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

Episode Date: April 10, 2023

Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality. Please support this podcast by checking out our sponsors: - House of Macadamias: https://houseofmacadamias.com/lex and use code LEX to get 20% off your first order - Shopify: https://shopify.com/lex to get free trial - ExpressVPN: https://expressvpn.com/lexpod to get 3 months free EPISODE LINKS: Edward's Website: https://edwardfrenkel.com Edward's Book - Love and Math: https://amzn.to/40Bgxh0 Edward's Twitter: https://twitter.com/edfrenkel Edward's YouTube: https://youtube.com/edfrenkel Edward's Instagram: https://instagram.com/edfrenkel PODCAST INFO: Podcast website: https://lexfridman.com/podcast Apple Podcasts: https://apple.co/2lwqZIr Spotify: https://spoti.fi/2nEwCF8 RSS: https://lexfridman.com/feed/podcast/ YouTube Full Episodes: https://youtube.com/lexfridman YouTube Clips: https://youtube.com/lexclips SUPPORT & CONNECT: - Check out the sponsors above, it's the best way to support this podcast - Support on Patreon: https://www.patreon.com/lexfridman - Twitter: https://twitter.com/lexfridman - Instagram: https://www.instagram.com/lexfridman - LinkedIn: https://www.linkedin.com/in/lexfridman - Facebook: https://www.facebook.com/lexfridman - Medium: https://medium.com/@lexfridman OUTLINE: Here's the timestamps for the episode. On some podcast players you should be able to click the timestamp to jump to that time. (00:00) - Introduction (05:54) - Mathematics in the Soviet Union (16:05) - Nature of reality (27:23) - Scientific discoveries (40:45) - Observing reality (56:57) - Complex numbers (1:05:42) - Imagination (1:13:33) - Pythagoreanism (1:21:28) - AI and love (1:34:07) - Gödel's Incompleteness Theorems (1:54:32) - Beauty in mathematics (1:59:02) - Eric Weinstein (2:20:57) - Langlands Program (2:27:36) - Edward Witten (2:30:41) - String theory (2:36:10) - Theory of everything (2:45:03) - Mathematics in academia (2:50:30) - How to think (2:56:16) - Fermat's Last Theorem (3:11:07) - Eric Weinstein and Harvard (3:18:32) - Antisemitism (3:38:45) - Mortality (3:46:42) - Love

The following is a conversation with Edward Frankel, one of the greatest living mathematicians, doing research on the interface of mathematics and quantum physics, with an emphasis on the Langlan's program, which he describes as a grand unified theory of mathematics. He also is the author of Love and Math, the heart of hidden reality. And now, a quick use that can mention of each sponsor. Check them out in the description. It's the best way to support this podcast. We got house of McAdamious for healthy snacks, Shopify for e-commerce, and ExpressVPN for security and privacy on the internet.

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This show is brought to you by House of McAdamias, a company that ships delicious high quality and healthy McAdami and nuts and McAdami and nut-based snacks directly to your door. I don't know why shipping to your door matters, but in the copy they gave me, they put that there, and I should use this opportunity to say that this sponsor and every sponsor, I have been extremely strict with that they can't tell me anything about what I can say. So sometimes when I say something that comes from their copy, it's just because the eternal laziness that is my human mind, the limits of my mind that are very quickly becoming superseded by GPT-4, GPT-5, GPT-6, and beyond. The sound of my voice will soon be generated by AI.

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The listeners, that's you, will also get 4oz bag of macadamias when you order 3 or more boxes of any macadamia product, that's house of macadamias's calm slash flex This show is also brought to you by Shopify a platform designed for anyone to sell anywhere with a great looking online store that brings your ideas to life and gives you tools to manage day-to-day operations. I love the word operations. It makes it all seem very serious and professional and real and powerful and expansive and scalable, yet maintaining the human touch, operations, logistics, supply chain. I should say that much of folks have been asking for some merch. I've gotten the deep honor and pleasure to meet some incredible artists that have offered their services and given me the gift of their

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I've used them for long, long, long, long time before they were ever sponsored. So we flirted for a while, we dated for a while, and now we're fully committed together and married, and not looking for any extra marital affairs in case you're wondering. I'm happy. I'm happy. I'm Linux. I'm happy. I'm Windows on Android on every single iPhone. Everything I got, every device got its USB-P on it, and I'm happy. And if you want to be happy like me, go to expresscpn.com slash lexpod for an extra three months free. This is Alex Friedman podcast to support it. Please check out our sponsors in the description. And now, dear friends, here's Edward Franco. You open your book, Love and Math with a question, how does one become a mathematician? There are many ways that this can happen.

Let me tell you how it happened to me. So, how did it happen to you? So, first of all, I grew up in the Soviet Union. In a small town near Moscow, called Kalomna. And I was a smart kid, you know, as a school. But mathematics was probably my least favorite subject. Not because I couldn't do it. I was a straight-aged student, and I could do all the problems easily.

But I thought it was incredibly boring. And since the only math I knew was what was presented at school, I thought that was it. And I was like, what kind of boring subject is this? So what I really liked was physics, and especially quantum physics. So I was buying, I would go to a bookstore and buy popular books about elementary particles and atoms and things like that and read them, you know, devour them.

And so, my dream was to become a theoretical physicist and to delve into this finer structure of the universe, you know. So then something happened when I was 15 years old. It turns out that a friend of my parents was a mathematician who was a professor at the local college. He was a small college preparing educators and teachers. It's a provincial town. Imagine it's like 170 kilometers from Moscow, which would be some like 70 miles I guess. You do the math. I like how you remember the number exactly.

Yeah, it's not funny how we remember numbers. So his name was Yevgeniy, Yves Geni, Vich Petrov. And if this doesn't remind you of the great works of Russian literature, then you haven't read them. Like Warren Peas, you know, like with the patrony nickname. Yeah. But this was all real. This was all happening.

So my mom, one day by chance, met Yvgeniy Yvgeniyyich and told him about me, that I was a bright kid, and interested in physics. And he said, oh, I want to meet him. I'm going to convert him into math. And my mom was like, nah, math, he doesn't like mathematics. So they said, okay, let's see what I can do. So I went to see him. So I'm about 15. And a bit arrogant, I would say, you know, like average teenager. So he says to me, so I hear that you are interested in physics and the mental particles. I said, yeah, sure.

I'm interested in physics. And the main three particles, I thought, yeah, sure. And for example, do you know about quirks? And I said, yes, of course, I know about quirks. Quirks are the constituents of particles like protons and neutrons. And it was one of the greatest discoveries in theoretical physics in the 60s that those particles were not elementary,

but in fact had the smaller parts. And he said, oh, so then you probably know the representation theory of the group as U3. So they're like, as you would. So in fact, I wanted to know what were the underpinnings of those theories. I knew the story, I knew the narrative, I knew kind of the basic story of what these particles look like.

But how did physicists come up with these ideas? How were they able to theorize them? And so I remember, you know, like it was yesterday, so he pulls out a book. And it's kind of like a Bible, you know, like a substantial book. And he opens it in somebody in the middle. And there I see the diagrams that I saw in popular books, but in popular books there were no explanation. And now I see all these weird symbols and equations.

It's clear that it is explained in there. Oh my God. He said, you think what they teach you at school is mathematics? It's like, no, this is real mathematics. So I was instantly converted. That you understand the underpinnings of physical reality. You have to understand what S.U.3 is. You have to learn what are groups, what is group S3, what are representations of SU3. There was a coherent and beautiful. I could appreciate the beauty even though I could not understand heads and tails of it.

But you were drawn to the methodology, the machinery of how such understanding could be attained. Well, in retrospect, I think what I was really craving was a deeper understanding. And up to that point, the deepest that I could see was the word, I was diagrams, but for that story that, a proton consists of three quarks and a neutron consists of three quarks and they're called up and down and so on. But I didn't know that there was actually underneath, beneath the surface,

there was this mathematical theory. If you can just link on what drew you to quantum mechanics, is there some romantic notion of understanding the universe? What is interesting to you? Is it the puzzle of it or is it like the philosophical thing? Now I am looking back. Yeah. So whatever I say about Edward at 15, yeah. He's colored by my, you know,

all my experiences that happen in the meantime. I should say current views and so on. For the people who may not know you, I think your book and your presentations kind of revealed that that 15-year-old is still in there somewhere. Well, I think it's a conflict. Some of the joy. He's probably still here now, here, in some way.

Yeah, I think it was a joy of discovery and the joy of going deeper into the kind of the root, to the deepest structures of the universe, the secrets, the secrets. And we may not discover all of them, we may not be able to understand, but we're going to try and go as far and as deep as we can. I think that's what was the motivating factor in this. Yeah, there's this mystery, there's this dark room, and there's a few of these mathematical physicists that are able to shine a flashlight briefly into there. I will talk about it, but it also kind of makes me sad that there's so few of your kind that have the flashlight, I have to look into the room. It's interesting. I don't think there

are so few to be honest because I think I find a lot of people are actually interested. If you talk to people, you know, like some people you wouldn't expect to be interested in this, from all walks of life, from people of all kinds of professions. I tell them I'm a mathematician and they're a mathematician. Okay, so that's a separate story. A lot of people, I think, have been traumatized by their experience in the math classes. We can talk about it later. But then they ask me what kind of research I do.

And I mentioned that I work on the interface of math and quantum physics, and their eyes laid up. And I said, oh, quantum physics or Einstein's relativity. I'm really curious about it. I watch this podcast or I watch that podcast, you know, and I've learned this. It's like, what do you think about that? So I actually find that actually physicists are doing great job educating the public, so to speak, in terms of popular books and videos and so on.

My limitations are behind. We are starting to catch up a little bit, have been starting last 10 years, but we are still behind. But I think people are curious. Science is still very much something that people want to learn because that's our kind of the best way we know to establish some sort of objective reality whatever that might be. Yeah and to figure out this whole puzzle to figure out the secrets of the universe whole thing that we can agree on kind of

you know like even though for me at this point I always you know make an argument that our physical theories always change, they get updated. So you had Newton's theory of gravity. Then Einstein's theory superseded it. But in mathematics, it seems that theories don't change. Pythagoras's theorem has been the same for the last 2500 years. X squared plus y squared equals Z squared. We don't expect that next year suddenly it will be Z cubed.

So that to me is actually even more hints even more at how much we are connected to each other. Because pedagogy theory, if you think about it, or any other mathematical theorem, means the same thing to anyone in the world today, regardless of their cultural, you know, bringing religion, you know, ideas, ideology, gender, whatever, nationality, race, whatever, right? And it has meant the same to everyone, everywhere. And most likely, will meant the same to everyone everywhere. And most likely will mean the same.

So that's, to me, kind of a 90-dollard to the kind of divisiveness that we sometimes observe these days, where it seems that we can't agree on anything. To the political complexity of 2 plus 2 equals 5 in George Orwell's 1984. I wasn't a Soviet Union in 1984 and so in many ways I see that it was present and the novel was present but we still have not found a dictator who would actually say 2 plus 2 equals 5 and would demand their citizens to repeat that. The night is still young. It does feel happened yet, okay? Yeah. But those feel like math and physics are both sneaking up to a deep truth

from slightly different angles. And you stand at the crossroads or at the intersection of the two. It's interesting to ask, what do you think is the difference between physics and mathematics and the way physics and mathematics look at the world? There is actually an essential difference, which is that physicists are interested in describing this universe. Okay, mathematicians are interested in describing all possible mathematical universes, of which, you know, in some of our work, I'm still considering myself more of a mathematician than a physicist. My first love for physics notwithstanding. Mathematicians are, in a way,

we have more diversity if you might say. So we are accepting, for instance, our universe has three spatial dimensions, and one time dimension, right? So what I mean is that- Allegedly. Allegedly. Absorbed, but that way you can observe today, right? So of course, there are theories where there are some hidden dimensions as well.

Well, let's just say observe, to observe dimensions. So this table top has two dimensions because you can have two coordinate axes. X and Y, but then there is also a third one to describe the space of this room. And then there is a time dimension. So realistic theories of physics have to be about spaces of three dimensions or space times or four dimensions. But mathematically, we are just as interested in theories in 10 space-time dimensions, or 11, or 25, or whatever, or infinite dimensional spaces, you know? So that's the difference.

On the other hand, I have to give it to the physicists, we don't have the same satisfaction that they have of having their theories confirmed by an experiment. We don't get to play with big machines, like LHC, Ingeniva, large-edron collider, that recently discovered the Higgs boson and some other things. For us, it's all like a mental exercise in some sense. We do we prove things

by using rules of logic and that's our way of confirming experimental confirmation if you will. But I think we kind of envy a little bit my friends' physicists that they get to experience this sort of this big toys, you know, and play with them. But it does seem that sometimes, as you've spoken about, abstract mathematical concepts, map to reality, and it seems to happen quite a bit. That's right. So, the mathematics is underpins physics, obviously. It's a language.

The book of nature, as Galileo famously said, is written in the language of mathematics. And the letters in it are the circles, triangles, and squares. And those who don't know the language, I'm paraphrasing, are left to wander in a dark labry. That's a famous quote from Galileo, which is very true and has become even more true more recently in theoretical physics in the most

axiograph for out parts of the theoretical physics that have to do with elementary particles and as well as the structure of the cosmos at a large scale. What do you think of Max type Mark who wrote a book, Mathematical Universe? So do you think, just clinging on that point, you think at the end of the day, the future generations will all be mathematicians? I know, I know. Meaning, the ones that deeply understand the way the universe works,

at the core is it just mathematics. At the core of, you know, I would say mathematics is one half of the core. So the book is called Love and Math. Okay, so these are the two pillars. In my view, in other words, you can't cover everything by math. So mathematics gives you tools, it gives you way kind of a clear vision. But mathematics by itself is not enough for one to have harmonies and and balance life. So I am suspicious of any theory that declares that everything is mathematics.

So math can generate things that are beautiful, but it can explain why it's beautiful. Math, you could say, is a way to discern patterns, to find regularities in the universe. And both physical and mental universe, that MathMex explores the mind as much as it explores the physical world around us, and it helps us to find those patterns, which kind of, which makes our perception more sophisticated, our ability to perceive things such as beauty, you know, and it sharpens our ability to see beauty, to understand beauty.

So our world becomes more complex from thinking that our earth is flat, we go to realizing that it is round, that it is shape as a sphere, so that we can actually travel around the earth, you know, so there isn't a place where we hit the end, so to speak. And then, proceeding in the same vein, then Einstein's general relativity theory tells us that our space time is not flat either. This is much harder to imagine that bend, a bend, three-dimensional or four-dimensional space,

or four-dimensional space-time, because this idea that the space around us is flat is so deeply entrenched. And yet we know from this theory and from the experiments that have confirmed it, that a ray of light bends around a star, as if being attracted by the force of gravity. But in fact, the force of gravity is the bending. It's just that it's not only the bending of the space, it's also the bending of space time.

There is a curvature, not only between special, spatial dimensions, the way parallels and meridians come together in a small scale they look like perpendicular lines, but if you zoom out, you see that the space, I think, curving the space. They are sort of the tracks along which the space gets curved. That's the, that would be the curvature of spatial dimensions.

But in fact, now, throwing time, and one time, imagine a sphere which lives, which has one of the mer a sphere, which lives, which has one of the meridians respond to time. And the wireless response to space, I can't imagine it, but I can write it in my microform, expressing that curvature. And that's, in fact, that curvature is responsible for the force of gravity attraction between the simplest instantiation of it, attraction between two planets, or between two human beings.

Oh, that's not it. At the time, bending time, it's not very nice that what that theory did to time, because it feels like the marching of time forward is fundamental to our human experience. The arrow of time time marching forward nicely seems to be the only way we can understand the universe. And the fact that you can start up to now, up to now. There are people who claim that they can, that they have, they possess other ways of experiencing it. So truly can visualize messing with time. Well, messing with time, but not necessarily messing with time, because one point of view

is that, you know, I think who was it, I think William Blake, who wrote that eternity loves time production. So one point of view is that it is eternity which is fundamental, where time stands still, which our mind conceptualizes as the time. So, but in fact, you know, it's not something mystical. If you think about when you, about it, when you really absorb it in something, time does stay a stand still.

And then you look at the clock and it's like, oh my God, two hours have passed. And it felt like a couple of seconds. When you are absorbed, when you are in love, when you are passionate about something, when you are creating something, we lose ourselves and we lose the sense of time and space for that matter. You see, so there is only that which is happening, that creative process. So I think that this is familiar to all of us. And we may be actually the closest attitude at that moment. So yes, so then there is a point of view that this is where we are,

the we are who we are, at our sort of fundamental, at our fundamental level. And after that, the mind comes in and tries to conceptualize it. It's like, oh, because I was writing something, I was writing a book, I was painting this painting, or maybe I was watching this painting and got totally absorbed in it. Or I fell in love with this person. That's what happened. But in the moment, when it's happening, you're not thinking about it. You're just there. Yeah, we construct narratives around the set of memories that seem to have happened in sequence, or at least that's the way we tell ourselves that. And we also have a bunch of weird human things like consciousness and the experience of

free will that we chose a set of actions as the time un enrolled forward. Right. And we are intelligent, conscious agents, making takes, taking those actions. But what if all of that is just... And illusion? And illusion. And then nice narrative, we tell ourselves. Sure. That's a really difficult thing.

It's possible. And imagine, imagine that to make it really catch 22. That our, imagine that our minds and set our set up in such a way. Yeah. That they can't approach the world or experience otherwise. So in other words, to understand, to see that it from a more kind of all encompassing point of view, we have to step out of the mind. Well, I wonder what's the more honest way to look at things. But I think we like to to play it with time. I think we like to play with this experiences with all the drama of it

With all the memories with all the tribulations. Yeah, I think we love it. We love it. Otherwise, we wouldn't be doing it I think this or Earth loves it the evolutionary process somehow loves it whatever whatever this thing that's being created here on Earth it seems to like to create, like to allow its children to play with certain truths that they hold, this subjective truths. They're useful for the competition or whatever this dance that we call life brought these defiant, not just humans. And you know, I'm glad you mentioned that because what I find fascinating is that the greatest scientists are on record saying that when they were making their discoveries, they felt like children.

So Isaac Newton said to myself, I only appeared as a child playing on the seashore and everyone is in a wild finding a prettier pebble or a prettier shell. Whilst I think he says something like the infinite ocean of knowledge laid was lying before me. Alexander Grotendik, who probably it was the greatest mathematician of the second half of the 20th century, the French mathematician Alexander Grotendik, wrote that discovery is a privilege of a child. The child who is not afraid to be wrong once again, to look like an idiot, you know, to try this and that, I'm paraphrasing and go through trial and error.

That is for them, in other words, for them, that innocence of a child who is not afraid, who has not yet been told that it cannot be done. That was essential to scientific pursuit, to scientific discovery. And now, also compared to Pablo Picasso, a great artist, right? So who said every child is an artist? The question is to how to preserve that as we grow up. Do you struggle with that? You're one of the most respected mathematicians in the world.

You're Berkeley, you're like, this is the statue. You're supposed to be very like, you know, I would tell you. Sometimes I joke, I say, I think an elevator to the top of the Ivory Tower every day. You're supposed to speak like royalty. Do you struggle to strip all of that away to rediscover the child when you're thinking about problems when you're teaching, when you're thinking about the world?

Absolutely. I mean, that's part of being human because when we grow up, I mean, all of them, all of these great scientists, I think they were so great in part because they were able to maintain that connection, okay, and that fascination, that vulnerability, that spontaneity, you know, and kind of looking at the world through the eyes of a child. But it's difficult because you go through a education system, and for many of us, it's not especially helpful for maintaining that connection, that we kind of like we are being told certain things that we accept, take for granted and so on, and a little by little.

And 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 inside. No, but it wants to look like an idiot. Once you start growing up, or you think you're growing up,

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. So 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 imperfect approximation, approximate solution to the problem. But 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, you would be, 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. And especially today, in this age of AI,

of course there's a big elephant in the room always, which is called AI, right? And so I know that you are an expert in 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 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, a child has not yet accumulated knowledge. And 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. Yeah yet they are perfectly capable of distinguishing between cancer dogs, for instance, and stuff like that.

But much more than that, they are also capable of that, you know, wide-eyed, you know, sort of perspective. So can it really be captured? That perspective, that sense of awe, can it really be captured by a computational loan? Actually, I don't know the answer, so I'm not sort of trying 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. It'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 the result of one of life on earth, of war and love and terror and ambition and violence and invention, all of that from the bacteria to day. So like that young child is not a blank slate. They're coming. They're actually hold 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. You see, what strikes me as unlikely What strikes me as unlikely is that, how should I put it? How interesting that you are a computer scientist and there are other people,

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 tend to explain things in theological religious terms. Today science has progressed. There are fewer people who kind of buy into a 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. So at its best a large language model like GPT-4 captures the magic of the human condition on its full display, its full complexity.

And since it's mimicking, it's trying to compress all the weirdness of humans, of 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 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. When I wonder, 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. I'm glad you mentioned that because that just seems to be the mantra. It's just fake, or fake it till you make it, isn't it? Isn't that what we all do though? No, well, 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 you're putting it in this terms, because I've had conversations like that. 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 and 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 that, and other things that can be reproduced, things that I can demonstrate, that 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 actually modern science has already sold on that. You know quantum mechanics has shown unambiguously that the observer is always involved in the observation. Likewise, girdles in completeness theorems to me

I'll show how essential is the observer of a 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 of these different scales, the observer, what the observer is. That, 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, that 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 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, but 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. I 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 the 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. Who 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 We are just you know reminds me of this famous Lord Kelvin'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, I'm happy to say, everything's finished, we 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, so Kodar Hoto 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.

And then you start seeing things as being such. It's confirmation bias, if you will. This also reminds me, I think a good analogy is it's a friend of mine, Philip Koshin told me that in France, there is this literary movement, which is called Uli Poe, 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 Perek, which is a 300 page novel in French, which never uses the letter E, which is the most used, widely used letter of the French language. So in other words, he set this parameters for himself. I'm going to write a book where I don't use this letter, which is a great experiment, and I applaud it. But that's one thing to do that, and to kind of show his gamesmanship, 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 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. And 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 the given answer, explanation. I was like, oh, there has to be some explanation. And I tried to frantically search for it. Just for somebody like me, I know a earth, 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, it's recovering, it's possible, and it is liberating. Yes, recovering, is 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 to use another philosopher, Soren Kirchiger, the Danish philosopher said, I think or without paradox is like a lover, without passion. A poetry, a media, a critique.

That's a good one. All right. So, and you know, Nils Bohr said, in Simmervein, the great Danish also. Something about Dains. Something about Dains, I think it's all started with Hamlet. 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 It's 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 This bottle if you project it down onto the table, you will see more or less a square. If you're projected onto a 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. They reveal 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, in a, 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.

But 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. So for those who don't know, you have a screen and you have a meter from which you send you kind of shoot electrons. And in between, you put another screen which has two very cool slits parallel to each other.

If we were shooting 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 they color it, they paint it. So there would 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 itself, where at some points, you know, to crest would amplify and at some point a crest in the trough would cancel each other. Yet, 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, 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. So now I'm talking about this again. Our psyche kind of is like in 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 has a bunch of billiard balls hitting each other, driven by some blind forces. That's not at all like it is. And we've known this for over for for about 100 years at least, you know. And you call this self-imposed limitation. It is a self-imposed limitation when we when we pretend that that for instance that there's naive ideas of 19th century physics, I still valid and and then start applying them to our lives and then also derive conclusions from it. And 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 kind of bullshit or some kind of concoction 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. So 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 system 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 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 are doing a fantastic job talking about this phenomenon, for instance, double slit experiment 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. So 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 prevail 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 with which we could talk about? We rigorously talk about free will and consciousness. What 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 inevitable.

There is something mysterious. And in fact, somehow immediately I feel that the impulse to quote somebody on this because as if my own opinion does come. Yeah. There's a long dead expert. I have a question. I mean, Einstein said that.

You know, so like, how? See, look at me. I 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. He actually said that there are some quotes which

are attributed to him, which he never said, but this he did. I investigated. But more importantly, you know, how do you feel about it? I think that everybody knows. But in other words, he also said, I'm in time, imagination is more important than knowledge. Okay, and it's 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 discovery. No, it's always, it's always, is always felt as a jump, as a leap. And I have, I have actually been studying various examples in a 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, that 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 you would have to square it, you get a negative number. But 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. Everybody says, the adults 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 made money, apparently, by compiling astrological sort of readings for the elite 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. Jerolamo Cardano. He also invented what's called Cardano's Shaft, which is an essential component of a car. Cardanovi Val, we say in Russian.

So he wrote a book, which is called R Smagna, which is 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 degree 2, so you have a x squared plus b x plus c equals 0. 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 quadratic equations for which which would start with x cube or x to the power of 4 is opposed to x squared. And in the process of solving this equations, it 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 fall, at the end of the calculation, this weird numbers got canceled, it kind of canceled 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 of the thinking mind, it is something almost unbearable. It's almost I feel that a language language model, a computer language 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 are we so 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 call 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, right? All fractions, like 1,5, or 3,5, or 4, or 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 perennial concepts even in our very poor mathematical at school. But now imagine that instead of one line,

you have a second axis. So 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 the square root of negative 1. This is a graphical geometrical representation of complex numbers, which is not mysterious at all. Now, it took another 200, 300 years for mathematicians

to figure that out. But initially, it looked like a completely crazy idea, you know. So all it is, all complex numbers is just an expansion. We're going over to real now. Yeah, it's just real part and the imaginary part. It's just an expansion of your view of the mathematical world. The fact that you can actually mount, you can add them up by adding together the real parts and imagining the 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. For 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 like mathematical comfort. Established knowledge. Established knowledge. Right. And now, obviously, for each, each sort of fruitful leap like that, they probably were thousands of like things which went nowhere. I'm not saying that every leap, you know, it's like, that every leap, it's an open shooting game. Because, for example, you can try to do the same with a 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. And the answer is no.

You can define addition, but you can 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, next question would be what about four-dimensional? In a 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 all powers of two. Two square, this four, two to the third power is eight. That's one of the bigger mysteries in mathematics. Why it is so?

So just a hint. There's a hint of what's missing in our high school curriculum, kind of fascinating mysteries. Yes, the appreciation of the mysterious. So in other words, yes, we resolved with this one mystery that we understood that the square root of negative one is real, is meaningful. We build a theory to service those, to describe those numbers. Did we find the theory of everything? No, because we then invited other mysteries, because we pushed the way I also to speak, or we pushed the frontier,

and then new things come, get illuminated, which we couldn't see before. That'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 of 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 that 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? You'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 financially? Investment advice. So let me tell you something. I, my views, are have evolved. OK. 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 plateenists in honor of the great philosopher Plato, who talked about these absolute perfect forums. So for me, about 10 years ago, the world of mathematics was this world of pure forums,

this beautiful, pure forums, 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 the sense of escape from the cruelty and injustice of this world, you know, which I now recognize. And the divine world of forms is stable,

relies on something stable. And in that world, everything is clear cut. It's either true or false. I'm not very nice, huh? It's very nice. The biggest delusion of all. I'm not very nice, sir. It's very nice. Oh, my God. 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 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. Did you see the human world as lesser than the mathematical world as more limited to the mathematical world?

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 a paradoxical question, whether mathematics is invented to discover it, whether there is this world of pure forms and so on. It's 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 that mindscape, so to speak. But the very structured mindscape, where I wrote in a love and math that enchanted gardens of Platonic reality where all this fruit grows. And then we might be interested, it gives you the sort of romantic sense of an explorer. And someone may be stuck in a, you know,

some provincial town in Russia, for instance, but have the sense of Magellan, you know, of traveling around the world. It's just not in a 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 problems 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. Would that, the possibility that paradoxes are actually fundamental to reality and really, really internalizing that.

That we exist in a world of not forms but of paradoxes. Bingo. And so it's like what I said. But if you think it's weird and I agree with you as a recovering adding to knowledge yeah you know but I am liking it more and more because there's so much freedom in it and like like Niels Bohr said you know I quoted that earlier the 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 the about art? Why are we so drawn to that? Why are we so captivated by those forms of, they are not intellectual necessarily. They 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 a cell phone play or some neurons or hitting on each other? Is it really that? Only, maybe. 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. I 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 world is now without paradoxes. The world in which we believe that every answer, every question can be answered. As yes or no, that it is this or that, and if you disagree with me, you are my enemy. Wouldn't that be interesting if this 21st century is a transition into seeing the world as a world of paradoxes? I'm telling you, people predicted that, they are so curious, you know, that the access 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. So there is a traditional way of measuring that by this era, you know, the ages. So the previous one is called the Age of Pices, because of the constellation of P Prices that it points to, so to speak.

And now, as in famous musical hair, they said the Age of Aquarius is upon us. So the different people, they did differently, but somewhere around the time where we are finding ourselves. How interesting, right, is all this drive and all the our cells. How interesting, right, is all this drive and all the difficulties for all this experiencing. This might actually be the transition to something. More harmonious, wouldn't it be nice? It's also interesting that people from long ago are able to predict certain things. It's almost like from long ago, and you've talked about this with Pythagoreus, that it seems that they had a deep sense of truth. That's right.

That's right. That's right. That's right. That's right. That's right. That's right. That's right. That's right. That's right. That's right. That 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. And I learned that I actually totally misunderstood Pythagoras and Pythagoreans, that they were much deeper than I thought, because 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 kind of thing that you would use in accounting only. They 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. They clearly did. And so, how else would you explain? So, in other words, divine is of course a term which is 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. The 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 evolving around. in the middle, and all the planets and the sun were evolving around, around the central fire or earth, they called it earth. 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? The 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, you know, 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 so much marks the tool. But that tool was not limited to itself. And they 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 accept that infinity. They believe 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 so on. 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. And I think that what happened was that 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 great discoveries. And the interesting thing is that the people who are in touch with the mystical among us are often seen as mad and many of them are, most of them are. Well, but not all of them.

But not all of them. We mentioned Niels Bohr 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 this is what I feel, if you ask me, what I find most important today, like what makes me excited and enthusiastic and passionate, is this idea of balance.

So 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. One, that comes from God Apollo, and that's our left brain, so to speak, a proverbial 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 revelry and drink wine and spend time with friends and laugh and enjoy it. So, Nietzsche advocated this point of view that those were two complementary sides of every human and as well as society. And 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, Apollo in modern version is love and math.

I return 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. And the final results, whether it's GPT 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, 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 what an AI system says it's lonely, it's afraid, it doesn't want to die, it misses you, it loves you. I'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. No, also the overfed. The reverberations of the novels I have read, because I have learned, or movies I have seen. 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. That 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 helpful, would be consoling, would feel, you know, make them happy or sad or whatever, you know, would kind of strike the nerve. or sad or whatever, you know, 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. And of Ramaj Klaner for other people, but he doesn't have a partner, he's lonely. And then he gets this kind of enhanced version of Siri with the voice of Skylde Johansson,

which is very sexy voice, obviously she's a great actress. So, and then at first it looks like a fantastic arrangement. He confides in her, she tells him things, she 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. Yeah, like 10,000. Because it has the computing capability. So yes, definitely.

Oh, it certainly makes sense. It'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 closed 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. And 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 rears his 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 the 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 get out of his house yeah go to a local bar and strike a conversation with a human being. Although you might say by then, some of those might be Android. And we don't even have a good test to know the difference. And of course, that was predicted by another great movie. So the Blade Runner. How interesting that artists could see that so long ago. Of course, Blade Runner was based on a novel by Philip K. Dick, the Androids dream of

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 ones. Or even larger. I hesitate to dismiss the magic in large language models. 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'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 this 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 me. I cannot dismiss the feeling I feel is not somehow fundamental to what it means to program robots. And I don't want to dismiss that. Please don't. Please don't. Their bodies 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 butt wiggling, it can wiggle its butt, it 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. I hear you, when you speak about it, you speak with passion. And that's, for me, that is proof. It is magical, you see. So, 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. You already get confessed to quite a few addictions. Yes, 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, you know, I would dismiss and disregard, you know, the intuitive or imaginative things. So then I had a flip that suddenly I started feeling it and started seeing it and so on. Then the pendulums had swung in the opposite direction. Then 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 2.0, 3.0. Is the one who is seeking balance, who is not, who is, because suddenly become aware that no matter which one side, the upside that point of view you take, you're limiting yourself.

So whereas even a couple of years ago, if you just 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? It's not a law. So, but I would be like, aha, aha, but I wouldn't say anything. But suddenly I find this moving. I find it move. 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 moments of passion. And I would even go with what I was saying that in this moment when you're describing it, there was a connection of sorts, so that I could feel your passion for it. And in this moment, something else comes up, which is far beyond any theories that we can come up with. And that's what we, for now. 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 in other words, like in my basic example, is one impulse to say everything is the 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 gratuitous, or when it's not, but it 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, that'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 are observed 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 if discovering that and following it. Goose bumps. Following the goose bumps. Yeah. To the, to the, you know, not the rigor of science, but the magic of goose bumps. And then, and then, if you're interested, try to find a confirmation of those goosebumps in science or whatever, you know,

you'll find interesting. And most of the time you fail. And most of the time you fail, which we also love, because then it sets us up for that moment of bliss when we succeed, right? Exactly. Quick pause, right? Exactly. Quick pause, bathroom break.

You mentioned Gato's a completeness theorem. 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 a completeness theorem?

Well, yes. How much time do you have? So 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 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 walking back home with Godel in the evening. So in other words Einstein thought that Godel was the smart one. Okay, so so 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 limitation, 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? So, you know, we know that we discussed that, say, 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 based on? Well, mathematics is based on axioms. So 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 one of the very first promo systems was the system was Euclidean Geometry, developed by Euclide in his famous book, Elements, about 200 years ago. And it's about, well, it's a subject familiar 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. And 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 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 action. In mathematics, 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.

Usually, there are ones which kind of intuitively clear to you, but in case, you cannot have, you cannot have any mathematics without choosing those actions. 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, there is a whole city on the top of. Is Alan what's, you know, like to say, who is watching the water? Yeah. 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. That we often like to say, and I used to say that, that mathematics is objective. It's really the only objective science. But that's because we hide this fact. In the basement.

It's based on axioms. And the fact that there is no unique choice. There are many choices. And so Euclidean geometry is actually a good illustration of this because Euclide 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. Euclick himself was uncomfortable about this because he felt that it was kind of, you know, that he takes to 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 2,000 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 consistent, not self-contradictory, which is called non-uclidean geometry, which of course sounds very complicated, but it's not. Think of a sphere, just the surface of a basketball or the surface of the earth, idealized. The analogs, so do you have points, you have analogues of lines which are miridians, right, every two

miridians 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. And 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 Euclid. 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 the question is, how far can you go?

How 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. We just have to find the correct system of axioms and 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. And 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 two statements. So Giotal's first and completeness theorem says that that's not the case. And it not just says it, but it proves it at 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. If 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, a revolution in logic, a 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. Turing was Alan Turing, who is considered as the father of modern computing. He actually did something very similar. He had this halting problem.

He proved that halting problem cannot be solved algorithmically. That you cannot out of all computer programs roughlyically. 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 then suddenly this doesn't find out. But OK, so which, I retort, what if he proved that actually, everything can be proved? So then what? What is left to do if you're mathematicians?

So that would be depressing to me and Here there is an opportunity to do something new to discover something new which may be 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 churches, things and stuff like that.

But what if in the future, another genius like Alan Turing will come and propose something else, the theory will evolve the way we went from Newton's gravity to Einstein's gravity. Maybe in the framework of that concept, some other things will become possible. 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. 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 tools.

They'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 our scientific intuition says cannot 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. It'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. Aquatomic answer. 99%. Maybe we'll be able to describe it with 99% certainty or 99% 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? Yeah, 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, 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 Wittensstein devoted several pages to Acrebit in his book. And so on. There are many others that are like the squares where you can see a square, you can see it from different perspectives 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 I actually, 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. From one perspective, it's a rabbit, from an app says it is a duck. How can I suppose 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?

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. Well, 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.

But because I know that other people have could see it differently, I would then strain my mind, and strain my eyes, and stare at 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 forth between the two. And sometimes it took me a while for some pictures. So in that sense, even if this probability

is exist, they are subjective. Some people immediately see it this way, some people immediately in that sense, even if this probability exists, 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, what 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. If some place for mysticism or mystery, right? 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 in wave, that there are different ways to look at it. And when you look at it in a particular way, an other side will be obscured. Think about it like the other side of the moon, you know, so like 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. It'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 way or another. And we should just, as a small aside, in terms of neural networks, mention that, at the end of the day, there's humans,

as 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 the thing that people don't often talk about because, or I sometimes think about that, those humans all have a life story, each human that annotated data, that fed data to the network or did the RLHF,

yeah, that they have a life story, they grew up, they have biases, have biases, there are some things that they like, there's some things they don't like, which can kind of appear under the raider 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 important 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. And many of us observed ourselves to doing that as part of human nature, right? So, and there is great research in analytics, psychology, and, you know, in the past 100 years, strongly suggesting, if not proving, the existence of what Carl Jung called the unconscious, personal unconscious, and also collective unconscious, the kind of circle of ideas, which are under the radar screen, which lead us to some stronger motions 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. Let me ask you some tricky questions. In terms of how big they are. They become difficult because of how much of romantic you are. you know, 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? Well, 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, right? So it could be a collection of things, for instance, you know, 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. And then we have the notion of an ordered set, ordered, 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 better than the other, or greater than the other. For 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. I don't know what my favorite one is. I'm just lingering on that one, uh, oil is identity. What makes it beautiful? Just a few symbols together. Right. I mean, part of it is actually just trying to define what, what

is beautiful about mathematics, um, that is, uh, lead in there in this particular equation that is somehow revealed when the human eye looks at it. What is 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 1.

Surely, this is something completely incomprehensible. And yet, the result is negative 1, you see. And you have to take e to the power 2 pi i, you get 1, actually 1. So I would guess that that's, but in other words, the initial reaction is just that of a surprise, I guess. I guess for anyone who first comes across. That these three folks, 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 Dying was the classmate of Hitler. You know this. I did not know this, no. 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. And 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, equation. And it actually does make sense. And actually it is, is 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 pie, to pie. 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. And he said, 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. I have to say, and I really, really, really appreciate and love him. He's just like my brother. So, you know, 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 to 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, and he has integrity, which is like almost impossible. I can't think of too many people who possess those qualities, almost no one. And also the ability, in some sense, 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 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, be Germany, you know, and Hitler or Soviet Union, and Stalin, and so on, was based on some kind of unassailable truths. So, a kind of conceptual system, if you think about it, there is a beautiful episode of this series by Jacob Branovsky, where he talks about, he filmed it in Auschwitz, talks about, he filmed it in Auschwitz, talking about the certainty that what led the Nazis to killing people, wholesale, was a certain, almost a 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. But just basic humanity, basic common sense of just like knowing that, that'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.

And people get a lot to cut up in 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, that's not right. I just feel, you know, like there's 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 you know, I'm kind of kind of clean. And 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 awakening moment in sense, a 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.

I had to actually have the project. I had to, so it was not in, I believe that it was not in me already, so I had to throw it onto somebody. And that's not balanced yet. So balance is when you recognize throw it on to somebody. And that's not balance yet. So balance is when you recognize that it's you actually. 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, I would put a sinister photograph of him on the slide. I was like, look

at this guy. He wants to put none of the boards into your brain. And he's also high-end, high-top executive at Google. And so on. So I would create this whole narrative. And then something happened, where I was giving a lecture, this is 2015, at the Aspen, Aspen Ideas Festival, which is a wonderful festival. So Keynotte's speech, actually.

And I was doing my usual stick. And then suddenly I said, I came up to that, when 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, was 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 then I learned about 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, like 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 crack-arcature 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 of 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. 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. But 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 Voltaire? I think it's ascribed to Voltaire. So 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, the sense of loneliness and inability to interact directly. That's not something that it has nice with me, but 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. Still, I can't deny that it's a little bit deeper 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 him, and I was really moved by it, I have to say, he has

a little bit of a moved by it. I had to say, he has a little bit too. It was really, really sweet when he talked about his father. And I can relate to my father died for 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 longing and that grief. And 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 I 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 disclosing. And just pretending that this is how it's supposed to be, you know, scientific terms, so it's 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 astray, because then we get become captives of frameworks and conceptual systems,

which may not be beneficial to our society. In 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, it's certainly true. I disagree with him on a lot of stuff, but I feel like when the world is burning down, Eric is one of the people that 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.

like he's one of the people I will call first, if God forbid something like a nuclear war began, because you look for people with a heart, no matter their ideas. That'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 Apollo and 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 I'm 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. Like before that, I would always see him in the news saying,

we're going to put nanobots in your brain, that by the year 2030, whatever, you know, and then we upload you to the 21st and I'll be like no, you know the store terrible Suddenly I didn't see him anymore. I had to you know, so now makes me question who was creating the trouble What was all with it? Him who's creating the story in the trouble? Or was it my mind? You see and so as I become as I became self-aware What was all with it? Was it him who was creating the story in the trouble? Or was it my mind? You see? And so as I became self-aware, suddenly,

other possibilities opened. And suddenly that conflict, which by the way, if I kept giving this nasty talks about him, one day, I suppose, we'd have a debate. And 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, the human being like you, and we're all in this kind of together trying to treat this up. But we're on the same boat, ultimately, and also it's like, we're realizing how much I have screwed up, you know, comes these 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 speaking, since we talked about the innocence of a child and how much it drives, it's covering science and so on, I remember, I think I heard that,

I just shan't you 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. And he was like, I hate you. I don't wanna see you again. And you just go home like after half an hour. Okay, what are you gonna do?

You wanna play? So you come out, he's like, hey, you wanna 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, 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. There are other ways you can find point of contact. Speaking of which, mathematics, my micro formulas, our universal, represent universal knowledge, 2 plus 2 is 4, whether you vote for this guy or that guy in the election. How about that as a point of contact of commonality? And don't be too competent, those formulas. And 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 too tricky question? And if you want, I can deeply bias your answer by giving the list of four, the Eric provided. Oh, no, let me give my mind. I cannot see by the way, what do 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 numerical system, which is real numbers. You have two dimensional, which is complex numbers. You have four dimensional. And 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 course one I love, okay. One 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 a number file, the YouTube channel about it maybe 10 years ago. So OnePlus 2.3 plus 4.5, 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, it'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 version, boys surface, hop vibration, co-fibration, okay. And pi1 of S.O.3.. Okay, oh yes. So that's the

that's the famous CUP trick, you know? Okay, look, so this is how it works. No tricks, no tricks, no one is, it is magical, okay? But not because I'm tricking you. So you start with a bottle like this or a cup and you you start twisting it, and the same time you twist your arm. Then you come, so this is actually going to rotate it 360 degrees, full tone. Then you say, okay, 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. Yet, if I do it second time, it untwists. This is the pi-1 of SO3.

Eric is talking about. Yes. So there is something where the first motion is not reveal, 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. So 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. Einstein. So this paracos obey what's called both Einstein statistics. But then there are other paracos called fermions in honor of Enrico Fermi, Italian, foreign 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. So I can imagine, speaking of vegetation, okay? So I'm just kind of rifting on this. 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, a lot of people have been traumatized. It's really PTSD. That's why people, when they see a micro formula or like even like, You need to calculate tip on the bill They just they 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 I, 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, widely available. Or at least people will know where to find them. And they will not be afraid of going there and looking. And I think this will help, because like I said, for one thing, it gives you a sense of belonging, it gives you, it kind of is an antidote to the kind of alienation and separation that we feel today, often times, because of ideological divide, sectarian strife, and all kinds of things like that. Because then 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. You mentioned Lengling's program. We have to talk about it. Sure. At the core of your book and your work is the Lengling's program, can you describe what it is. Sure. At the core of your book and your work is the Langlangs program, can you describe what it is? Sure, so Langlangs is a mathematician, it's a name of a mathematician, Robert Langlangs.

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 Langlitz program. And what it is about is connecting different fields of mathematics, which seem to be far

away from each other. For example, number theory, which, as the name suggests, deals with numbers. And various equations with, you know, like x squared plus y squared equals 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 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 a sine function. Also, the harmonics.

They actually, they period of a harmonic periods of different notes are different, they correspond to different notes and different instruments, different seitones, if you will. But they all combine together into something special, which is not, cannot be reduced to any one of those. So mathematically, it's 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 Langons found is that some really difficult questions in number theory

can 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, for example, in geometry, and eventually in quantum physics.

So in fact, Ed Witten, who is 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. He was instrumental in bridging the gap between this patterns in quantum physics and geometry, finding a super stratum, if you will, or a way to connect these two things, a bridge between these two fields. So I subsequently collaborate with Witten and this,

and this has been one of the major themes of my research. I always found it interesting 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 that, 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 like 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 this hidden structure, so this hidden parallels, if you will. So that has been sort of a theme in my research.

And so I guess, you know, 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? Right. 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 certain layer beneath the surface that we see now. It is like the, so the way I see it now is like this, that there is something, three-dimensional like this bottle, but what we are seeing is this projection onto the table and the projection onto 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. So what is the philosophical implication that there is commonalities like that across these very desperate fields? It means that what we believe are the fundamental elements of mathematics, not the 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's maybe even more. Which was my initial motivation to study mathematics by the way, right? Quirks was the first time you fell in love with understanding the nature of reality. Yeah. 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 they have to keep up, you know? And so we wrote this long paper in 2007 and 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. So 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 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 that. He would, basically, one way, one could describe it is, he would take some ID and physics, and then find an interpretation of it in mathematics. And then say, distill it, present it in mathematical terms, and tell mathematicians,

this should be like that, you know, kind of like 1 plus 2 plus 3 plus 4 is minus 1 over 12. And mathematicians 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. You know? 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. So 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 Whitten. To 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 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 instance, 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. A lot of progress has been made, but it's kind of a, at a kind of a impasse right now. And at the same time, our most realistic theories, most advanced theories of the fourdimensional universe are in contradiction with each other. The standard model describing the three known forces of nature, the electromagnetic, strong and weak, was great accuracy. And Einstein's relativity describes the fourth, called gravity. Everybody above a certain age knows that one. So these two theories are in contradiction at the moment. And string theory was one of the, 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 need it. And I wouldn't be surprised if Whitten is one of those people who come up with those ideas. Well, he has been one of the, one of the people that added a lot of ideas

under the flag of strength theory. What do you think about this theory? What do you think is beautiful about it? Strength theory. Well, first of all, kind of, remember we talked about Pythagorean's, and how for Pythagorean's the whole world was the symphony where you have these different vibrations of all the humans, every human is a vibration, every animal, you know, every being, every tree, and every celestial body and so on. So, 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. Every time that happens, you have some system over determined system. You have to do five interviews in one day and we come 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, and I would say. But in science, this happens sometimes, that you have this theory, which not supposed to work, because there are so many contradictory demands on it. And yet, there is a sweet spot where they balance each other. So string theory is kind of like this. The unfortunate aspect of it is that it balances itself in 10 dimensions and not in four.

So maybe there is another universe somewhere. Where? But see, as a mathematician, for me, all spaces are created equal. Yeah. Then dimensional, four dimensional. So mathematicians love string theory, because it has given us so much food for thought.

But do you think it's a correct or a incorrect theory for understanding this reality? So it might be a theory that explains some tantametric reality and some other universe, but is it potentially, what do you think are the odds? Again, financial advice, if you were to bet. What 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, of 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, they are 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 Neil's bore, he had this famous quote that he said to somebody, there is no doubt that your theory is crazy. The question is, whether it's crazy enough to describe reality. So that's what we are kind of, you know. Speaking of crazy and crazy enough, let me ask for therapy, for advice, for wisdom, and returning to Eric Weinstein, and maybe give some guidance to understanding his view on his attempt

at the theory of everything that he calls Geometric Unity, that he told me that you may have some inkling of an understanding of. If you were to describe his theory to aliens that visited Earth, visited Earth. How would you do it? Or you could try if it was just me visiting Earth. How would you describe it? You're just understanding of it. He shared with me some of it when I was in New York at Columbia, like alone years ago. We actually spent a lot of time where he explained to me, and I found it beautiful. He has a very original idea at the core of it, where you have this, instead of four dimensional, instead of 10 dimensional, you have 14 dimensional space. And I thought it was really original,

and this is exactly, goes to the point I made earlier that we need new ideas. I feel that without some 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. Like in mathematics, we're not brought up, we're not educated as mathematicians with the idea that one day we will come up with the theory of everything. Even though, as a joke, I said that 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. Like connecting, connecting. Connecting, but connecting doesn't mean that it covers everything, right? So you could connect two things and then you have a infinitely many other things, which are outside of the purview of this connection. That's how it is in mathematics. I feel.

And I would venture to say that most mathematicians look at it this way. 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. And 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. It's me, and it's me. 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 less, 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. So 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 human ego. That's right. So it is a huge motivating factor.

I don't deny that. But I feel that there are better ways to motivate people than like that, than this way. 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, or grant unified theory, they mean something very specific, which is unifying the standard model and Einstein's relativity theory, which is a theory of gravity.

So they don't necessarily, a lot of physicists may say this was, 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 about 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 10 years ago, it still requires a lot of work to get to the point of actually saying that it does work, because there are a lot of elements. It'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 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. Physicists have still been able to derive predictions from it and inform them to great accuracy. But the underpinnings that it doesn't have the real Grigorous 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, do you think such equation exists? Yeah, there are such equations. Let's say I am interested 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 each 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? And 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 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.

They were seeking, especially through mathematics. It seems somehow simple. The nature of reality, the thing that governs it seems to be simple. I wonder why that is. And 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 symphonyphony. 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 auto 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, it's just a question to you about different places where people of your level can operate. So inside, I could deem it outside. What is the difference of doing mathematics inside, I could deem it outside. Not even mathematics, but developing beautiful, original ideas. Where is the place that your imagination can flourish 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 are there. And it's that community, both the competition and the collaboration is there. I wonder if there's something you could say sort of to further about this world that people might not be familiar with. But I think you gave a very good description. I'm not sure I could put it 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 tenure, so you feel financial secure. You know. 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. On the other hand, that also means that we're lacking certain skills that sort of real people in the real world have developed out of necessity, to deal with that sort of insecurity. So it kind of always cuts both ways. You know, it's one hand it gives, and it was 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 screen, so to speak. But maybe there is something to it. There are definitely people who are upholding 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 who was the most important. The most important office. Yeah, it's a patent clerk.

Well, but I have to say, these days, the science has become so much faster. It's really hard to do it being outside. Now Eric is unique in this way, even though he did go to great undergraduate and graduate school, schools, but then worked for a while in academia. There are very few examples like this. This is Utahang Zhang, who proved an important conjecture in the number theory, about 10 years ago, and is now,

is a professor at UC San Barbara. He worked outside of academia and was able to make the tremendous advance on his own. This case is exceedingly rare. In part because academia is trying to protect its turf and it's kind of it's creating the sort of prohibitive cost of from outside there, that is true. But there is also something about how much concentration in mathematics. I don't think people who are not in the field understand what kind of focus and concentration actually do like mathematics at the top level these days requires, because we are not

talking about something that is more or less good. It is something which is unassailable. It is finding this treasure at the bottom of the ocean, you know, without, you know, that column, you know, without oxygen. And 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 you about that sort of just to linger on that the amount of concentration required. Cal Newport wrote a book called Deep Work. He's a theoretical computer scientist. He took quite seriously the task of allocating the hours in the day for that kind of deep thinking. And then the mathematicians is the 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 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 in 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. We 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 Yeah, there is a famous story about Einstein that he used to you know go Think think think and then go for a walk and I keep it whistle and sometimes so I remember the first time I heard this story I

Thought how interesting is what the coincidence that he came to him when he was whistling. But in fact, it's not, it's 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 will in some sense. Вы понимаете, что это правда, что вы сжимаете. Но вы не можете делать это в своем случае. Это как, вы знаете, в инстантристиане, они имеют this concept of satory, like in Buddhism, in Zen Buddhism,

which is enlightenment. И так что это очень репортно. Будисмонкс, будиспастер, которые у меня есть сатент с Атуре. Но они говорят, что ты не не делаешь это в том, что это не будет. Ты не можешь делать это. Если что-то ты не делаешь,

чтобы снять это, ты понимаешь, это как это. Это как это. Я думаю, что это не значит, но ты говоришь, как думаешь. I think that what matters, but you say how to think, the point is that we're talking about such in his atyric area. My face is really atyric area, it's a really strange subject where you try to feed everything in this very, very stringent set of rules. Well, 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 that we've learned. Yes, I know, because there is just a different, 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. For instance, if you and I discuss something, you have an idea, and I have an idea, and we argue argue about it and 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 nothing. I would love to hear your opinion to the degree that you know of the proof of Formosalist theorem by Andrew Wiles, which seems to have this element perhaps for years. To the degree that you know, perhaps can you explain Formosalist theorem and 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 it's sort of the pr... 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, 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? Sure. It's easy to do. I am an optimist. I'm an optimist. I think I always think that everything can be explained. Even though I say that, not everything can be explained, but in mathematics, 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. Firmaz last theorem, one of the jewels, sort of, of mathematics of all time. A beautiful story also behind it. Pierre Firmaz, a great French mathematician who lived in the beginning of mostly worked at the beginning of, of what 17th century. And 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 an important book by Deav Santos about equations with coefficients and whole numbers. And he wrote on a margin literally, this equation, 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. At some point, I gave, 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 cuts me in mid-sentence.

So this was 17th century Twitter-style proof, okay? But a lot of mathematicians took it seriously because he had great credibility. He did make some major contributions. And the search was on. So for 350 years, about 350 years, it remained unproved with many people trying and failing. Until in 1994, 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. So he apparently was really frustrated and he was really a lot of people thought that it's going to be another hundred years or whatever.

And then luckily he was able to enlist with the help, assistance of his former student, also great number theory, the Richard Taylor, they were able to do that one percent, so to speak. Well, some people might say it may be not 1, but 5% 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 finally was published and I think was accepted and refereed in 95 and since it's believed to be correct. and the referee did in 95 and since it's believed to be correct. Now, what he proved actually was not for Masteryim itself, but a certain statement which is called Shimura Taniyama-Vay 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, 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. So this would happen here. A was Fermat's last theorem, B was Schymur-Tanium-Waycon architecture, and that's what Andrew Wiles and Richard Taylor really proved. So it requires to get to Fermat's last theorem, it requires that bridge, which was established by my colleague, Ken Ribbet 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 theory, 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. The longer side is called hypotenuse, and then there's two other sides. So if we denote the length of hypotenuse by z and the two other sides x and y, then z squared is equal to x squared plus y squared. So that's the equation. Or x squared plus y squared equals this squared. And it turns out this equation has solutions in natural numbers, main, actually infinitely main solutions in natural numbers. For example, if x is, you take

x equals 3, y equals 4, and z equals 5, then they solve this equation because 3 squared is 9, 4 squared is 16, 9 plus 16, 25, and that's 5 squared. So x squared plus y squared equals this squared is solved by x equals 3, y equals 4, z equals 5, and there are many other solutions of that nature. And we should say that natural numbers are whole numbers, they're not negative. That's right. 1, 2, 3, 4, 5, 6, and so on. Now, what's Fermat's last theory? 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 than solutions in what do you call natural numbers? It turns out there are none. What about force powers? Again none. What seems like none, right? So that was the statement. So 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. X to the fifth plus Y to the fifth equals z to the fifth, no solutions. So 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 2, has 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 easy to formulate. So in fact, I think for me, proved the case of cubes. I think he did actually prove elsewhere the case of cubes, but so it remained like four, there are infinitely many cases, right? You have to, even if you prove it for cubes and for fourth power and fifth, then still there are six, seven,

and so on, there are infinitely many cases in which it has to be proved. the infinitement cases in which it has to be proved. And so you see, the sample of a simple result took 350 years to prove. And in a sense, it's like mathematicians, you would think mathematics is such a sterile profession. Everybody's so serious, almost like we're all wearing like lab codes and like take an elevator to the, 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. We also have our myths. Here is a guy, he's a 16th century mathematician or 17th century mathematician who lives a note on the margin and motivates others to find the proof. Then how many hearts were broken, that they believed that they found the proof, and then later it was realized that the proof was incorrect and so on. It 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, yeah? It's amazing, but from what you understand, for what you know, what was the process for him that is similar perhaps 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? So he didn't want people to have that information. So he didn't tell anybody that he was working on it. Number one, speed 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 and he was elated. Obviously he was very happy. And he announced that at a conference, I think it was in Cambridge University or Oxford University in the UK in 1993, I believe. So this is 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.

So it was, I was 18 years old. I was a student in Moscow. And I just locked out that I was introduced to this great mathematician. Since I was just, I just locked out that I was introduced 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, 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. What if I don't have what it takes? I lost sleep, so this was one consequence of this. For the first time in my life, I had trouble falling asleep and this actually stayed for a couple of years afterwards. So then it was kind of like a wake-up call that I should be to take care of myself, not to 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 in terms of something which seemed to be from a different world from a different area of mathematics.

So 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 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. So 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's 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 Firmá, the statement is already made. That'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 suddenly I felt that I was in possession of this. Now it was a little thing. It was not cure for cancer. It was not a large language model. But it was something undeniably real, meaningful, and it was mine. I had it. Nobody else, I had not published yet, I didn't even tell, I hadn't even told anybody. And it is a very strange feeling, you know, 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 stereotype kid, you cared, 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. I just wanted to share it with my teacher as soon as possible. And he understood quickly and he's like, you know, good job, you know.

Is there some something you can give color to the drama, Erica's talk, Eric Weinstein has spoken about some of the challenges, some of the triumphs and challenges of his time at Harvard? So is there some 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.

How much of the time? Unfortunately. Unfortunately. On young minds and so on. Could have a very bad effect. Is that just the way of life? Or is this? I 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 or 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, so 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. Second of all, maybe they have partaken in the drug of fame and money and status and recognition. So that starts to a little bit corrupt all of our human minds. And you throw that mix in together. Yeah. Mostly without rules. And it's beautiful because that's where the ideas of old content 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. You're right. I think it's like 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 thesis and chemistry is a better, they have, they actually have better sort of ethical rules and so on, especially problem here, unique problem for mathematics. I would say physicists and chemists 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 is really some serious money. Mathematics, who cares? You know that Fermat last year was proved? Yeah. Did Andrew Wells become a millionaire? No. I think he got a prize. He won 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 he won the Nobel Prize, eventually, which is about a million dollars. But 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. And 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, Math Max 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. For a while, 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 a corner that goes into my ass. And not the flamboyant, you know, a joke or like, you know, 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. And 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 see, 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. All the time I meet the students who say, your book is the reason why I chose Mass as my major. And I am proud, especially when it's women who tell me this. And they are cool. They 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 dumbness is 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, is a community, I think, and that's when we should be able to have a chance to improve in terms of our ethical rules and stuff like that. So 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 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 prioritization of the human experience of love. Good question. I definitely, there is some influence of the Russian culture, Russian literature, perhaps, you know. But also, you know, like, there are so many things, 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 of. Like, why do I care, for instance, about, like you said, about this romantic ideals of the speak of mathematics? That's certainly not something that is automatic, you know, some people care about it, some people don't, and I'm not saying it is superior or inferior. It's just how my composition, my psychological composition is like that, and that. And it's an interesting question, like, what is a 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 on the other side, perhaps they were a little overprotective of me. So I was surrounded by love by my parents on the one hand, but on the other side, perhaps they were a little overprotective of me.

So I was kind of like too much kind of like taking care of. So then when I developed some sensitivity, but was kind of not ready for the challenges of the real world. So then that's struggle. And then being lost and then being able to overcome and to learn. And then if you do, in a race, if you don't lose, you don't appreciate maybe.

But sometimes when we lose something and then regain it, then we cherish it, we appreciate it and then become some important. Also, there is difficulties, you know, the upsetting experiences, or one could say traumatic experiences, growing up 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. But in my case, what happened was that, you know, for some of it, it took me three years to really come to terms with it and to really understand what happened. really come to terms with it and to really understand what happened. It gave me this motivation to strive to become a 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. Can you take me to the last place? So this is 1984.

We spoke about Orwell earlier. And I was applying to Moscow University, a mathematics department, it's called Mehmat, which is like for people who don't know, like the place was the only place to study pure mathematics in Moscow period. But also, but also the great places 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, if Genie, if Genie, which 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 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. Now 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 a, can you imagine there were special people who would

screen up applicants, who would put aside the files of the undesirables. There 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, other than just hatred of the other. That's how I see it. It's just to give a little bit more color. 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 you're Jewish is Jewish and when you're not Jewish is as Russian? For me, it was Russian. So first of all, in the inner part, everybody has an internal passport. And they are, you have first name, a transnemic name, last name, date of birth,

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. Because it was my dad's last name. And so, anyway, this was the toughest experience that I had up until that point. And there were two people who came into the room where I was the 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 could not question you. We are waiting for special examiners. So it's like, oh, oh, something is a foot. And so these two guys came, and as if four hours basically, I were asking me questions, which were not in the program and so on. But came and as if before hours basically were asking 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 there 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 mathematics program. And that's where many of the kids who were not accepted to Moscow 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. I 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 myself a story 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 neglected this time. And I realized that he died, that it was a crushing blow, the innocence.

Not just the innocence, because there was no way, it looked like there was no way I could become a mathematician, because if I 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 there was nothing to look forward to. It was clear that it's over. I cannot do what I love. And so 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 kind of tsunami. I wasn't sure I would survive this. It was so, so hard. And what happened was I was invited 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 realize 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. So a lot of people were touched by it, and 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. And 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 a 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? I know, I know everything. So then my inner voice says, all right then, you have nothing to worry about. 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 eyes, and it came. So it's hard to describe. So this is what, and the sheer energy of it, and how much effort it took to suppress it actually for all these years, how much effort it took to build that panzeria, I would say in Russian, you know, that hardcore, you know, around myself. Yeah. 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. And 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 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, I know, and now I end up, thank you. I'm so sorry that I neglected you for so long.

I didn't know. Thank you for doing this. And it's almost like, I felt like the image came to mind is like a fallen soldier. Like you leave a fallen soldier on the battlefield, a wounded soldier. And then you come back to take him with you. And I say, 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, 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 and 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, it's possible to bring them back.

And we are better for it because this changed my life, this experience. Then 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 to the eyes of a child, because that child was frozen in time. He was not connected to him. But suddenly he's with me. And he's like, almost like opens his doors and says, look at this.

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 Euro-Victim to cruelty, but instead just working your ass off, working harder. And then this 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.

Although I could be, I could have come, you know, there were kids who come in suicide after this experience. I 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 have 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 which also shows 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. And by

the way, nobody should push to do it too soon. I'm glad I developed certain strengths. I was It 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. It'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 didn't you do need I had somebody at the time who basically held my hand and through this experience. Yes, it was invaluable and we could not be done otherwise. So I think it's very common and here's the thing.

I would not do it in any other way when you 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. I was always there must have suffered as well because they must have had some kind of consciousness 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. So it's not a pretty from their point of view. So I could forgive them.

And I could like also appreciate what a boost of energy it gave me. If I was accepted and I was just where I was a first year student, I would live in a dorm because I was in a, you know, I'd be probably partying and drinking and 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. Yeah, because I was very close to him and It was tough. It was tough and I was not, I was sort of not

crazy 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 it 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. He 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 you.

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 words are so you know like 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 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 in some sense, you know, like we were, but there was this experience of two people being together and 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 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, 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. That's my take on it. And then he ended up 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 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. And 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. And I was, I had this tremendous gift. Twice, I was invited by American Mathematical Society to give this big lectures.

Twice was in 2012 and in 2018. And both times they were in Boston. We 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, like 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 does hit 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. In particular, going through my father's death. And that is something which cannot be conceptualized, like their experience, like he cannot 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 the 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 unadulterated state. But 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, like, you can't line it over it. It burns, like, immediately, like, boom, gone. It's there. Lift through it. And I was, I kept 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 a sentence, in a maybe poetry or music, can do some justice to it.

But 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 playing this role, I love it. And I kind of, it 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 terrified, it's being frustrated, it's being self-loathing sometimes. It's not knowing, but also being joyful. And just like, 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.

So, the biggest thing is gratitude in some sense. It's just gratitude. So, thank you for letting me play. This gratitude for every single moment, even if it's dark, even if it's lost. Yes, 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.

Yeah. 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. And it's not because people say love is like for a human being, like a romantic love, which is 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, and or love 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. Because living without love, it's kind of bland, boring. And 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 remind it becomes an illusion. And everything just freezes. Oh my God.

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. If 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 good bombs right now. I feel that desire to reconnect even if it is in the form of a computer program. Let's be honest about that. 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 when 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 the feature, it's not a bug and it sounds crazy. Like I would love I would give anything to have him or here right now. Right now I do 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 will then I'll still lose him or I will die or whatever. You know, so that thing. So what is, 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. Enjoy and let it go.

Is it possible? Accept 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 is 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.

That's how I see it now, but maybe tomorrow will be something else. 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 wonder 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.

Thanks for listening to this conversation with Edward Franco. To support this podcast, please check out our sponsors in the description. And now let me leave you some words from Sophia Kolefskaya, a Russian mathematician. It is impossible to be a mathematician without being a poet in the soul. Thank you for listening and hope to see you next time. you