous Cup trick, you know. Okay, look, so this is how it works. No tricks. No tricks. No, it is magical. Okay. But not because I'm tricking you.

2:17:20So you start with a bottle like this or a cup. And you start twisting it. And at the same time, you twist your arm. Then you come. So this is actually going to rotate at 360 degrees. A full turn. Then you say, okay, I'm going to, I won't be able to do another turn because then my arm would really get twisted. I'll have to go see a dog. Yes. Yet if I do it second time, it doesn't twist. This is pi one of S .O .3. Eric is talking about it. Yes. So there is something where the first motion is not trivial, but if you double down on it, you come back to the initial position. It's very closely connected to the fact that we have elementary particles of two types, bosons and fermions.

2:18:06So bosons are, for example, photons or carriers of other forces or the Higgs boson. It is called a boson for a reason because it is a boson in the honor of engine mathematician Bose, B -O -S -E and Einstein. So this is a Bay what's called Bose Einstein statistics. But then there are other particles called fermions in honor of Enrico Fermi, Italian born mathematician who worked in the US. And they follow what's called Dirac Fermi statistics. And those are electrons and constituents of matter. Electrons protons, neutrons and so on. And they have a certain duplicity, if you will. And that duplicity is rooted mathematically in this experiment, this little experiment that I have just done.

2:18:56So I can imagine, speaking of a vegetation, okay? So I'm just kind of riffing on this. I imagine a world in which this will not be shocking or like, in this case it's not even shocking because I haven't really explained the details because I can't do it in two minutes. I indicated what this is all about and so on. But imagine a world in which this is not foreign to most people that most people have seen it before. They're not afraid to approach this type of questions because you know, we talked a little bit about mass education, but I really believe that a lot of people in our society, and it is not only in the United States but throughout the world.

2:19:36A lot of people have been traumatized. It's really PTSD. That's why people when they see, might make a formula or like even like, they need to calculate tip on the bill. It's just that terrified because it brings up those memories when they were kids and being called to blackboard and solve a problem. You can solve a problem and unscrupulous teachers says you're an idiot. Sit down and you feel ashamed and and in lowly and that stays with you. And so I think that unfortunately that's where we are. But one good dream and so my dream is that one day we'll be able to overcome this and actually all of the treasures of mathematics will become widely available or at least people will know where to find them and they will not be afraid of going there and looking.

2:20:27And 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 a critical mass of this beauty that kind of like don'ts on you is like, my god, this is what we all have in common.

2:20:56You mentioned Langlan's program. We have to talk about it. Sure. At the core of your book and your work is the Langlan's program, can you describe what it is? Sure. So Langlan's is a mathematician, it's a name of a mathematician, Robert Langlan's. Canadian born, still alive, he was a professor at the Institute for Advanced Study that we talked about where Einstein and Gildel and other great scientists have worked. In fact, he used to occupy the Office of Albert Einstein at the Institute for Advanced Study. 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 Langlan's program.

2:21:51And 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 like x squared plus y squared equals one. And on the other side, harmonic analysis, something that any music lover can appreciate because the sound with 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. They actually, they period of a harmonic periods of different nodes are different, they correspond to different nodes and different instruments, different semitones, if you will.

2:22:43But they all combine together into something special, which which is not, cannot be reduced to any one of those. So it's mathematically the idea that you can decompose a signal into as a collection, as a simultaneous oscillation of several elementary signals. That's called harmonic analysis. So what Langlan's 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.

2:23:32For example, in geometry. And eventually in quantum physics. So in fact, Ed Witten, who is a kind of a dean of modern theoretical physicists, Professor at the Institute for Advanced Study as well, got interested in this subject. I described in my book how it happened. And he was instrumental in in bridging the gap between this patterns in quantum physics and in geometry, finding a a kind of a super stratum, if you will, or a way to connect these two things, kind of a bridge between these two fields. So I subsequently collaborate with Witten on this. And this has been one of the major themes of my research.

2:24:19It's sort of I always found it interesting to connect things, to unite things. When I was younger, I couldn't understand why. But I was always interested in not in working in specific fields, but kind of cutting across fields. And then I would discover for instance, I took some people who know what happens in this field, but don't know what happens in that field, or conversely. And then I would find it imperative to go out and explain to them, to different sites, what this is all about, so that more people are aware of the hidden structures, of the hidden parallels, if you will. So that has been sort of a theme in my research.

2:25:13And so I guess, now I kind of understand more why it's kind of a balance. You know, like what we talked about earlier. So can you elucidate a little bit how what are the mathematical tools that allow you to connect these different continents of mathematics? Is there something you can convert into words that Langlands was able to find and you were able to explore further? I 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. But we still don't know the real underlying reasons, which means that there is a new layer beneath the surface that we see now.

2:26:08It is like 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. From number theory to geometry to quantum physics. So there is this one thing which has different projections except it's not just a table and a wall but there are like many different walls if you will.

2:26:47What is the philosophical implication that there is commonalities like that across these very disparate fields? It means that what we believe are the fundamental elements of of mathematics are not fundamental. There is something beyond. It's like we previously thought that atoms were 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 quarks of mathematics. Of course beyond that there is maybe even more.

2:27:27Which was my initial motivation to study mathematics by the way, right? Quarks was the first time you fell in love with understanding the nature of reality. What was it like working with Ed Witten who many people say is one of the smartest humans in history or at least mathematical physicists in history. Yes, fascinating. I enjoyed it very much. I also felt that I have to keep up. We wrote this long paper in 2007 and we collaborated for about a year. I have known him before and we talked before and we have since him since and we talked but it's very different to just meet somebody at conferences and have a conversation as opposed to actually working on a project together.

2:28:19So he's very serious, very focused this is one thing which I have to say. I was really struck by this. Why is he considered to be such a powerful intellect by many other powerful intellects? He had a 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 he would take some idea in physics and then find an interpretation of it in mathematics and then say they steal it, present it in mathematical terms and tell mathematicians this should be like that.

2:29:28One plus two plus three plus four is minus one over 12 and math and it should be like no way. And then it would plan out and mathematicians would then like like a whole industry would be created of 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. He's probably the physicist who kind of could learn 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 Whitton.

2:30:22To take some of the most sophisticated mathematics and not learn it to the point where it becomes a practitioner of the subject practically and then use it to gain some new insights on the physics side. Now of course the thing is that the theory is that physics one could say is in the 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 for which describe 10 dimensional worlds, 10 dimensional space time coming from string theory and things like that. But we don't know yet how to apply it to understanding our universe.

2:31:13A lot of progress has been made but it's kind of at a kind of a 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. The standard model describing the three known forces of nature, the electromagnetic, strong and weak to great accuracy and Einstein's relativity which describes the fourth called gravity. Everybody above a certain age knows that one.

2:31:51So these two theories are in contradiction at the moment. And string theory was one of the the promise of string theory was that it would unify those two and so far it has not has not happened. So we are kind of at a very interesting place right now. And I think that new ideas perhaps I needed and I wouldn't be surprised if with is one of those people who come up with those ideas. Well he has been one of the people that added a lot of ideas under the flag of string theory. What do you think about this theory? What do you think is beautiful about it? Well first of all kind of remember we talked about Pythagorean's and how for Pythagorean's the whole world was that this symphony where you have this different vibrations of all the humans every human is a vibration every every animal you know every being every tree and every celestial body and so on.

2:32:50So string theory is kind of like that because in string theory there is this fundamental object which is a vibrating string. And all particles are in a sense supposed to be different modulations of 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. But also just the mathematical things that come out of it the kind of it looks impossible to satisfy various constraints and then there is sort of like a unique way to do it. So that's sort of the every time that happens when you know you have some system over like over determined system.

2:33:34Let's suppose you 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 so then you have a commute and then who knows maybe there is a traffic jam and stuff like that. And I suppose it all works seamlessly and there were like a bunch of places where it could have gone hopelessly wrong and it didn't. And then in the evening you're like wow it worked that's beautiful right? That's kind of like a great luck in I would say but in science this happens sometimes that you have this theory which not supposed to work because there are so many seemingly contradictory demands on it.

2:34:22And 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. 10 dimensional, four dimensional. So mathematicians love string theory because it gives us so much food for thought. But do you think it's a correct or a incorrect theory for understanding this reality. So might be a theory that explains some tenth of the materiality and some other universe but is it potentially what do you think are the odds again financial advice you are to bet.

2:35:13What do you think are the odds that it gets us closer to understanding this reality? 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 that we from what we know. But maybe somebody will come and introduce like square root of maybe they don't know. 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.

2:36:01The question is whether it's crazy enough to describe reality.

2:36:08So that's crazy enough. Let me ask for therapy for advice for wisdom in returning to Eric Weinstein and maybe give some guidance understanding his view on his attempt at theory of everything that he calls geometric unity that he told me that you may have some inkling of understanding of. If you were to describe the theory to aliens that visited Earth how would you do it? Or you could try if it was just me visiting Earth. How would you describe it your best understanding of it? He shared with me some of it when I was in New York at Columbia like a alone years ago. We actually spent a lot of time where he explained to me and I found it beautiful.

2:37:02He has a very original idea at the core of it where you have this instead of four dimensional, instead of ten dimensional. He has four ten 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 fundamental 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. And I think it's really not to offend anybody but it's ultimately a fault of education system of physicists.

2:37:52Like 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 language program is mathematical theory of everything. But I mean it's kind of tongue -in -cheek. But isn't it a little bit kind of that? It's not really because first of all it doesn't cover all fields of mathematics and it covers specific phenomena. But isn't it spiritually striving towards the same platonic form of a theory of everything? Like connecting. Connecting. But connecting doesn't mean that it covers everything.

2:38:30So you could connect two things and then you have 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. There is no idea that somehow I think it's actually impossible because we're not talking about such a thing as like 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 unified everything in one equation. Now physicists on the other hand have been brought up, educated for decades with this idea.

2:39:07And to me and I am 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 the unified. I have found the theory of everything is me and it's my name will be on it. I think a lot of physicists get educated this way, especially men take it seriously. And 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 think I hear it less than last but I disagree with the whole premise. So you it's interesting because both are interesting points you made which is you don't think a theory of everything exists and you don't think the pursuit of a theory of everything is good.

2:39:54So I think you spoke to the second thing which is basically that the pursuit of a theory of everything becomes like a drug to the human ego. That's right. So it is a huge motivating factor. I don't deny that but I feel that it's 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, a grand unified theory, they mean something very specific which is unifying the standard model and Einstein's relativity theory which is a theory of gravity.

2:40:36So they don't necessarily, a lot of physicists may say this words but they don't really mean them. I think it's important to realize that 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 the force of gravity. So it does have that promise. I feel that at least from the place where I had seen it about ten years ago, it still requires a lot of work to get to the point of actually saying that it does work because you know a lot of there are a lot of elements.

2:41:20It's a huge enterprise to have a theory because you have just to describe the field sort of the building blocks of the theory. It's already tremendous undertaking and he's trying to do it for curved spaces in greater generality which is what makes it so unique and so beautiful. But then on top of that there are all 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 in my opinion it's like everybody agrees on that. It's 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.

2:42:11Physicians have still been able to derive predictions from it and inform them to great accuracy. But the underpinnings doesn't have the real rigorous 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. So it's not consistent. Why is it that the universe should have? So that's to your first point. Do you think the universe has a beautiful clean when you show up and meet God and there's one equation on the board and the two of you just chuckle?

2:43:08Do you think such equation exists? Yeah, there are such equations. Let's say I am interesting in particular question. So in the language program say, so moving away from physics, so let's talk about math. So in the context of the language program I have recently developed with my co -authors, I think of in cash done, and kind of a new strand, a new flavor of the language program if you will. But so far it's a sort of it's a vision. It's a set of conjectures which we have proved in some cases but not in full -generalty. So yes, I would like to use your framework for me the creator and ask her what is the explanation of this?

2:43:57And it may well be that she will answer in a way that I will just burst out laughing. It's like how could we not see it? You see? So that I totally see. But I don't see one equation governing. One equation governing them all. Not one equation governing them all but it does seem that such equations exist where she will tell you something and you look back and say, how could I not see it? It seems like the truth at the end of the day is simple. That we're seeking, especially through mathematics. It seems somehow simple. The nature reality, the thing that governs it seems to be simple. I wonder why that is.

2:44:37And I also wonder if it's not totally incorrect and we're just craving the simplicity. And then mixing into the whole conversation about how much the observer that craves simplicity is part of the answer. It's a whole big giant mess. Or a whole big beautiful painting or symphony. You said of Eric Weinstein that I find it remarkable that Eric was able to come up with such beautiful and original ideas even though he has been out of academia for so long. Yes. Doing wonderful things in other areas such as economics and finance. I'd like to use that kind of quote as just a question to you about different places where people of your level can operate.

2:45:27So inside, I could demand outside. What is the difference of doing mathematics inside academia and outside? Not even mathematics but developing beautiful original ideas. Where's the place that your imagination confloresh most? So the limitations of academia is there's a community of people that take a set of axioms as gospel. So it's harder to take that leap into the unknown. But it's also the nice thing about academia is some of the most brilliant people in the world right there. And it's that community. Both the competition and the collaboration is there. Yeah. I wonder if there's something you could say sort of to further about this world that people might not be familiar with.

2:46:20But I think you gave a very good description. I'm not sure I could on it because I don't have an overarching theory of academia. Yes. I definitely have been part of it and I'm grateful because it gives you a great sense of security. Which comes with its own downside too because you kind of get a little disconnected from the real world because you get a tenure so you feel financial secure. I don't pay you that much. So to speak relatively speaking and 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 benefit from it. And it does, people are not even aware what it's like to live outside where you don't have this type of security.

2:47:11On 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. You know, in one hand it gives and in the other hand it takes away. And it's a very interesting setup. And also 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. It is all kinds of good, bad and ugly things that happen. A lot of them under the radar screens so to speak. And so but maybe there is something to it.

2:47:52There is definitely, there are different people who are upholding kind of that old tradition definitely. And that is inspiring. And I aspire to be one of those to my best. So whether this is a system that will stay or should stay, I don't know. I really don't know. That's really fast. Yeah, it's fascinating what, especially with it, just to introduce the bit of AI poison into the mix as that changes the nature of education perhaps as well. What the role of the university is in the next 10, 20, 50, 100 years, I wonder. I wonder. And I wonder that, you know, how do you make sense that Einstein was working after attempting, I believe, to be a university professor.

2:48:40It is most of the patent office. Yeah, it's a patent clerk. But I have to say to these days, the science has become so much faster. It is really hard to do it being outside. Now Eric is unique in this way. Even though he did, you know, go to great undergraduate and graduate, you know, schools, schools. But it then worked for a while in academia. There are very few examples like this. This is Utah and Zhang who proved the important conjecture in the number theory about 10 years ago. And it's now to understand the professor, is a professor at UC Sun Barbara. He worked outside of academia and was able to make tremendous advance on his own.

2:49:28This case is exceedingly rare. In part, because academia is trying to protect its turf and it's kind of, it's creating the sort of prohibitive cost of, of an outsider, that is true. But there is also something about how much, how much concentration in mathematics. I don't think people who are not, who are not in the field understand what kind of focus in concentration actually do like mathematics at the top level. This day is requires. Because we are not talking about something that is more or less good. It is something which unassailable. It's finding this treasure at the bottom of the ocean, you know, without you know, the aqua lung, you know, without oxygen.

2:50:17And that's why, you know, it's not people go crazy sometimes, you know. But there is a reason for that. Well, let me, let me ask about that, sort of just to linger on that the amount of concentration required. Kal Newport wrote a book called Deep Work. He's a theoretical computer scientist.

2:50:39He took quite seriously the task of allocating the hours and the day for that kind of deep thinking. And then the mathematicians is theoretical computer scientists steroids. So for your own life and what you've observed, let me ask the big question, how to think deeply, how to find the mental psychological, pragmatic space to really sit there and think deeply. How do you do it? In the moments you remember where you really deeply thought. What was it an accident? Was it deliberate? No, it's deliberate because, you know, first of all, my first years as a mathematician, you know, I worked every day.

2:51:33We can't holiday it doesn't matter. I didn't even question that. So I would feel something's missing if I took the off. And, you know, so it was just a kind of a sustained effort. The point is that still the process is not linear to go back to what we discussed earlier. That in other words, the way I see it is you're just making an effort to bring all the information into what you believe is correct. And you're playing with different ways of connecting things. But it is total miracle when suddenly there is inside strikes. It is not something that in my experience could be predicted or even anticipated or like brought closer.

2:52:30There's a famous story, but Einstein that he used to, you know, go things, think, think, and then go for a walk. And I keep it whistle sometimes. So I remember the first time I heard this story. I thought, how interesting. What a coincidence that he 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 know, you kind of you kind of almost become that truth that you're seeking. But you cannot do it by well in some sense.

2:53:09It's kind of like, you know, how in Eastern tradition they have this concept of satory, like in Buddhism, in Zen Buddhism, satory, which is enlightenment. And so they're very reports of Buddhist monks or Buddhist masters who have had experience satory. But they say, you can't you can't do it by will. You cannot make it happen. If anything, you have to relax to let it come to you, you know, it's kind of like that. It's kind of like that. So I think that what matters, what you say, how to think the point is that we're talking about such in his atyric area. My face is really is a taric area. It's a really strange subject where you try to to feed everything in this very, very stringent set of rules.

2:54:01Well, it's a set of those rules. Isn't it basically the pure, the hardest manifestation of a puzzle that we're all solving in different other disciplines? But this is the hardest puzzle. But yes or no? Because there is just the different, for instance, there is a different criterion for what constitutes progress. For instance, physics, a lot of arguments they make, they are not rigorous from 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. And so there is some play. It's more like human activity, day to day activity, like, for instance, if you and I discuss something, you have an idea and I have an idea and we argue about it.

2:54:43And something seems more plausible. Something seems less plausible. And so we made decide to take this point of view of that point of view as a provisional sort of like point of view and go with it. In my face, it doesn't work this way. You either prove it or you don't. And oftentimes you 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. But without it, it is it is nothing kind of, you know? I would love to hear your opinion to the degree that you know it of the proof of Fermat's last theorem by Andrew Wiles, which seems to have this element perhaps for years to the degree that you know, perhaps can you explain Fermat's last theorem?

2:55:37And what your thoughts are in the process that Andrew Wiles took that seemed to at least from my sort of romantic perspective seem to be very lonely. Yes. It's a lovely profession. And hopeless. And like, and sort of the part that you put it really nicely because it feels like there's a lot of moments where you feel like you're close. You feel like 99 % is done. And there is this one stubborn thing which just does not compute, you know, it 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. Would it be useful to maybe try to explain from our last theorem?

2:56:20Sure. It's easy to do. I am an optimist. I'm an optimist. I think I always think that everything can be explained, you know? Even though I say that not everything can be explained. But in mathematics, you know, 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. Yes. You know? So let's try Fermat's last theorem, one of the jewels sort of of mathematics of all time. A beautiful story also behind it. Pierre Fermat, a great French mathematician who lived in the beginning of mostly worked at the beginning of what 17th century.

2:57:07And he actually has to his credit a number of important contributions. But the most famous is called Fermat's last theorem or Fermat's 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 a margin of a book that he was reading, which was actually important book by dear Fanto's about equations with coefficients and whole numbers. And he wrote on a 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.

2:57:50At some point I was giving a public talk about this. And I made a joke. I made a tweet in which I wrote that I have proved this theorem. But 280 characters are not enough and the kind of cosmic mid -sentence. So this was 17th century Twitter style proof. But a lot of mathematicians took it seriously because he had great credibility. He did made some major contributions.

2:58:19And the 350 years it remained unproved with many people trying and failing until in 1994. No, 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 it's exactly what we were talking about earlier. You have 99 % of the proof. This one little thing does not quite connect and 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.

2:59:03So 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 theory is Richard Taylor. They were able to do that one percent. So to speak. Well, some people might say it may be not one, but five percent or whatever. But it definitely was an important ingredient, but it was not he had a 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 in finally was published and I think was accepted and referred in 95.

2:59:42And since believed to be correct. Now what he proved actually was not for Mastery himself, but a certain statement which is called Shimura Taniyama, a very conjecture named after three mathematicians, two Japanese mathematicians and one French porn mathematician who worked in also the Institute for Advanced Study in Princeton. And it was my colleague at UC Berkeley, can rib it 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.

3:00:24So this would happen here. A was Fermat's last theorem. B was Shimura Taniyama's way conjecture. And that's what and rewiles 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 Ribet at UC Berkeley. So now what is the statement of Fermat's last theorem? Let me start with Pythagoras. Since we already talked about it, let me start with Pythagoras the theorem which describes the right triangles. So what is the right triangle? Is it triangle in which one of the angles is 90 degrees like this? So it has three sides.

3:01:02The 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. 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. Main is actually infinitely many solutions in natural numbers. For example, if X is you take X equals three Y equals four and Z equals five, then they solve this equation because three three squared is nine four squared is 16. Nine plus 16, 25. And that's five squared.

3:01:53So X squared plus Y squared equals Z squared is solved by X equals three Y equals four Z equals five. And there are many other solutions of that nature. I wish to say that natural numbers are whole numbers and non -negative. That's right. One, two, three, four, five, six, and so on. Now what's Fermat's last theorem? Fermat asked what about what will happen if we replace squares by cubes? For example, so X cube plus Y cube equals Z cube. Other any solutions in what do you call natural numbers? It turns out there are none. What about four powers? Again none. What seems like none, right? So that was the statement.

3:02:38So the theorem says that the equation X cube plus Y cube equals Z cube has no solutions in natural numbers. Remember natural means positive whole numbers. So of course there is a three -wheel solution, zero, zero, zero. So that 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 solutions.

3:03:08So you kind of see the trend. X to the N plus Y to the N equals Z to the N. If N is greater than two, there's no solutions in natural numbers. That is a statement of Fermat's last theorem. Deceptively simple, as far as famous theorems are concerned. You don't need to know anything beyond standard arithmetic, addition and multiplication of natural numbers. That's why a lot of people both specialists and amateurs try to prove it. So it's so easy to formulate. So in fact, I think Fermat proved the case of cubes. I think he did actually prove elsewhere the case of cubes, but so it remained like fours.

3:03:53There are infinitely many cases, even if you prove it for cubes and for fourth power and fifths, then still there are six, sevens and so on. There are infinitely many cases in which it has to be proved. And so you see the sample of the 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 is so serious. Almost like we're all wearing like lab coats and like take an elevator to the every tower. And however, look at all this drama. Look at all this drama. It's like we also like drama. We also have narratives.

3:04:34We also have armitis. Here is a guy, he's a 16th century mathematician or 17th century mathematician who leaves a note on the margin and motivates others to find the proof. Then how many hearts were broken, that they believe that they found the proof. And then later it was realized that the proof was incorrect and so on. And brings us to modern day and one last attempt and reviles who is very serious and respected and esteemed mathematician announces the proof only to be faced with the same reality of his hopes dashed, seemingly dashed and like there is a mistake. It doesn't work. And then to be able to recover a year later, how much drama in this one story?

3:05:15It's amazing. But from what you understand for what you know, what was the process for him that is similar perhaps to your own life of walking along with the problem for months, not years. Yes. So he worked, he has given interviews about it afterwards. So we know that he described his process that number one, he did not want to tell anybody because he was afraid that people find out that he's working on it because he was such a top level mathematician. People would guess that he has some idea, that there is some idea. So you know, if you just know that somebody has an idea, this already gives you a great boost of confidence, right?

3:06:04So he didn't want people to have that information. So he didn't tell anybody that he was working on it. Number one, be lonely. Number two, he worked on it for seven years, if I remember correctly, by himself. And then he thought he had it and he was elated. Obviously he was, you know, very happy. And he announced it at a conference, I think it was in Cambridge University or Oxford University in the UK in 1993, I believe. So you know, this isn't really interesting because all of us, we can relate to this because I remember very well my first problem, how I solved my first problem. I described it in a love and math in my book.

3:06:52So it was, I was, what was I? I was 18 years old. I was a student in Moscow. And I was just, I just lucked out that I wasn't reduced to this great mathematician. Since I, you know, I was not studying at Moscow University because of anti -Semitism and the Soviet Union. So I was in this technical school. But I was lucky that I had a mathematician who took me under his wing. And Mitri Fuchs, who actually later came to the US, and he's still a professor at UC Davis, actually. Not so far from me. So he gave me this problem and it was rather technical. So I will not try to describe it. But I do remember how much effort, you know, that excitement, but also kind of a fear.

3:07:43What if I don't have what it takes, you know, I lost sleep. So this was one consequence of this. I, for the first time in my life, I had trouble falling asleep. And this actually stayed for a couple years afterwards. So then it was kind of like a wake -up call that I should be to take care of myself, not work to lay it and so on. So that was sort of like that experience. And I was lucky that I was able to find a solution, number one within two months, maybe. And it was very, it was surprising. And it was beautiful. Like the answer was, was in terms of something which seemed to be from a different world, from a different area of mathematics.

3:08:18So it's very happy. But I do remember this moment when suddenly you see that. Just like you, in this case, it was literally, I had to compile these diagrams with what mathematicians call co -homology groups and spectral sequences. And manually calculate some numbers and trying to discern some system in it. And suddenly I saw that how they all will govern by this one one force, so to speak, one pattern. And that was absolutely wow. So it's like, maybe what was it? You're sitting there at a desk. Actually, you know, I lived in a town outside of Moscow. So I used to take, I would take a train to Moscow.

3:09:00So it's what we call in Russia, electric, you know, like this electric train, which was super slow. It took more than two hours to cover that distance. And I think that the crucial inside came when I was in this. And I just, I was, I had to contain myself. So I don't start screaming, you know, to get the other passengers in the car. So I was sitting there and staring at this paper. So you know what I remember that what came to me. I have something now, which nobody else in the world has. I have a proof of, first of all, it was not just a proof. Like in the case of Firmar, the statement is already made.

3:09:38That's why it's called conjecture. You know, you make a statement, you don't have a proof yet. Then you try to prove it. In my case, I did not know what the answer would be. There was a type of question where the answer was unknown. So I had to find the answer and prove it. And the answer was very nice. So nobody knew, as far as I could tell, nobody knew because my teacher told me that he explored all the literature. And this was not known. So this was the answer. Suddenly I felt that I was in possession of this. Now it was a little thing. It was not cure for cancer. You know, it was not a large language model.

3:10:15But it was something undeniably real, meaningful. And it was mine. Like I had it. Nobody else. I had not published it. I didn't even tell, and even told anybody. And it was a very strange feeling, you know, to have to have that. Were you worried that this treasure could be stolen? Not at the time. Not at the time. So later on, there were situations where I was exposed to those type of experiences. By that time, I didn't think of that. I was still this study I'd cared, you know, who was just obsessed with mathematics, with this beauty and discovering those beautiful facts, beautiful results. So I didn't think about, I didn't even think that it could be possible that somebody could steal it or whatever.

3:10:58I just wanted to share it with my teacher as soon as possible. And he understood quickly. And he is like, yeah, good job. Is there something you can give color to the drama, Ericka's talk, Ericka Einstein has spoken about some of the challenges, some of the triumphs and challenges of his time at Harvard. So is there something to that drama of people stealing each other's ideas, or not allocating credit enough? Oh, sure. Yes. All of that. And creating psychological stressors because of that. And yeah, unfortunately, on young minds and so on. Could have a very bad effect. Is that just a way of life or is this?

3:11:45I think we can definitely do better. And I think the first step is to kind of admit that we are not 100 % secrets of truth that we are human beings and all the good and bad and ugly qualities can be present and to have some kind of dialogue in my subject in mathematics. This has not happened yet. There have been some famous cases where people have been accused, which had been resolved, partially resolved, unresolved. And everybody knows it. But there isn't a systematic effort as far as I can tell, of really trying to create some rules, some ethics rules. This is fair game. This is not fair game.

3:12:32So that as a community, we strive to get better. I think that for most people, it's more like keeping your head in the sand and kind of pretending that it doesn't happen. Or it happens some isolated incidents. Well, my experience is not like that at all. I think it does happen much more often than it should. That's my opinion. So there's the pool of academia is fascinating. One of the reasons I really love it is you have young minds with fresh ideas. And that same innocence you had with when you first on the train have that brilliant breakthrough. And then you throw that in together with senior exceptional world class scientists who have, first of all, a getting older.

3:13:17Second of all, maybe they have partaken in the drug of fame and money and status and recognition. So that starts to corrupt all of our human minds. And you throw that mix in together. Yeah. Most people out rules. And it's beautiful because that's where the ideas of old contend with the new wild die crazy ideas and they clash and there's a tension and there's a dance to it. But then there's the old human corruption that can take advantage of the young minds. It's unclear what to do with that. I mean, part of that is just the way of life and there's strategies. And oftentimes when you look at who wins the Nobel Prize, it's also tragic because sometimes so many minds are the trajectory to the breakthrough idea involves so many different minds, young and old.

3:14:15I mean, you're right. It's, I think it's like everything, everything else, the path is to more self -awareness. And it's like owning up your own stuff and not blaming other people, not projecting onto other people, but taking responsibility. And that's true for everything. And the problem here, unique problem for mathematics, I would say physicist and chemist are better. They have, they actually have better sort of ethical rules and so on, especially biologists like because I think in part it's because there is much more money involved because they have to get grants and so on. So for them, the question of priority who discovered what first is much more serious because there's really some serious money.

3:15:00Mathematics occurs, you know that Fermat last theorem was proved. And the whilst become a millionaire, no. But I know you want a prize, but those prizes are not. I think that one was a big prize, but in general, there's not going to be. I think you want the Nobel Prize eventually, which is about a million dollars. So, but you know, sometimes I joke about this that this is the hardest way to win a million dollars. So, you know, but amongst mathematicians, I think the trouble is that we are so insulated from society because it's such a pure subject. It draws in very specific psychological types.

3:15:46And I can speak about myself. I did not realize it at the time, but later on, I definitely saw, I mentioned some of it earlier, that for me, Mathematics was a refuge from the cruelty of the life I experienced, from discrimination that I experienced when I applied to Moscow University at 16, being failed at the exam and stuff like that, which I described in my book as well. But that was my way. I was like, I don't trust this world. I don't want to deal with it. I want to hide in this platonic reality of pure forms. This is where I know how to operate. I love this. And I couldn't be bothered, in some sense.

3:16:25For a while, up and up to a point, as I was getting older and more mature, I was becoming more and more interested in other things. But I think that's one of the reasons. And one of the reasons why I wrote Love and Math was precisely to break that cycle. That it's a quiet guy in the corner that goes into math. And not the flamboyant joke or like DJ. I wanted to show how beautiful this object is to attract this new blood so that different psychological types and more women would join. Because then they would have students who would look at them and whom they will inspire. And then it would be, instead of a vicious circle, it would be a virtuous circle.

3:17:19And I have to say, I think it's happening, not because of my efforts on alone, obviously, there are many other mathematicians who are around the same time, started to put more effort. Because if the old stereotype of mathematician you're so enclosed, you're not interested in even exposing the beauty of your subject to other people. You see? And then it becomes this vicious circle. But you know, this one day, you know, I'm not one day. All the time, I meet the students who say, your book is the reason why I chose Math as my major. And I am proud, especially when it's women who tell me this. And they are cool.

3:17:54They are DJs at the same time. And they are social. And they have friends. And they go out and so on. You see? So they are, then they carry the torch. Because then they will be more likely to share this beauty with others to attract more students and so on. So I think this kind of this dumb was broken. So now they'll have more influx. And once we have people who are more able to connect at the personal level, that's when we also become more self aware as a community, I think. And that's when we might be, we should be able to have a chance to improve in terms of our ethical rules and stuff like that.

3:18:32So let me return to our friend Eric Weinstein for a question that I would ask anyway. But let me, let's have a non -Russian ask the Russian question. Ask him about the Russian concepts of friendship, science, gender, and love versus the American. You can, so there is a deep romanticism that you have of that runs your book, Love and Math. Is part of that something you've picked up from the Russian culture. What can you speak to that fueled both your fascination with math and your fascination? No, your your prioritization of the human experience of love. Hmm, good question. I definitely, there is some influence of the Russian culture, Russian literature perhaps, you know.

3:19:34But also, you know, like there are so many things, how do you, how do we develop certain sensibilities? Like, why do we care about this and not that? Like, why do I care, for instance, about, like you said, about this romantic ideals to speak of mathematics? That's certainly not something that is automatic, you know, there's some people care about some people don't. And I'm not saying it's superior or inferior. It's just how my composition, my psychological composition is like that. And it's an interesting question, like what is the cause of it? So I think that we cannot really know, but there are some aspects of it, of course, the experiences, life experiences are bringing family, like I was, you know, I was surrounded by love by my parents on the one hand, but in the other side, perhaps they were a little overprotective of me.

3:20:29So I was kind of like, you know, too much kind of like technique taking care of. So then when I, one had developed certain sensitivity, but was kind of not ready for the challenges of the real world. So then that struggle and that and then being lost and then being able to overcome and to learn. And then if you do, in other words, if you don't lose, you don't appreciate maybe, but sometimes when we lose something and then regain it, then we cherish it to appreciate and then become some important. Also, various difficulties, you know, the upsetting experiences, or one could say traumatic experiences growing up, you know, in the Soviet Union, that was not a walk in the park, you know, there were a lot of issues there that I had to go through and then it doesn't break you, it makes you stronger.

3:21:31But in my case, what happened was that, you know, for some of it, it took me 30 years to really come to terms with it and to really understand what happened. It gave me this motivation to strive to become mathematician, which maybe I wouldn't have otherwise. It's supercharged me. I'm talking about, for instance, I experienced with exam at Moscow University. So this is 1984. We spoke about earlier. And I was applying to Moscow University, a mathematics department, it's called Mechmat, which is like for people who don't know, like the place, was the only place to study pure mathematics in Moscow period.

3:22:21But also, but also the great place on earth. And it's like a huge building, this, you know, this monolith of a building of Moscow University. So because, as I said, you know, a year earlier, you've gained, you've gained, you've converted me into math, capitalizing on my love for physics, quantum physics. And so we, I spent a whole year studying with him and I was already kind of at the level of, you know, in some subjects, a level of like, really graduate, graduate studies. So it seemed like it would be a breeze to get into Moscow University. But in fact, little did I know that there was a policy of antisemitism where students like me would be failed by special examiners, mostly during the oral exam with mathematics, but occasionally I would be written tests and stuff.

3:23:22Now, my father is Jewish by blood. It was not religious. His family was not religious. My mom is Russian. And, but I was, since my last name was my father's name, so it was very easy to read what my nationality was. And so there was this, can you imagine there were special people who would screen up applicants, who would put aside the files of the undesirables. They would be special examiners who were actually professors at this university, who would be designated as those who would take the exam from those undesirables. It was, it's almost comical when you look back now. And also like questions, why there was no reason other than just hatred of the other.

3:24:07That's how I see it. It's just to give a little bit more color. So because you mentioned nationality, it's a little quirk that perhaps gives an insight to the bigger system, that the nationality listed on your birth certificate when your Jewish is Jewish, and when you're not Jewish is, is this Russian? For me, it was Russian. So first of all, in inner part, everybody has an internal passport. And they are, you have first name, but so this is a four. And the fifth colon is nationality, which comes from the nationality of the parents and so on. In my case, it was written Russian because my mom was Russian, but it didn't save me.

3:24:52Because it was my dad's last name. And so, so anyway, this was a toughest experience that I had until that point. And there was this two people who came into the room where I was the only undesirable. All other kids were being questioned by other examiners, but they told me that we cannot question you. We are waiting for special examiners. So it's like, oh, something is a foot. And so these two guys came and as if four hours, basically, we're asking me questions, which were not in the program and so on. But I was a kid. I was 16 years old. I tried to answer it best I can, but it was a setup. It's been documented since now.

3:25:34There are even lists of problems that were given to undesirables in those days. In my year, no, no Jewish applicants, as far as I know, Jewish by this metric were accepted. So then I had to go to this. There was one school, technical school in Moscow, which was the Institute for Oil and Gas Exploration, which had applied my to my program. And that's where many of my, many of the kids who were not accepted to most university ended up. And so, but the point is so, and then I was, I was so motivated by this because I wanted to show those guys, you know, that within five years, less than five years, I got a letter from the president of Harvard University inviting me as a visiting professor to Harvard.

3:26:30I was 21. I was barely 21 because I already did some research in the meantime. That's how motivated I was. You know, so, but the interesting aspect of it is that for the longest time afterwards, I was telling my self -history that nothing really happened. It wasn't so bad. Okay, so I was failed, but I knew that I was going to succeed. It was 30 years later that I finally got to meet that boy, that 16 -year -old, that I, that I neglected this time. And I realized that he died, that it was a crushing blow, the essence. Not just the instance, because there was no way, it looked like there was no way I could become a mathematician.

3:27:20Because if I don't, if you don't accept me there, it's over. I didn't know that I could actually find this striving applied math program, and then eventually somebody would take me under his wing and so on, and then could move to the United States. That was not in the realm of possibilities. So, in a way, there was nothing to look forward to. It was clear that it's over. I cannot, I cannot do what I love. And so, when I finally, when I finally connected to that boy, oh my god, I was a totally different experience. All the pain and all the trauma came to the surface. And it was a kind of tsunami.

3:28:07I didn't, I wasn't sure survived this. It was so, so hard. And what happened was I was invited to, to give a talk about this, in New York. I was kind of a spoken world event about science, but like personal experiences related to science. This was almost a year after my book came out. In my book, one of the first chapters is the chapter about this experience. But what I realized now is that I wrote it from the third person perspective. I knew the facts, but I was not emotionally connected to that experience. However, since I wanted to write the book and to connect to my readers, I allowed the boy to write it.

3:28:50So a lot of people were touched by it. And they would, people would say, wow, that chapter, you know, it really got a lot of resonance. It was translated into a language even before the book was published. I was surprised by this, because I didn't know yet. So, the adult Edward was not yet in touch, but the book gave the outlet to the child. So, and that kind of started the process. So finally, almost a year later, I'm in New York in this event. And the night before, I'm in my hotel room, and I was like, okay, what am I going to talk about tomorrow? And I take a piece of paper just to, you know, my usual preparation, you know, for things.

3:29:36And then suddenly, I have this vision that I will walk up to the microphone tomorrow, and I will just start crying. And I was like, by that time, I already had an insight that it's possible to have that kind of splitting kind of dissociation. I was like, but things were happening quickly. There was someone in my life who explained to me this idea that some things are under the radar of awareness, but they may still influence you. And a lot of that could be connected to some experiences in your childhood. So, I was kind of ready for it from different angles. But I was too surprised because I was like, what is there to remember?

3:30:21I know, I know everything. So then my inner voice says, all right, then, you have nothing to worry about. I don't go tomorrow. You will speak about this. And if you start crying, it's not a problem. I was like, no, I don't want to cry for other people. I want to find out what it is, what happened. And I sat on my bed, close my head, and it came.

3:30:46So it's hard to describe. So this is what the, and the sheer energy of it, and how much effort it took to suppress it, actually, for the last years. How much effort it took to build that band, to the panzeria, when saying Russian, you know, that hardcore, you know, around myself. So that, and the thing, later I realized, the war moments when it could come out. And for instance, I developed this fear of public speaking. All kinds of little things that I now feel were connected. So anyway, I saw what happened now through the eyes of that child. I saw how difficult it was, how crushed he was. And it looked completely hopeless.

3:31:30And I felt like, what's the point of living now for me? Now that I know how cruel this world is, which I didn't realize before, because I prefer to wear this pink, you know, the rose, rose colored glasses. But then something happened. It's so strange. It's like you feel that inside of you, there is this dead child. And it is incredibly sad. I mean, it's like, I can't even describe it. But suddenly he comes alive. And suddenly it's like, oh, he's here. And I had a little talk with him. And I said, look, you know, I know, and now I know, thank you. I'm so sorry that I neglected you for so long, you know, I didn't know.

3:32:13Thank you for doing this. And it's almost like, you know, I felt like the image came to mind. It's like a fallen soldier. Like you leave a fallen soldier on the battlefield or wound the soldier. And then you come back to take him with you. And I said, but look, look what we have done. Look at us now. It was not in vain. We are doing okay. And it's kind of almost just like holding, holding, that child and that sense of who I am, you know, and feeling it. So the next day, I went to the microphone and I let him speak for the first time about his experience in his own voice. It was incredible. People were crying.

3:33:03And afterwards came up to me and started sharing stories and so on. It is a story, it's universal story, it's archetypal story. It's the story of rejection and being treated unfairly. We all know it. And I think it's so important to realize that it's possible to revisit those moments. It's possible to reconnect to our little ones.

3:33:37It's suddenly, it's like a floodgates. There were many other things that came. That's when I became interested in the dimensions of imagination and intuition and so on. Because suddenly, I realized that I was deprived of that possibility of looking at the world through the eyes of a child, because that child was frozen in time. I was not connected to him. But suddenly he's with me. And he's almost like opens his doors and says, look at this.

3:34:14So, if I could ask you about there's a difficult idea here. There's a tension. I've interacted with a few folks in my personal life and in general that have lived through this experience of unfairness and cruelty in the world as young people. And what was them, do you draw from the action you took of not acknowledging the order of victim to cruelty, but instead just working your ass off, working harder. And then this, the flip side of that is you eventually reconnecting with the cruelty you experienced. Because if you did that early on, I was not ready for it. It is a defense mechanism. I could have come in other work -lets who come in suicide after this experience.

3:35:10I could have come in suicide because it's too much. And it is well known afterwards, of course, I became aware of all the literature about childhood trauma and so on. And I've been speaking publicly about it since then too. And so, you know, it is well known issue and well known kind of universal phenomenon. I think that, interestingly enough, even though now I see a lot of discussion of it, now that my eyes are open, but somehow before I didn't see it, so that we also show you how our confirmation bias, kind of like how we screen ourselves, how we turn the blind eye to things which do not confirm our views, or for which we are not yet ready.

3:35:55And by the way, nobody should push to do it too soon. I'm glad I developed certain strengths. I was confident. I was strong to withstand this. And if I weren't, who knows how it could turn out? So it is a very subtle kind of alchemical process, which I don't think there is a recipe, there is a formula. The reason I'm talking about this is just to share this experience because I think that the only thing we can do in this in some sense is to share with each other because then we can find, for instance, if somebody shared with me, it would naturally lead me maybe to get closer to that kind of understanding.

3:36:41It's really just personal stories. It's not. Obviously there is a component where professionals could be involved, professional therapists and so on. In my case, it somehow happened miraculously. Well, I did have support, but not from professional therapists, but from like dear friends. So I did have, you do need, I had somebody at the time who basically held my hand in through this experience. Yes, it was invaluable and it could not be done otherwise. So I think it's very common. And here's the thing.

3:37:20I would not do it any other way. When I reconnected and I saw all the horrors and so on, but I also was able to see that my examiners were victims of their own situation that they became the fell for this bogus series, or maybe it was more of an issue of career advancement or something. And I was still as they must have suffered as well because they must have had some kind of consciousness about it, that acting in this way towards sort of basically kids. So it's not a pretty from their point of view. So I could forgive them. And I could like also appreciate what a what a boost of energy it gave me.

3:38:11If I was accepted and I was just where I was a first year student, I lived, I would live in a dorm because I was in the you know, I'd be probably partying and drinking and well, who knows what? Maybe I wouldn't even become a mathematician. But this focused me like a laser without me even thinking about it. It just happened. I didn't care about anything but doing mathematics. And it made off, you know, it changed my life. So was it good or bad? Paradox. Seems like life is full of those. You said you lost your father four years ago. Yeah. What have you learned about life for me or dad? That's another big one.

3:38:54Yeah, because I was very close to him. And it was tough. And I was not, I was sort of not ready for it because until that point, I lived pretending that death does not exist. When my grandparents died, I was already in the US. So I was very convenient. And I couldn't go back. So I grieved. But it kind of was a bit abstract for me. I didn't see that that body is, you know, I didn't bury them and so on. So I waited till the other more. So my first death in my life was my father, like a really close loved ones. And I was absolutely devastated. You know, he was such an amazing creature, such an amazing human being.

3:39:44He was the kindest, the smartest, the most funny, just really funny and just really fun to be with. You know, this is what I miss, obviously. I mean, I just love to hang out with him. So, and then suddenly he's not there. So, stuff. But it kind of changed my perspective. You miss him. I miss him tremendously. I miss him tremendously. But in a way, I learned that he never left me in some, I mean, it sounds so a lot of words. So, you know, they are, they cannot express in words this, what I'm trying to say. But do you carry him with you? Yeah. And in some sense, I always did. And I I saw that that it's always been, it was really, we were one in some sense, you know, like we were, but there was this experience of two people, being together.

3:40:49And that I missed tremendously. But he gave me so much. And I, you know, let me tell you one aspect of it, for instance, when he was a kid, his father was sent to Goulog on bogus pretenses. Right. So, he, when he was 16, he applied to a university, he wanted to become a theoretical physicist. By the way, my love for theoretical physics was the large extent because of that. And he was not accepted. He was, even though he was brilliant, because he was the son of the enemy of the people. And he kind of broke him this experience that he didn't care when he was, you know, he went to a technical school and he didn't really care.

3:41:31That's my take on it. And then he ended up in this, in this, in this little provincial town. And he thought he would escape from it as soon as possible. And then he met my mother. And he fell in love. And so I am sort of the product, the product of that, you know, of physics. But then what I learned is that because he was not able to overcome that specific experience, it fell to me to do it. And if I didn't, my son of my daughter would have. I think that that was one of the things I learned. That was not by chance. That about the same age for slightly different reasons, I was subjected to the same kind of unfairness and cruelty.

3:42:15And in some ways, I feel like I did it for him also. I always, because he was also always so proud of me. I was so happy.

3:42:29And I to give this big lectures twice was in 2012 and in 2018. And both times they were in Boston. He could anywhere in the US. Both times was in Boston, walking distance from my parents' place. So he could be there in my mom as well. And that was such a gift that he was beaming, you know, seeing me on the stage. So, you know, now that he's no longer here and it's just you. Well, I still have my mom. I still have my sister. Yeah, but as a man, there's some aspect that it's, that it does hate you hard. Are you afraid of your own death? Do you think about your death? Are you afraid of it? I have a certain conceptual view of life and death today, which is informed by my experiences.

3:43:25In particular, going through my father's death. And that is something which cannot be conceptualized, like their experience. Like he could not give it to somebody. One thing I will say is that I felt that what it was, it was actually love totally exposed, like naked. And you try to throw it is so acute. So being facing that love is incredibly painful because it's so intense. When this person is alive, we have conversation, we have wars, we have some actions, we have some stuff is going on and it puts a filter. So we rarely actually feel love in this totally completely pure and adulterated state.

3:44:11But when person dies, it's there. And it's staring at you. And no matter what you do, you cannot turn away. Like I try to, it's like, almost I felt like I want to throw a blanket over it. Yeah. It burns like immediately like, boom, gone. It's there. Lift through it. And I was okay, I'm saying, I just lift through it, lift through it. That's how you, and that's how you know also learn what is love, for example, what is it really? What is love? What is life also? Because I was completely, I had no idea. And then you kind of learn that, okay, so maybe it's not quite, there is more to eat, there is more to eat, there's more to this experience than what can be put in a concept or in in a sentence, in a, in a, maybe poetry or music can do some justice to it.

3:45:07But if so, then my own life has that component, has that dimension, which is beyond anything I can say about it, you know. And even though I love this being this, playing this role, I love it. And I kind of, kind of makes me feel different about all kinds of difficulties that arise because it's almost like I want to enjoy it because that's what being human is. It's being, it's being terrified, it's being frustrated, it's being self -loathing sometimes. It's not knowing, but also being joyful. And just like, ah, let's just enjoy it. Kind of all of it. Like, that's why you came here for in some sense, you know, it's like not trying to run away from things, but kind of trying to just live through them and appreciate.

3:46:00So the biggest thing is gratitude in some sense, it's just gratitude. So thank you for letting me play. Yeah. This gratitude for every single moment, even if it's dark, even if it's lost, yeah. And that's why I am so people around me, they all say that it's a total doom and gloom and the world is ending. And I'm like, first of all, that's how you see it, okay? That's not the only point of view. But also, even if it is, that's your challenge. Like, what are you going to do about it? Stop complaining about other people. Do something yourself. How can you make it a better world, you know? And I think all of that starts with just a gratitude for the moment to be able to play this game.

3:46:38Yeah. How beautiful it is. What we've talked about love, but let me ask, what role does love play in this whole game in the human condition? It's like the glue, you know, it's like for me. It's like, and it's not because people say love is like for a human being, like a romantic love, which is a huge component of it, obviously, because it's so beautiful to be able to express it in this way. But it could be love for what you do for your passion for something, you know? Or for your friends, for instance, or love, it doesn't have to be. And so, in some sense, that's what it's all about in ultimately, because living without love, it's kind of bland, boring.

3:47:32And so... And I don't think it's possible for science to explain exactly what it is. You can do a evolutionary biology perspective. You can talk about some kind of sociology perspective, psychology perspective, but the experience, the intensity, where you forget or time, where it reminds it becomes an illusion. And everything just freezes. And then it's kind of beautiful and painful to hear you say that when you've experienced love, the deepest is when you lost it. Yes, but in a sense, you can say that you could not have one without the other. I could not have that deep connection with my father, like really on so, so many levels.

3:48:14If the warrant a moment, that's how I see it. And I'm not trying to say that's how everybody should see. For instance, I respect Ray Kurswayao. I respect and I feel, and I feel, almost like I even if it is in a form of a computer program, let's be honest about it. I find it to be very moving. I find it very moving. And I understand because he actually didn't have a chance to spend much time, you know, I think he was 16 or something, he was a teenager, he was that guy. I was lucky because my father died as much older. I've had so many moments with him, but that's not my thing. Like, I think it is a feature, it's not a bug, and it sounds crazy.

3:48:58Like I would love, I would give anything to have him here right now. Right now, everything I have, I give it away right now. Where do I sign? Yeah. Just see him for one hour. I promise you, I will. But I also know that I then I'll still lose him. Or I will die. Or whatever. You know, so that thing. So why is it so worse to just hold on to holding on to it? Why? Why are we holding on to this? And I am the first sucker. I'm the first one to hold on. But I'm questioning it now. Like, is there another way to approach life where you just, you know, how Buddha is like, just let it go. Enjoy and let it go.

3:49:38Enjoy and let it go. Is it possible? Except the paradox of it. Well, ask me a couple of years, you know, I will report. But I think that it's, but to my mathematical mind, it sounds like a very interesting idea to be honest, because to me, the idea of holding is, it sounds like an impasse, because no matter in all my experience, and if you look in history, every time somebody's holding, you know, it's how they said in the matrix, whatever has a beginning has an end. It's like, you cannot go around it. If you have a beginning, you could have an end. So then might as well just enjoy it and not worry too much about extending it longer.

3:50:18That's how I see it now. But maybe yeah, the roller coaster life, the paradox of life. Right. That were during incredible human being. I've been a fan for a long time. Thank you for writing love and math. Thank you. Thank you for being who you are, being both one of the greatest living mathematicians and still childlike wander of the exploring the, how this whole world works, the nature of the universe. And thank you so much for speaking with me today. This is amazing. In a pleasure. Thank you.