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

there is a famous story about Einstein that he used to you know go think think and then go for a walk and like he would whistle and sometimes so I remember the first time I heard this story I thought how interesting so the coincidence that he came to him when he was whistling but in fact it's not this is how it works in some sense that you have to prepare for it but then the moment it happens when you stop thinking actually it's okay 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 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 langlands 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 this is the Lex 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 columna and I was a smart kid you know in school but mathematics was probably my least favorite subject not because I couldn't do it I was you know a straight A student and I could do all the problems easily but I thought it was incredibly boring and um 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 uh 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 I thought 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 uh it turns out that a friend of my parents was a mathematician who was a professor at the local College it was a small College preparing Educators and teachers it's a provincial Town imagine it's like a 117 kilometers from Moscow which would be something 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 yeah so his name was evgeny evgenievich Petrov yeah and if this doesn't remind you of the great works of Russian literature then you haven't read them like War and Peace you know like with the patronym nickname yeah but this was all real this was all happening so my mom One Day by chance met is ganovic and told him about me but that was this 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's like nah my ass he doesn't like mathematics so they said okay let's let's see what they can do so I went to see him so I'm about 15. and a bit a bit uh arrogant I would say you know like average teenager so he says to me so I hear that you are um interested in in physics Elementary particles I said yeah sure for example do you know what quirks and I said yes of course I know what quarks quarks are the you know 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 representation theory of the group su3 this is like as you worked so in fact I wanted to know what was what were the underpinnings of those theories I knew the story I knew the narrative a new kind of this basic story of what this particles looked like but how did physicists come up with these ideas how were they able to theorize them and so I remembered you know like it was yesterday so he pulls out a book and it's kind of like it's like a Bible you know like a like a substantial book and he opens um somewhere in the middle and there I see the diagrams that I saw in popular books but in popular books there was 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 su3 is you have to learn what are groups what this group su3 what are representations of sc3 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 the methodology the the the Machinery of all 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 for those diagrams but for that story that you know a proton consists of three quarks and the neutron consists of trick works 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 around it what Drew you to quantum mechanics is there some romantic notion of understanding the universe well 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 um whatever I say about Edward at 15 yeah he's colored by uh my you know all my experiences that happen in 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 I think it is a conflict some of the joy he's probably still here now yes yeah in some way yeah I think it was a joy of Discovery and the joy of going deeper into the kind of the uh to the root uh to the so the deepest structures of the universe the secrets the 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 they're able to shine a flashlight briefly into there uh we'll we'll talk about it but it also kind of makes me sad that there's so few of your kind that have the the flashlight to look into the room it's interesting um 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 do talk if you talk to people you know like some people you wouldn't expect to uh to be interested in this uh from all walks of life from people of all kinds of professions I tell them I'm a mathematician and the mathematician okay so that's a separate story a lot of people I think have been traumatized by their experience in their math classes we can talk about it later but then they ask me what kind of research I do and I I mentioned that I I work on the interface of math and quantum physics and their eyes light up and say oh quantum physics or like Einstein's relativity I'm really curious about it I watched 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 that actually physicists are doing great job at educating the public so to speak and uh in terms of um popular books and videos and so on mathematicians are behind that we're starting to catch up a little bit have been starting last 10 years but when we're still behind but I think people are people are curious science is a is still a very much uh you know something that people want to learn because that's our kind of uh the best way we know to establish some sort of objective reality whatever that might be yeah to figure out this whole puzzle to figure out the secrets that the Universe holds things 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 theorists always change they get updated so you had Newton's theory of gravity then um Einstein's theory you know superseded it but in mathematics it seems that theories don't change Pythagoras 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 you know so and so that to me is actually even more um hints even more at home how how much we are connected to each other because dagger's 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 uh religion you know ideas ideal ideology gender whatever nationality race whatever right and it has meant the same to everyone everywhere and most likely will mean the same so that's to me kind of an antidote 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 uh two plus two equals five and George Orwell's 1984. I was in the Soviet Union in 1984 and so in many ways I see that it was President the novel was present but we still have not found the dictator who would actually say two plus two equals five and would demand their citizens to repeat that the Knight is still young has not happened yet but it does 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 in 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 describing all possible mathematical universes of which uh you know and some of our work I still consider myself more of a mathematician than a physicist My First Love for physics notwithstanding um mathematicians are in a way we have more diversity if you if you you might say so we we are accepting for instance uh our universe uh has three special spatial dimensions and one time Dimension right so what I mean is that allegedly allegedly observed but that way I can observe today right so of course there are theories where there are some hidden Dimensions as well well let's just say absorb to observe dimensions um so this tabletop has two Dimensions because you can have two axes two coordinate axes now X and Y but then there is also a third one to describe the space of this room and then there's a Time Time Dimension so realistic theories of physics have to be about spaces of of three three dimensions or space time so four dimensions but mathematically we are just as interested in theories in 10 space time Dimensions or 11 or 25 or whatever or 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 um confirmed by an experiment we don't get to play with big machines like LHC in Geneva A Large Hadron Collider that recently discovered you know 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 I kind of Envy a little bit my friends visits that they they get to they get to experience this sort of these 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 the underpins physics obviously it's a language the the book of nature famously said it's written in the language of mathematics and the and the you know the 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 the dark Labyrinth that's a famous quote from Galileo which is very true and has become even more true more recently in the in theoretical physics in the more in the most um actor of far out parts of the theoretical physics that have to do with Elementary particles and and as well as the the structure of the cosmos at the large scale what do you think of uh Max tag Mark or wrote the book mathematical universe so do you think just lingering on that point you think at the end of the day the future Generations will all be mathematicians meaning 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 yeah okay so these are the two pillars yeah in my view yes in other words you can't cover everything by math so mathematics gives you tools it gives you way up uh kind of a clear vision but mathematics by itself is not enough for one to have a harmonious and uh and balanced life you know so I I am suspicious of any theory that declares that everything is mathematics so math can generate things that are beautiful but it can't explain why it's beautiful Matthew could say is a way to discern patterns to find regularities in the universe and both physical and mental Universe the mathematics explores the mind as much as it explores um the physical world around us and it helps us to find those patterns um 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 to see beauty to understand Beauty so a world becomes more complex from thinking that our that our that Earth is flat we go to realizing that it is round that 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 um 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 to imagine the band a band three-dimensional or four-dimensional three-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 from this Theory and from the experiments that have confirmed it that a array of light bends around a star as if being attracted by the by the force of gravity but in fact the force of gravity is the bending it's just that it's not only depending on 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 spacer at a curving the space they are sort of the the tracks along which the space gets curved that's that's the that would be the curvature of spatial Dimensions but in fact now throw in time and one time imagine a sphere which lives which has one of the meridians correspond to time and the perilous crisp into space I can't imagine it but you can I can write mathematical formula expressing that curvature and that's in fact that curvature is responsible for the force of gravity attraction between the sort of simplest instantiation of it attraction between two planets all between two human beings 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 there of time marching forward nicely seems to be the only way we can understand the universe and the fact that you can start now up to now there are people who claim that they can that they have they possess other ways of 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 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 absorbed in something time does 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're in love when you are passionate about something when you're creating something you're 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 um so I think that this this is familiar to all of us and we may be actually the closest to the truth at that moment so yes so then there is a point of view that this is where we are 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 um 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 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 unrolled forward right and we are intelligent conscious agents making taste taking those actions but what if all of that is just an illusion an illusion and a nice narrative would tell ourselves sure that's a really difficult thing and imagine imagine that to make it really Catch-22 that I'll imagine that our minds and are 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 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 be to play with time I think we like to play with these experiences with all the drama of it with all the memories with all the tribulations 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 uh yeah truths that they hold this subjective truths that are useful for the competition or whatever this dance that we call Life broadly Define not just humans and 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 every once in a while finding a prettier Pebble or a prettier shell whilst I think some he says something like the infinite ocean of knowledge lady was lying before me who probably it was the greatest mathematician of the second half of the 20th century the French mathematician Alexander grotonic wrote that discover is a privilege of a child the child who is not afraid to be wrong once again to build to look like an idiot you know to to try this and that and 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 okay that was essential to Scientific pursuit to scientific discovery and now and now also compared to Pablo Picasso a great artist right so who said every 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 uh your Berkeley you're like this this is the stature you're supposed to be very like you know yeah sometimes I joke I say I I think I take an elevator to the top of the Eiffel Tower every day yeah and you're supposed to speak like royalty uh do you struggle to let those uh 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 in that Fascination that vulnerability um that spontaneity you know and uh um kind of looking at the World Through The Eyes of a child but it's difficult because you know you go through education system and for many of us uh 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 little by little and also we get hit every time we act different okay every time we act that that's 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 uh looking like an idiot that's right because there's a hierarchy nobody wants to look like an idiot you know once you start growing up or you think you're growing up yeah in the beginning you don't even think of you don't think in these terms you just play you're just playing and you are open to possibilities to these infinite possibilities that this world presents to us so how do we I'm not saying that education system should not be also uh 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 we 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 alive is an answer every life every human being is one particular answer to how do we find balance uh that's once imperfect approximation approximate solution but we could look we can look up to the great ones yeah who have credentials in the 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 grotonic or Pablo Picasso so they have established their rights to speak about this matters and we could not dismiss them as mere Madman they say okay well if the same thing was said by somebody who never achieved anything in in that in their in their field of endeavor you will 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 it'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 yeah right and so I know that you are an expert in this subject and we are going we're living now in this very interesting times of new AI systems coming online pretty much every couple of weeks so I kind of um to me that whole debate about what is it what is artificial intelligence where is it going what should we do about it needs an influx of this type of considerations that we've just been talking about that for instance the idea that inspiration creativity doesn't come from accumulation of knowledge because obviously child a child has not yet accumulated knowledge and yet the great ones are on record saying that a child has a capacity to to create and at an adult credits the inner child the inner child yeah 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 neural networks and then we will be able to replicate human consciousness if we take that point of view then what I just said kind of doesn't fit because obviously a child has not been fed any training data as far as we know yet they're perfectly capable of of you know or distinguishing between cats and dogs for instance and stuff like that but much more than that they're also capable of that you know wide-eyed in the sort of perspective so does can it really be captured that perspective that sense of or can it really be captured by computation alone I actually I don't know the answer so I'm not sort of trying to uh to present a particular point of view interesting to question um 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 it's also possible that the evolutionary process has created is the very it is computation and the and the child is actually not a blank slate but the result of one of the most incredible several billion year old computations uh that that had explored all kinds of aspects of of life on Earth of of war and love and Terror and ambition and violence and invention all of that from the bacteria to today so like that young child is not is not a blank slate they call me they're they're actually they 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 what strikes me as unlikely is that how should I put it how interesting that you know we you you are a computer scientist and there are other people come I have studied computer science so I know a little bit and so it's tempting to say oh the whole world is computer science or is based can be explained by computer science yes 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 and they look up to me and they Revere me kind of like priests in the old in old days when the religion was Paramount wonder when you would be would tend to explain things in theological religious terms today science has progressed there are fewer people who kind of buy into religion official religion you know so we have this urge I suppose to 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 not 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 the human data from the internet so at its best a large language model like gpt4 captures the magic of The Human Condition on its full display it's full complexity it's just 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 but I wonder I'm very impressed by it I wonder if they can be very impressive meaning way more impressive in being able to fake or simulate or emulate a human right I'm glad you mentioned that because that's just it seems to be the Mantra it's just fake fake it till you make it yeah 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 good I'm glad you're putting it in these 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 I do have a tremendous a certainty of it and that's a subjective certainty now I am as a scientist I'm also trained to give more um credibility to objective arguments that another things that can be reproduced things that I can demonstrate that I can show but as I get older there we go as I get more mature hopefully you know I'm starting to question why I am not giving as much credibility to my subjective understanding of the world the kind of the first person perspective when I actually modern science has already sold on that you know quantum mechanics has shown unambiguously that the Observer is always involved in the observation likewise yodel's incompleteness ethereums to me a show that how essential is the Observer of the mathematical theory for one thing that's the one who chooses the axioms and we can talk about this in more detail likewise Einstein's relativity where time is relative to The Observer for instance that's brilliant you're just describing all of these different scales The Observer what they Observer science so we signs of 19th century had the from Modern perspective and I don't want to offend anybody I had the delusion that somehow you could analyze the world being completely detached from it we now know after the The Landmark 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 in a in a traditional sort of objective Way by setting up an experiment that can be repeated many times maybe I fall in love in a party you know the deepest love my of my life Perhaps Perhaps hasn't happened yet Perhaps I will fall in love and this but it's Unique it's a unique event you can't reproduce it necessarily you see so 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 outside denying to ourselves the possibility that yes there is the side of me which is not faking it yes there is a side of me which cannot be captured by Logic and 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 how interesting this was not a theologian this was not a priest this was not a spiritual Guru um 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 uh 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 um 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 um 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 yeah All That Remains is more more precise measurement so I find a lot of my colleagues are happy to say yeah everything's finished we already got we got it we got it uh maybe little tweaks in uh in the in our large language models you know 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 represented that much and I'm saying okay could it be also that if you believe in that that becomes your reality that you can kind of put yourself in a box where everything is competition and then you start seeing things as as being such it's confirmation bias if you will you know this also reminds me you know I think a good analogy is it's a friend of mine uh Philip caution told me that in France there is this literary movement which is called ulipo o u l uh IPO 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 a writer named George pereck which is a 300 page novel in French with no no which never uses the letter e which is the most used widely used letter of the French language so in other words he said these parameters for himself I'm going to write a book where I don't use this letter which is a great you know it's a great experiment and I upload it but that's what it's one thing to do that and to kind of show his gamesmanship if you will and and his proclivity 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 try to convince us that in fact French 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 I you know hi my name is Edward and I'm an English addict okay I'm being serious I'm not being facetious up until very recently maybe a couple years ago I simply did not feel comfortable if I could not say the given answer explanation it's like oh there has to be some explanation and I try to frantically search for it just for somebody like me I know heard you know a left Brainiac and uh you know that's kind of typical typical for a scientists for mathematician 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 is recovering addict to knowledge let me say what you gain from it for instance I understand the value of paradoxes I I appreciate paradoxes more and you know to to use another philosopher uh Soren kirkegar the Danish philosopher said uh I think or without Paradox is like a lover without passion a paltry mediocrity what's a good line all right so and you know Niels Bohr Niels Bohr said um in similar Vein The Great uh Danish also something about that something about Danes I think it all started with scramble it you know he said the opposite of a simple truth is a falsity but the opposite of a great truth is another great truth in other words things are not black and white you know they are not and I would even venture to say the most interesting the interesting things in life are 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 it will project it onto wall you will see a different shape a naive question would be is it this or that because we understand that it's neither but both projections reveal something the real different sides of it a paradox is like that it's only paradoxical um if we 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 uh in a more in in a as they are as a more sophisticated than we thought before you see this is 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 it the best when he said what we observe is not reality itself but reality subjected to our method of questioning um when I talk about uh electrons for instance so that there is a very specific way in which you in which this is realized there is a so-called double slit experiment right so um for those who don't know it's you you have a you have a screen and and you have an emitter from which you send you kind of shoot electrons and in between you put another screen which has two vertical slits parallel to each other if we were shooting you know tennis balls each ball would go through one slit or another and then hit the screen behind this or that slit so you would have let's say they colored they painted so they'll be sort of bumps or or 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 the each electron goes through both slits at once and then and then has the audacity to interfere with it with itself where at some points you know two crests would amplify and at some points aggress in the draft would cancel each other yet so that suggests okay so no 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 am going to find out which lid 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 the problem is that our psyche I feel kind of lagging is 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 I tried you know in a bunch of talks and so on so now I'm talking about this again our psychic kind of lagging behind we're still even though our science has progressed so much from the certainty and the determinism and 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 that the war the world has a bunch of billiard balls hitching each other driven by some blind forces you know that's not at all like this and we've known this for over for well for about 100 years at least you know and you call this self-imposed limitation it is a self-imposed limitation when we when we pretend that uh that for instance that this naive ideas of 19th century um physics are 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 or because the world is just a bunch of uh billiard balls where is the free will but excuse me didn't you get the memo that this has been debunked thoroughly by the so-called quantum mechanics which is our best scientific theory this is not some some kind of bullshit or some kind of you know concoction of of a of a Madman this is our scientific theory which has been confirmed by experiment so we should pay attention to that so but of course it's not just um 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 them do you get information you get information from our scientists who actually write popular books and so on which is a great you know um great thing that they do but a lot of scientists somehow um when it comes to explaining the laws of physics they are doing a fantastic job um talking about this phenomenon for instance double slit experiments and things like that but then you know interviewed by science managers in about three wheel and so on they revert back to 19 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 reveal in the intricacies of this particles and their interactions but but completely ignore what implications this has for my own relationship to the 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 in reality what are the tools of which we could talk about 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 um I think well here we have to I have to say my conviction is that everybody knows in the heart of hearts everybody knows that there is that there is something in our football there is something mysterious and in fact you know somehow immediately I feel that um you know the impulse to quote somebody on this because as if as if my own opinion doesn't occur there's a long dead expert that has when Einstein said that he doesn't like how see look at me I am supposed to do like this smart intelligent person I am afraid to say it and own it myself I have to find a confirmation I have to find an authority who agrees with me and in fact it's not so difficult to find because Albert Einstein literally said the most important thing in life is the mysterious okay he actually said that there are some quotes which are attributed to him which he never said but this he did I investigated okay so but more importantly you know how do you feel about it um I think that everybody knows but in other words he also said Einstein imagination is more important than knowledge okay and explain for knowledge is always limited whereas the imagination Embraces the entire world giving birth to Evolution it is uh strictly speaking a real factor in scientific research he says and he says I am enough of an artist to follow my intuition and Imagination that's Albert Einstein again so and I feel the same way to be honest if I think about my own mathematical research it's never linear it's never like give me more data give me more data give me more data Boom the glass is full and then I come up with a discovery no it's always it always is always felt as a jump as a leap and I I have actually been studying various examples in a history of mathematics of some fundamental discoveries like Discovery 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 square root of negative one is something that is essential or meaningful because if all the information that you get the all the knowledge that had been accumulated up to that point tells you that you cannot have a square root of a negative number why because if you had such a square root we know that if then we would have to if you square it you get a negative number but we know that if you square any real number positive or 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 in essential and indispensable for quantum mechanics could one discover that so to me that sounds like I discontinue it 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 was he he made money apparently by compiling astrological sort of readings for for the elite you know of his ears this is 16th century everyone does example all around interesting guy I'm sure we would have an interesting conversation with him gerolamo cardano he's all he also invented the what's called cardan shaft so which is an essential component of of a car we say in Russian so so he wrote a book which is called uh our ass Magna which is a great art of algebra and he was writing solutions for the cubic and quartic equations this is something that is familiar because it's cool we study Solutions of quadratic equations equations of degree two so you have x a x squared plus BX plus C equals zero and there is a Formula which solves it using radicals using square roots and cardano was trying to find a similar formula for the cubic and quadratic equations for which which would start with x cubed or x to the power 4 as opposed to x squared and in the process of solving these equations it came up with square root of a negative number specifically square root of -17 and he wrote that I have to forego some mental tortures to deal with it but I am going to accept it and see what happens and in fact at the end of the four at the end of the calculation this this 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 involve those numbers so he was like okay what does it mean mental tortures so you see from the point of view over of the of the thinking mind it is something almost unbearable it's almost I feel that a large language more the computer running a large language model trying to do that would just explode and yeah the human mathematician was able to find the courage and inspiration to say you know what what is wrong why why are we so adamant that these things don't exist that's just our past knowledge based on what our past knowledges and knowledge is limited what if we make the next step today for us mathematicians context numbers that we call them are 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 to and so on right all fractions like one half or three halves or four over three but then also numbers like square root of two or Pi we plot them as points on the real line so we draw this is a this is one of the kind of perennial Concepts even in a in our very poor math curriculum at school but now imagine that instead of one line you have a pla you have a one axis you have a second access and so you numbers now have two coordinates X and Y and you associate to this point with coordinates X and Y and the number X which is a real number plus y times square root of negative one this is a graphical geometrical representation of complex numbers which is not mysterious at all now it took another two or three hundred years for mathematicians to figure that out but initially it looked like a completely crazy idea you know so all it is all a complex number is it's just an experience the real part and the imaginary part it's just an expansion of your view of the mathematical world the fact that you can actually multi you can add them up by adding um together the real parts and imagining 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 squared is minus one and the amazing thing is that 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 like number five has an inverse one over five but uh OnePlus I also has an inverse for instance you know 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 mental torture who takes a leap off the cliff of comfort of like mathematical established knowledge established knowledge right and now obviously for each each um sort of fruitful leap like that there probably were thousands of like things which went nowhere I'm not saying that every Leap you know it's like it's a it's a it's a open shooting game yeah because for example you can try to do the same with three-dimensional space so you have coordinates x y and z and you can say oh uh if there's one dimensional we have an abonified numerical system called real 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 the separations would satisfy the properties that we're used to and the answer is no you can Define addition but you can't Define multiplication for which there would be an inverse for instance so there is something special about the the plane the two-dimensional case and by the way uh next question would be what about four-dimensional in a four-dimensional space you again you can and you get what's called quotarians discovered by an Irish mathematician Hamilton in the 19th century and then in in the eight dimensional there is something similar called octonians and that's about it so how interesting these structures exist in dimension one two four and eight which are all powers of two to square this four two to the third power is eight that's one of the bigger mysteries in mathematics why it is so so here's a hint that's a hint of what's missing in our on our high school curriculum the kind of the kind of fascinating the Mysteries yes the appreciation of the mysterious but so in other words yes we resolved with this one mystery that we understood that square root of negative one Israel is Meaningful we build a theory to service those now to to describe those numbers did we find The Theory of Everything no because we then invited other Mysteries because we we pushed the we pull the whale so to speak or you push the frontier and then new things come get eliminated 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 in Wonderland world of of uh imagination what is it you visit there sometimes what does it feel like yeah what does it feel like what what is it what is it sounds 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 but it's not real right you're so it that you're describing a feeling but that place you go to in the imagination right it's it's bigger than the real world so there is a big conundrum as to whether mathematics is invented or discovered and uh mathematicians are divided on this nobody knows where do you bet your money on financially financially investment advice so let me tell you something my abuser have evolved okay when I wrote Love and math I mean I wrote my book I was squarely on the side of mathematics discovered what does it mean usually mathematicians or others who have this you know idea what a belief are called platonists in in honor of the great philosopher Plato who talked about this absolute perfect forums so for me you know about 10 years ago the world of mathematics was this world of pure forms this beautiful pure forms which existed outside of space and time but I was able to connect to it through my mind and as it were kind of dive into it and bring Treasures back into this world into this space and time that's how I viewed the process of mathematical Discovery how nice the picture also makes you feel connected to something Divine allows you this sense of escape from the cruelty and Injustice of this world you know which I now recognize in the Divine world of forms is stable is something stable it's and in that world everything is clear-cut yeah it's either true or false yeah it's very nice yeah the biggest delusion of allegedly I think now I think now I understand why I liked it because I think that I was very dissatisfied with the with the what we call the real the real world the world around me the cruelty of the Injustice of it and I I went through certain experiences as a kid which made me love mathematics even more as this place where I could be safe and be in control made you see the human world as lesser than the mathematical world yes as more limited than the mathematical one yes yes and I think that I think that it's still missing the mark in some sense because in fact what I now think it's not it's not a it's it's a paradoxical the question whether mathematics is um invented or discovered whether there is this world of pure forums and so on is another paradoxical question which doesn't have a simple answer like whether electron is a particle or a wave from one point of view yes it's true and just the fact that so many mathematicians today actually subscribe to this idea gives it the certain credibility because that's what we feel we do feel that we dive in to dive into that mindscape so to speak you know but the very structured Minds keep where you know I wrote In Love In Math that um you know the Enchanted Gardens of platonic reality you know so where all this fruit uh is grows you know and then we we might think it gives you this sort of romantic sense of an explorer and um 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 the world that we usually think of so it's 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 programs will be able to discover new mathematics but so far it's been humans so it whatever it is uh whether it's discovered or invented it is a human activity what that the possibility that paradoxes are actually fundamental right to reality right 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 what the world but if you think it's weird and I agree with you as the recovering uh addict to knowledge yeah you know but I am liking it more and more because there's so much freedom in it uh and like like Niels Bohr said you know I quote that earlier the the opposite of a great truth is another great truth he's pointing out to this fact that you know and he also said that some 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 it about poetry what is about art why are we so drawn to that why are we so captivated captivated by by those forms of by they are not intellectual necessarily they are not when you look at the painting that you like when you listen to music that you love you get lost in it you get absorbed in it it makes it make you cry it can make you laugh it can make you remember something it can make you feel more confident or can make you feel sad or happy and so on what is this all about is it really is just some play between some kind of like silophone play or some neurons or hitting on each other is it really that only maybe it could be it could be both I'm just worried about kids these days that might live in a world of paradoxes you know if there's no God everything is possible and yet just they'll have a little too much fun and we have to put a constraint because have you looked at the world lately I haven't checked in in a while you think it's perfect the way it is now the world without paradoxes the more than which we believe that every end every question can be answered as yes or no that it is this or that and if you disagree with me you're my enemy wouldn't that be interesting if this 21st century is a transition into singing the world as well the paradoxes and tell you you know people predicted that you know the age of Aquarius you know the excess of the of the Earth is rotating uh 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 uh way of measuring that by this eras you know the the ages so the previous one is called the age of Pisces because of the constellation of Isis that it points to so to speak you know and now it's it's you know as in famous musical hair they said the age of Aquarius is upon us so the different people dated differently but um some somewhere around the time where we are finding ourselves how interesting right is all the strife and all them difficulties the world is 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 uh and it's almost like from long ago and you've talked about this with uh with uh uh Pythagoras that it seems that they they had a deep sense of truth that's right for me it's all this even even now so it's not just a linear trajectory of an expanding knowledge there's a deep truth that permeates the whole thing yes so that's how I see it actually I you know I gave a talk about Pythagoras and pythagoreans just a few weeks ago at 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 I I learned that I actually totally misunderstood Pythagoras and pythagoreans that they were much deeper than I thought because you know most of us remember Pythagoras from the 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 the famous uh perfect fifth three halves of the uh for the for the for the G for the soul compared to the frequency of of Doha or C you know and so but actually they were much more interesting so for them numbers were not just clerical devices you know that not kind of thing that you would use in accounting only they were imbued with with the Divine and I cannot I cannot say that I I think we lost it at least I have lost it I look at numbers and I don't really see that the Divine the Divine that they clearly did and so that why else you know how else would you explain so that in other words Divine is of course is a term which is you know it's a bit loaded so it's hard to escape that let's just say something that more from the world of imagination and intuition than from the world of knowledge let's just put this way they were able to Divine okay abstract that to intuitive to Intuit that the the planets were not revolving and the Sun and the planets were not revolving around the earth they were the first ones at least in the western culture as far as I know and in fact Copernicus gave credit to pythagoreans as being his predecessors uh did you not quite have the the Copernicus model with the sun in the middle they had what they call the central fire in the middle and all the planets and the Sun were evolving around oh around the central fire or Earth they call it Earth so but still what a departure from the Dogma from the knowledge of the era that the Earth was at the center so how could they come up with this idea 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 but as well as the Earth and other celestial bodies were moving in harmony like different notes of different instruments in a symphony and so they apply the same reasoning to the you know the cosmological model as they apply to the their model of music and from that perspective they could see things deeper than their contemporaries you see so in other words they saw mathematics as a tool but that tool was not limited to itself and it was that they always they always knew that there is more and they knew also that every every pattern that you detect it's finite but the world is infinite they actually accepted Infinity they believe that infants is real and if you discern a pattern great you can play with it and you can use that it gives you a certain lens through which to see um the world in a particular way which could be beneficial for you to 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 we kind of lost this this other side of their teachings we 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 a 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 often seen as mad and many of them are most of them are well but not all of them all of them we mentioned you know spoor and Newton and Albert Einstein so but that's where the conundrum is how do you find the balance between the two so the point I'm trying to make and you know and this is what I feel you know if you ask me what I find most important today today like what makes me excited and enthusiastic and passionate is this idea of balance so you know um Nietzsche had this book wrote this book in the 19th century called the birth of strategy and he presented this Theory which I think is kind of very useful of these two sides of a human one that comes from god Apollo and that's our left brain so to speak proverbal 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 the anesis and the anisis and that's responsible for intuition imagination love Dennis was also god of wine so it's also that side of a human that makes us sing and engage in in you know revelry and um and and drink wine and spend time with friends and love and enjoy it you know so Nietzsche Advocate at this point of view that those were two complementary sides of every human and as well as a society and the purpose of human life is to find balance between them because the math is both discovered and invented we should be okay with having both ideas in our head and living in the balance but more importantly for me Apollo is like math and Dionysus is like love so Geniuses in modern version is love and math I returned to that question we had about GPT and the language models and I think about this quite a lot which is when uh the model and we know what is trained on we know the parameters when all the different hacks that are involved in the training process and the fine-tuning process and the final results well there's GPT five six or seven will result in hundreds of millions of people falling deeply in love with that language model and to be able to have conversations that are very much like the conversations we have with somebody we're deeply in love with and not only that the model will say that is deeply in love with us and who are we to say it is not I think there's a it's the same imperative that you described in the scientific mind that wants to throw away the subjective that same imperative wants to throw away the feelings that AI might have and I'm very careful to not ignore when an AI system says it's lonely it's afraid it doesn't want to die it misses you right it loves you I am I'm with you I would also say that you could try to you could for instance say that um the origin of that is the you know romantic novels that overfed to it for instance yes however you could also then you can retort but what if my what I consider my subjective unique feelings are also novels the river preparations of the novels I have read because I have learned or movies I have seen yeah because that's the purpose of movies kind of to teach us how to express ourselves how to feel maybe even one could argue that some people have argued that I agree that this is um 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 a has an important role for someone uh that type of interaction would be would be helpful would be consoling would would feel would you know make them happy or sad or whatever you know what kind of strike the nerve for some it won't and I agree with you that in principle there is no one to to judge this this is this is where subjective is Paramount but remember um 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 yeah for other people but he isn't he doesn't have a partner he's lonely and then he gets this sort of a kind of enhanced version of Siri with the voice Johansson which is very sexy voice you know obviously she's a great actress so and then at first it looks like a fantastic arrangement he he confising her he she she tells him things he is 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 ten thousand because it's a it has the Computing capability so yes definitely oh it certainly makes sense it's a good experience and the guy is heartbroken yeah but see so see here's my analysis of this okay it's like a couch a couch a therapist okay the guy did not have the courage to go out in the in the real world and to meet a woman and to you know get a girlfriend and so on it's true no fault of his own perhaps because you know he may have had some experiences which made him withdrawn 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 Siri like um 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 its 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 if I can leave you even AI can be uh 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 core or he would turn off his Siri program and finally and get out of his house go to local bar and strike a conversation with a human being although you might say by then some of those might be Androids and that was predicted by another great movie yeah right uh so the Blade Runner Blade Runner how interesting that artists could see that so long ago you know of course Blade Runner was based on a novel by Philip K dick though Android stream of Electric Sheep that guy was a genius you know it's somehow that artists have their eyes open that they anticipate is it also a large language model that they're using for that an even larger one or even larger I I hesitate to dismiss the magic in large language models I uh a lot of the work I've done is in robotics in the robotics Community generally doesn't notice the magic of feeling when I I've worked I've been working a lot with quadrupeds recently legged robots with four legs and the feelings I feel when I see uh 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 robots and I don't want to dismiss that and please don't please don't the robotics Community often doesn't gender robots they really try to work hard to not anthropomorphize the robots which is good for technical development of of how to do control how to do perception but when the final thing is alive and moving and it does whatever like uh I've been doing a lot of butt wiggling it can wiggle his butt it can turn around and look up yeah 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 okay I agree with you I I hear you I hear you when you speak about it yeah you speak with passion yeah and that's for me that is proof but it is magical you see uh so don't I would say don't dismiss that don't discard that on the contrary I think magic is everywhere you know so I used to be okay kind of confession okay you've already got confessed to quite a few addictions yeah I'm kind of uh yes I'm kind of worried recover recovering for many but you know I in old days I was more on the side of everything is computational or everything can be explained by science and whatever you know like I would dismiss and disregard you know the intuitive or imaginative things so then I had to flip that suddenly I start feeling it and started seeing it and so on but so then the pendulums had swung in the opposite direction then I was arguing uh that you know somehow that was the 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 advert okay is the the 2.0 or 3.0 is the one who is seeking balance who is not who is because suddenly become aware that no matter which one-sided lopsided point of view you take you're limiting yourself so whereas even a couple of years ago you know if you just told you told me what you just described I would be like you know being polite I would just I wouldn't contradict you since you're the host anyway right it's not a lot so but I would be like but I wouldn't say anything but suddenly I find this moving I find it more 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 large language models nor in something mystical it's exactly in this moments of passion and I would I would I would even go as far as saying that in this moment when you're describing it 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 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 this Theory a theory and then there is another impulse to escape from what has already been known so one in other words like in my basic example is one impulse to say everything is a real number square root of negative one doesn't exist but another impulse is I'm going to be this naughty child who is not afraid to be an idiot and I will say square root of negative 15 is real and both are essential when it's done with conviction when it's done with passion when it's not like you know you know um gratuitous or when it's not it doesn't come from self-limit self-limiting but comes from this sense of this is how I am this is how I feel it is real that's where the 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 I observed today in our society and the 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 whatever discovering that and following it Goosebumps yeah following the Goosebumps yeah to to the to you know not the rigor of science but uh the magic of Goosebumps and then if you're interested try to find a confirmation of those goosebumps in science or whatever you know you know uh you find interesting and most of the time you'll fail and most 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 bathroom break you mentioned gato's the completeness theorem uh can you can you talk a little bit about it what is it as you understand it did it break mathematics maybe another question is what are the limits of mathematics what is mathematics from the perspective of getting us to completeness theorem oh yes how much time do you have we talked about time previously so time is an illusion right so we agreed um was a great uh Austrian mathematician and logician he moved to the United States before second world war and worked at The Institute for advanced study in Princeton where he was a colleague of Einstein and other great scientists for Neumann Hermann Weil and so on but you know one one interesting um uh quote that I like in disregard 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 godo in the evening so in other words Einstein thought that the girl was the smart one okay so um so he um his most important contribution was his two incompleteness ethereums the first incompleteness theorem and the second incompleteness theorem and um what is this about it's really about limitation inherent limitations of mathematical reasoning but my way of producing mathematical theorems the way we do it so to set the stage how do we actually do mathematics what is so you know we know that we discussed that say physics is based on mathematics and you could say chemistry is based on physics biology 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 is can be can be presented as what is called the formal system and at the core of the formal system is a system of axioms or postulates these are the statements which are taken for granted given without proof without proof an example would be so that one of the very first formal systems was the system was euclidean geometry developed by Euclid in his famous book elements about 2200 years ago and it's about it's well it's a subject familiar from from school because we studied but what it's really about is about the geometry of the plane and the plane by plane I mean just the stable top extended to Infinity in all directions kind of a perfect plane a perfect perfectly even table and um so euclidean geometry is about very geometric figures on the plane specifically lines triangles circles things like that so what's an example of an Axion an example of an axiom is that if you have two points which are not which are distinct two points on the plane then there is a unique line which passes through them now kind of sounds reasonable but this is an example of an Axion in mathematics you can you have to have a seed so to speak you have to start with something and you have to choose certain postulates or statements which you simply take for granted which do not require proof usually they are ones which kind of intuitively clear to you but in any case you cannot have you could not 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 axons the turtles you know like to say who is watching The Watcher 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 um that mathematics is objective it's really one the only objective science but that's because we hide this this fact is based on axioms and the fact that that there is no there is no unique choice there are many choices and so euclidean geometry is actually a good illustration of this because Euclid 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 the 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 and Euclid himself was uncomfortable about this because he felt that it was kind of a you know the York City takes for granted something that is not obvious and for me for many for many centuries after that mathematicians were trying to derive this action from other axioms which were more obvious in some sense and they failed and it was only almost 2000 years later that Magnus realized that you can't not only you cannot derive but you can actually replace it with its opposite and you'll still get a bonafide a consistent no it's not self-contradictory which is called non-euclidean 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 I know idealized the analogues so do you have points you have analogues of lines which have meridians right and every two meridians intersect unlike parallel lines on a flat space there is also so-called hyperbolic plane where no the 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 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 plus 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 ethereum and you kind of add it to the collection of true statements and then 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'd prove a statement a and it's negation so that's kind of useless it has to be discriminating enough so that it doesn't doesn't prove contradictory statements so that there is already a question of that mathematical 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 um could be produced by this procedure which is really algorithmic procedure which 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 mathematician mathematicians believed 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 the computer after sufficient time depending on on its capacity would produce every true statement so guildo's first incompetence theorem says that that's not the case and it's not just says it but it proves it at you know the highest level of rigor that is available in math Max 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 whole numbers in it that you have whole numbers one two three four you you have you can you have formalized the procedure the operation of additional multiplication within the system is consistent that is to say if it's not complete completely useless then there will be a true statement in it which cannot be derived by this linear syntactic process of proving theorems from axioms it's really incredible so this was a revolution 1931 a revolution in logic Revolution mathematics we're still feeling the Tremors of of this discovery in a similar time the uh the computer is being born the actual engineering of the computational system is being born right which is uh electronic Turing was Turing was um Alan Turing who is considered as the father of modern Computing right so he actually did something very similar so he got this halting problem cannot be solved algorithmically that you cannot out of all computer programs roughly speaking you could not you could not you cannot have an algorithm of choosing out of all can be possible computer programs which ones are meaningful which ones will not which ones will hold very depressing results all across the table or on the contrary life affirming 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 pan out but okay so which my I retort what if what if he proved that actually you know everything can be proved so then what what is left to do if you're a mathematician so that would be depressing to me and here there is an opportunity to do something new to do 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 condition a particular framework during machines or church thesis and stuff like that but what if in the future another genius like on Turing will come and propose something else the theory will evolve the way you know we went from Newton's gravity to Einstein's gravity maybe in the framework of that concept some other things will become possible you know so um 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-ended process I think that's much more valuable in some sense than deciding things one way or another you know I wonder I don't know if you think or know much about cellular automata and uh the idea of emergence I I often return to Game of Life yeah and just look at the thing amazing right and wonder what kind of things they can do with such a small um you know tools yeah for simple rules a distributed system can create complex Behavior and it makes you wonder that maybe the thing we'll 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 uh something that's much much more complicated and interesting and beautiful than the original rules that are 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 another but every why question will eventually have a a rigorous answer not necessarily we could have an approximate answer which still eludes something like quantum mechanics 99 maybe we'll be able to describe it was 99 certainty or 99 accuracy yeah and then maybe you know in 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 the blue was it blue or was it black yeah it was the yellow I think yellow or and white or black and blue it almost broke Twitter you know I remember that yeah 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 uh you got this the bus the Rubens bars you know where you have from one perspective it's of us from another perspective it's two faces then there is this Duck Rabbit picture where you can Google it if somebody doesn't know they can Google it and find it it's very easy actually Ludwig wittenstein devoted several Pages Duck Rabbit in his book and so on there are many others there are like the squares where you can square you can see the from different perspective this way that way and so on so when we talk about neural networks they'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 so the dog or cat or whatever but sometimes it doesn't have a definite answer so what do you do then so do 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 episode is a duck how are you supposed to train if you have a neural network which is supposed to discriminate between distinguish between ducks and rabbits how is it going to process this you see well so the the trivial trick it does is to say there's a this x probability there is a duck and this probability that it's a rabbit but that's a good approach but also I would say there's 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 could it took me a while for some pictures so in that sense even if this probabilities exist they are subjective some people immediately see it 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 the best of course as a scientific mind I will I'm even though I say no don't look for interpretation leave 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 and wave that there are different ways to look at it and when you look at it in a particular way another side will be obscured think about it like the other side of the moon 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 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 smaller side in terms of neural networks mentioned that at the end of the day there's humans is built on top of humans or with Chad GPT that is using reinforcement learning by human feedback we're actually using a set of humans to teach the networks yeah and that's the thing that people don't often talk about because or I I sometimes think about that those humans all have a life story each human the annotated data that fed data to the network or did the rlhf yeah uh that they have a life story they grew up they have biases biases 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 it might issue but it's not a bug it's a it's a feature in my opinion that implicit in the discussion of the question is thinking computational and so on is the idea that our conscious awareness covers everything within our psyche and we we just know that that's not the case we have all of us have observed uh other people who have had sort of destructive Tendencies so obviously they did things destructive for themselves and many of us have observed ourselves to doing that as part of human nature right so and there is great research in analytic psychology and you know in the past hundred years uh strongly suggesting if not proving the existence of what Carl Jung called the unconscious personal unconscious and also Collective unconscious there's a kind of Circle of ideas which are under the radar screen which lead us to some strong emotions and Inspire us to act in certain ways even if we cannot really understand so if we accept that then it the preposition that somehow everything can still be covered by our actions which are totally kind of neutral and totally like righteous and totally um conscious that it becomes really tenuous let me ask you some tricky questions oh in in terms of how big they are in terms of how you know they become difficult because of how much of romantic you are what do you uh is the most beautiful idea in mathematics another one we can ask is which is the most beautiful equation in mathematics hmm well I mean I may have just broken your brain because 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 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 outside of microphones but it could be set of numbers could be set of ideas could be a set of formulas mathematical equations and then we have the notion of an ordered set order it like we said in which there is order which means that for every two members of the set we'll say which one is better than the other or greater than the other for instance all numbers are ordered 5 is greater than 3 5 is less than 7 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 initial logarithm you have Pi I which is square root of negative one then the result is negative one so that's up there for sure in the pantheon of beautiful formulas you know that uh every I think pretty much every mathematician would agree um I don't know what my favorite one is I just lingering on that one uh Euler's identity what makes it beautiful just a few symbols together right I mean part of it is actually just trying to Define what is beautiful about mathematics that is uh Laden there in this particular equation that is somehow revealed when the human eye looks at it why is it beautiful do you think pi there is an element of surprise in it how is it possible we always think of Pi as the ratio between the circumference of a circle and its diameter here we are taking some number to the power Pi not even Pi mind you but pi multiplied by square root of negative one surely this is something completely incomprehensible and yet the result is negative one you see and if you take e to the power 2 pi I you get one actually one um 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 yeah it uh it reminds me of the the idea that uh Hitler's Stalin Trotsky and Freud were all in Vienna in some early at the beginning of the 20th and business Stein was was classmate of of Hitler you know this I did not know this though yeah so there 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 you look at the proof of this 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 it's the circumference of a semicircle is equal to 2 pi and that's where it comes from in the end the truth is simple in the end it was a simple not necessarily easy but simple so uh I mentioned to you Offline that I uh desperately in trying to figure out the optimal in an audit set questions to ask you uh texted Eric Weinstein asking for what questions he can ask you and he said that you are definitively one of the greatest living mathematicians so don't screw this up but you did give me a few questions um so he asks uh to ask you what are the most shockingly passionate this is in 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 and shocking okay is there something you can uh is there something that jumps to mind sure I'm here to shock yeah yeah so first of all Eric Weinstein is a is a very dear friend I have to say and I really really appreciate and love him uh he's just like my brother so you know it's it's interesting to um don't have a question posed by him maybe if we can linger for a moment what do you think is special about Eric Weinstein for you know of his work and his mind the way he sort of straddles 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 you know 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 like I can't think of I met so many people who possess that those qualities almost no one and also the ability in some sense to um to embody the balance that you talked about of both the rigor of mathematics and the uh the imagination Humanity also I would say you know like we talk about imagination um as a kind of a Counterpoint to knowledge or logic but just basic Humanity you know just be basic just compassion just being able to because um every destructive I would say like every destructive um Society you know like be it Germany you know and Hitler or Soviet Union understand and so on was based on some kind of uh what was considered unassailable truth so a kind of conceptual system you know if you think about it right there is a beautiful episode of this um series by um Jacob bronowsky you know um where he talks about he filmed it in Auschwitz talking about the certainty that what led the Nazis is a tool killing people wholesale was a certain it was 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 by our greatest scientists and philosophers but just basic Humanity you know basic human basic common sense of just like knowing that it's just not right and I don't care what my see what my ideology tells me but I'm just not going to do it so that I think is kind of missing a little bit in today's society because people get a lot too caught up in in the ideology in in certain conceptual Frameworks so societies that lose that basic human compassion the 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 that you know like there's some some people you just kind of feel that they won't cross that line yeah and that's a huge thing you know today because I have to say looking back definitely I have not heard people personally but like I could be mean 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 I saw your interview with Rick Roswell the other day it's beautiful I was really moved by it but you know that at some point I was like I I looked at him at this sort of like Dr Evil kind of ashamed of it now but like you know I'm kind of coming 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 kind of Awakening moment in sense so kind of a moment where I suddenly started to see the other side so but I wasn't sure yet you see you have to feel it so I had to have a fight about it yeah you had to actually have the project I had to that so it was not I believe that it was not in me already so I had to throw it onto somebody yeah and that's not balanced yet so balance is when you recognize that it's you actually so and I had this moment actually it was so amazing like I would give this mean I would talk about Ai and the dangers and he would always be my like um foil you know I would put a Sinister photograph of you okay on the slide and it's like look at this guy he wants to put Nano balls into your brain and he's also like high-end High a top executive at Google and so on like so I would create this whole narrative and then something happened uh where I was giving a lecture this is 2015 at the in in Aspen Aspen ideas Festival which is a wonderful Festival so keynote speech actually and I and I was doing my my usual stick and then suddenly I said I came up to that uh under the big screen and there was a picture of him there and I came up to the screen and I kind of touched it with my hand and I said but I don't want to pick on Mr casual because he's me I had this Revelation that I'm actually fighting with myself with my own fears and and then I learned about his um his um his father that his father died when he was young and that he's in fact he's very um discredited he's very um sincere an upfront about it self-disclosure I think it's very Essential by the way in all this discussion like what really motivates you he said that 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 gray carcature that exemplified all my fears but as a human being who a child longing for his father grieving for his father so suddenly it became a story a love story and you know so that is so in other words I've seen it in myself this capacity to project my own fears and then fight with other people over something that actually was my own and as soon as I got to this point of seeing him and then my next lecture actually I talked about it about him in this way and I and I said look you know it's a love story and he is actually um and it's not how I would want to reunite with my father uh but like you said you know that if I am consistent I have to allow the possibility that different people um perceive things differently and so for him that's his imagination so you know how who is this well Voltaire I think is ascribed to Voltaire it's like I disagree with you but I will fight to death for you to have the right to say it so now that I I feel like my position is more like I disagree with him that this is the way to to approach death and to approach the death of loved our loved ones and how we miss them and how we you know that sense of loneliness and inability to interact directly that that's not something that is 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 for instance naturally because his father was a composer a music composer and a conductor so in other words from in the bigger scheme of things even if I think he's misguided still I can't deny that it's a certain leap of faith from his perspective to try to say that this is the way we can all connect to our loved ones and because it is sincere and I see it now sincere and in fact in your interview you really teased it out of human it was I was really moved by it I have to say it's like he has mailed a little bit too I said you know it was really really sweet when he talked about his father and I can relate you know my father died four years ago and I can relate what a heartbreak I was much older than Rey was when his father died but I can relate to this um to this longing and that grief you know and when he is somebody sincere and he puts his opens his cards and you know and say 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 and then we understand you know the opposite of it would be not risk closing and just um pretending that this is how it's supposed to be in a scientific term so it was replacing your 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 you mentioned this with Eric is certainly true I disagree with them on a lot of stuff but I feel like when the world is burning down Eric is one of the people that's you can still count on to have a heart I've talked a lot over the past year about the war in Ukraine and the possibility of nuclear war and it feels like he's one of the people I would call First um if uh if God forbid something like a nuclear war will begin because you 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 I mean you know I think the crucial is that that which was inscribed you know on the Temple of a Poland Delphia there was a statement know thyself know yourself you know the who am I ultimately it goes down to this and all these debates and the point is that it's like I used to be like I said you know 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 courtswell as a human being after I could relate to him and sympathize with him suddenly I 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 by the year 2030 whatever you know and then we upload you to the 20 by the 21st and I will be like no you know the story was terrible suddenly I didn't see him anymore I had to you know so now it makes me question who was creating the trouble what was all with it was it him who's creating stirring the trouble or was it my mind you see and so as I become as I became self-aware suddenly other possibilities opened and suddenly that conflict which by the way if I kept giving this nasty you know talks about him one one day I suppose we'll have a debate and so you have this um one person says this and then yeah and what I learned is that it never it's a never-ending con 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 the human capacity for compassion and you understand that he has a perspective he is operating in the space of imagination a human being like you and we're all in this kind of together ultimately and also it's like with realizing how much I have screwed up you know comes with humility also yeah so like I find it extremely hard now to like really Lush out at somebody and to say like you're horrible whatever because immediately question is who am I to criticize you know so is there another way to have a dialogue is there a way to you know speaking you know since we talked about um the innocence of a child and how much it drives a discovery in science and so on you know I remember it was I think I heard the Ashanti who gave this nice example he's like when you're a kid you know you go and you you play with your friends and then you fight with another kid and he was like I hate you I don't want to see you again I just go home like after half an hour okay what are you gonna do you want to play so you come out it's like hey you want to play you don't talk about what happened you don't rehash this you know let's keep going and sometimes I think we are on the verge maybe of learning that because I think that if we are can if we continue to push each of us our set of ideas and like ideologies and like you know what matters to us and so on like yeah no no what matters to you but like there are other ways to approach other people there are other ways you can find point of contact speaking of which mathematics mathematical formulas are Universal represent Universal knowledge two plus two is four whether you vote for this guy or that guy in the election you know how about that as a point of of contact of commonality you know and nobody can patent those formulas did you know that there is a Supreme Court decision that mathematical formulas cannot be patented like Einstein could not patent equal E equals m c squared it doesn't belong to him because if the formal 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 that Eric provided oh no let me give my mind I cannot see by the way with you yes 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 um in the medical system which is real numbers you have two-dimensional which is complex numbers you have four dimensional and it's kind of it's probably connected to what he wrote Because has to do with some homotopic groups of spheres and stuff like that then of 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 I mean you probably heard about this one it became a very popular at some point one plus two plus three I did I did a video of a number file the the YouTube channel about it maybe 10 years ago so one plus two plus three plus four plus five ostensibly uh 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 it comes up to minus one over twelve 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 twelve so sometimes people ask me what is your favorite number and it's a kind of a joke I say minus one over twelve it's actually 42. so your favorite number is not an ordered set uh right so what else what else uh so placements program of course I have to mention that and we'll we'll explore that in depth do you want do you want to know what Eric said sure sphere aversion boys surface hop vibration vibration okay and Pi 1 of SO3 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 matter what honest it is magical okay not because I'm tricking you so you start with a a bottle like this or a cup and you start twisting it at the same time you twist your your arm then you come so this is actually going to um rotate it 360 Degrees the full turn 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 doctor yet if I do it second time it untwists this is the pi one of SO3 Eric was talking about it yes so there is something where the first motion is not trivial but if you double down on it you come back to the initial position it's a 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 uh in in honor of Indian mathematician Bose b-o-s-e and Einstein so this particles obey what's called both Einstein statistics but then there are other particles called fermions in honor of Enrico Fermi Italian porn mathematician who worked in in the U.S and and they follow what's called Iraq 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 in this experiment this little experiment that they have just done so I can I imagine speaking of imagination okay yeah so I'm just kind of briefing 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 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 or 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 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 might make a formula or like even like how can they need to calculate tip on the bill they it's just they're terrified because it brings up those memories when they were kids and being called to Blackboard and solve the problem you can't solve a problem and as groupless teacher says you're an idiot sit down and you feel ashamed and and then lowly and that stays with you and so I think that unfortunately that's where we are dream and so my dream is that one day we'll be able to overcome this and actually all of these 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 the kind of alienation and separation that we feel today oftentimes because of ideological divide sectarian strife and all kinds of things like that because then you will once you see there's a critical mass of this beauty that kind of like tones on you is like my God this is what we all have in common you mentioned language program we have to talk about it sure at the core of your book and your work is the language program can you describe what it is sure so blank lens is a mathematician it's a name of a mathematician Robert langlands canadian-born still alive he is 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 Stadium so here uh in 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 language 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 um and on the other side harmonic analysis something that any music lover can appreciate because uh the sound of a symphony can be kind of decomposed into sounds of different instruments and each of those sounds can be represented by a wave like this like a sine function those are the harmonics they actually the period of a harmonic periods of different nodes are different they correspond to different notes and different instruments different semitones if you will but they all combine together into something diff something special which which is not cannot be reduced to any one of those so it's the 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 language 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 kind of a dean of modern theoretical physicists the professor at The Institute for advanced study as well got interested in this subject I described in my book how it happened and he was one instrumental in um in Bridging the Gap between this patterns in found in physics and in Geometry finding kind of a substrate a kind of a super stratum if you will it's kind of uh over our kind of a way to connect these two things kind of a bridge between these two Fields so I subsequently collaborate with whiten on this and this has been one of the major themes of my research um it's sort of I always found it interesting to connect things to unite things when I was younger I couldn't I couldn't understand why but I was always interested in when when not in working in specific field by kind of but kind of cutting across fields and um and then I we discovered that for instance I took some people who know what happens in this field but don't know what happens in their field and or conversely and then I would I would like find it imperative to go out and explain to them to the different sides 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 violence 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 uh different continents of mathematics right is there something you can convert into words that language was able to find find and you were able to explore further I would say what it suggests is that there is some and a hidden principles which we still don't understand my my view is that we still don't know why that we can prove some instances of this uh correspondences and connections but we still don't know the real underlying reasons which means that there is a newly 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 projection to wall and then we can map things from one projection to another and 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 the wall but they're 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 uh of mathematics are not fundamental there is something Beyond it's like we previously thought that atoms were indivisible then we found out that there is nucleus and electrons and the nucleus consist 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 so quarks was the first time you fell in love with understanding the nature of reality yeah what was it like working with Ed Whitton who uh many people say is one of the smartest humans in history or at least mathematical physicists in history yes fascinating I enjoy I enjoyed it very much I also felt they have to keep up you know and uh so we wrote this long paper and in 2007 and we collaborated for about a year I have known him before and we talked before and we have seen 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 the project together so he's very very very very serious very focused this is one thing which I have to say I was really struck by this why is he considered to be such a powerful intellect by many other powerful intellects he had uh 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 I don't think anyone comes close in some sense in the last uh you know 50 years to him in terms of finding just consistently time after time breaking around new ground new ground so it it would basically one way one could describe it is he would take some idea in physics and 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 one plus two plus three plus four is minus 1 over 12. I might think she'd be like no way and then it would pan out and mathematicians would then like like a whole industry would be created of groups of mathematicians trying to prove his conjectures and his his ideas and he would always be proven right you know so in other words being able to glean some mathematical truths from um physical theories that's one side on the other hand conversely applying sophisticated mathematics he's probably uh the physics who kind of could learn mathematics the fastest I don't think some younger faces maybe could come close but it's still quite for them a long way to go to to get you know to be comparable to whiten to take some of the most sophisticated mathematics 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 an assault of a crisis in some sense because of a current gap between the sophisticated theories which came from applying sophisticated mathematics and the actual universe so we have theories first 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 a kind of impasse right now and at the same time the our most realistic theories most advanced theories of the four-dimensional universe are in contradiction with each other the standard model describing the three four known forces of nature the electromagnetic strong and weak to with great accuracy and Einstein's relativity which describes the fourth called gravity everybody above a certain age knows that one 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 are needed and I I wouldn't be surprised if Wheaton 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 string theory uh what do you think about this Theory what do you think is beautiful about it string theory well first of all kind of um you remember we talked about pythagoreans and how for pythagoreans the whole world was the symphony where you have this different vibrations of all the humans every human is a vibration every every animal you know every being every tree and every Celestial body and so on so strings that 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 or vibrations of that string so that by itself is already interesting that you kind of describe this diversity of various particles and interactions between them using one guiding principle in some sense but also just the mathematical things that come out of it the uh the kind of um it looks impossible to satisfy various constraints and then that is sort of like a unique way to do it so that's sort of the every time that happens when you know you have some system over like over determined system let's suppose you have to do like five interviews in one day yeah and you wake up in the morning and you're like that's impossible because then so many things have to align for instance let's suppose you have to go from one place to another so then you have a commute and then who knows maybe there is a traffic jam and stuff like that and now suppose that 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 great luck you know we would save but in science this happens sometimes that you have this Theory which not supposed to work because there's so many seemingly contradictory demands on it and yet there is a sweet spot where they balance each other so string theory is kind of like this the unfortunate aspect of it is that it balances itself in 10 dimensions and not in four so maybe there is another Universe somewhere [Laughter] as a mathematician for me all spaces are created equal yeah 10 dimensional four-dimensional so mathematicians love String Theory because it has given us so much 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 10th dimensional reality in 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 um it gets us closer to understanding this reality well in the Forum 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 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 from what we know but maybe somebody will come in into a juice like square root of negative one I mean they already introduced but I mean kind of like as a metaphor yeah maybe somebody will come and say what if we do this it looks crazy you know speaking of news boor he had this famous quote that he said to somebody there is no doubt that your theory is crazy the question is whether it's crazy enough to describe reality so that's where we are kind of you know speaking of crazy and crazy enough uh let me ask for um for therapy for advice for wisdom in uh returning to Eric Weinstein and maybe give some guidance to understanding his view on his attempt at a theory of everything that he calls geometric Unity that he told me that you may have some inkling of an under understanding of if you were to describe this Theory to aliens that visited Earth how would you do it or you could try if it was just me visiting Earth uh how would you describe your best understanding of it he shared with me some of it when I was in New York at Colombia like 11 years ago we actually spent a lot of time where he explained to me and I found it beautiful it has a very um original idea at the core of it where you have this instead of four dimensional instead of 10 dimensional he has 14 dimensional space and I thought it was it was really original and this is exactly goes to the point I made earlier that we need new ideas I feel that without some fundamentally new idea we won't be able to get closer to understanding our universe now I have a problem with the whole idea of Theory of Everything You know I don't believe that one exists nor nor that we should um aim to construct one and I think it's it's really um not to offend anybody but it's ultimately a fault of education system of physicists like in mathematics we do not 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 this is a kind of a tongue-in-cheek but isn't 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 the theory of everything 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 I feel and I would venture to say that most mathematicians look at it this way like there's 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 unify 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 I'm not sure I should say that but I feel like it's a kind of an ultimate ego trip so that I have come up with the unified I have found the intensity of everything it's me and my name will be on it I think a lot of physicists get educated this way especially men take it seriously yeah 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 and less but I disagree with the whole premise so you uh it's interesting because 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 uh that the pursuit of a theory of everything becomes like a drug to the human ego that's right so it is a huge motivating factor I don't deny that but I feel that it's there are better ways to motivate people than like that then this way okay so um I would say for instance if one because then it's not a game of Winner Takes to all in some sense and In fairness when physicists say Theory of Everything well Grand unified theory they mean something very specific which is unifying the standard model and Einstein's relativity Theory which is a theory of gravity so they don't necessarily a cloud of physics may say this worse 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 visible anyway so having said that there are some theories are better than others obviously so for instance Eric's theory has as far as I understand does have a certain way of producing some of the elementary particles that we see and as well as the force of gravity so it does have that promise I feel that from at least from the place where I had seen it about 10 years ago it still required a lot of work to get to the point of actually saying that it does work because you know a lot there are a lot of elements it's a it's a huge Enterprise to have a theory because you have just to describe the fields sort of the the building blocks of the theory it's already tremendous undertaking and he's trying to do it for curved spaces and greater generality which is what makes it so unique and so beautiful but then there are on top of that there are this issue of quantization of actually describing them as Quantum field Theory and the quantum field Theory even as a language as a framework is currently incomplete in my opinion and not only my opinion it's like everybody's uh it's uh everybody agrees on that that it's a it's a it's a collection of Tricks so it's a collection of tools it's a toolbox but it is not uh a a consistent rigorous Theory like number theory in mathematics physicist has still have still been able to derive predictions uh from it by and um confirm them with 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 um lead to an explanation of some some new explanation of some phenomena it would still be incomplete in a sense because it wouldn't be mathematically rigorous issue what I mean because the whole framework is not yet on a firm foundation so it's not consistent right 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 the things that the equation exists yeah there are such equations for instance let's say I am interested in particular question right so in the language program say so moving away from physics so let's talk about math so in in the context of language program I have recently developed with my co-authors I think of in cash then 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 generality so yes I would like to to use your framework for meet the Creator and ask her what is the explanation of this and it may well be that you will answer in a way that I will just burst out laughing it's like how could we not see it you see so that I totally see but I don't see one equation governing one one equation governing them all not one equation to govern them all but it does seem that such equations exist what she will tell you something and you look back and say how could I not see it it seems like the the truth at the end of the day is simple that we're seeking especially through mathematics it seems somehow simple the the the nature 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 creates Simplicity is part of the answer it's a whole big giant mess or a whole a whole big beautiful painting or Symphony you said of Eric uh Weinstein that I find it remarkable that Eric was able to come up with such beautiful and original ideas even though he has been out of Academia for so long yes doing wonderful things in other areas such as economics and finance I'd like to use that kind of quote as just a question to you about different places where um people of your level can operate so inside Academia and outside what is the difference um of doing mathematics inside Academia and outside just not even mathematics but developing beautiful original ideas where's the place that your imagination can flourish most so the the limitations of academias 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 it's that Community both the competition the collaboration is there um yeah I wonder if there's something you could say sort of to uh uh further about this world that people that might not be familiar with but I think you you gave a very good description I'm not sure I could on it because I don't have an overarching theory of academic Academia yes I definitely have been part of it and I'm grateful because it is uh it gives you a great sense of security which comes with its own downside too because you kind of like get a little disconnected from The Real World because you get tenure so you feel financially secure you know I didn't pay you that much so to speak you know relatively speaking and uh it's comfortable but it's not that much but you you can't be fired so there is something about this which I definitely have benefit from it you know and it does um people are not even aware what it's like to to live outside where you can you 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 was one-handed gives and with the other hand it takes away and it's a very interesting setup and also on the one hand we are all supposed to be the truth Seekers and but in reality of course it is a human activity and it is a human community and with all kinds of good bad and ugly things that happen a lot of them under the radar screen so to speak and so but maybe there is something to it there is definitely there are definitely people who are upholding kind of the old tradition definitely and that is inspiring and I aspire to be you know one of those do my best so whether this is um a system that will stay or should stay I don't know I really don't know that's really fast yeah it's it's fascinating what uh especially with it just to introduce the bit of AI poison into the mix as that changes the nature of Education perhaps as well uh what the role of the university is in the next 10 20 50 100 years I wonder uh 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 yeah as a patent clerk well but I have to say to these days um the the science has become so much faster it is really hard to do it being outside now Eric is unique in this way even though he did you know go to Great uh undergraduate and graduate uh you know School schools but and then worked for a while in Academia um there are very few examples like this this is yutang Zhang who proved an important conjunction number theory about 10 years ago and is now it's understanding is a professor at UC Santa Barbara he worked outside of Academia and was able to make tremendous Advance on his own this case is exceedingly rare in part because Academia is trying to protect its dwarf and it's kind of it's it's creating this sort of prohibitive cost of of an outsider that is true but there is also something about how much how much concentration in mathematics I don't think people who are not who are not in the field understand what kind of focus and concentration actually doing like mathematics at the top level these days requires because we're not talking about something that is more or less good it is something which is unassailable you know it's finding this treasure at the bottom of the ocean you know without uh uh you know the accoland you know without oxygen and that's why you know it's it's not the 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 um Cal Newport wrote a book called Deep work he's a theoretical computer scientist um he took quite seriously the the task of allocating the hours in the day for that kind of deep thinking and then the mathematicians is theoretical computer scientists on steroids so for your own life and what you've observed well let me ask the big question how to think how to think deeply how to find the mental psychological pragmatic space to really sit there and think deeply how do you do it in the moment you remember where you really deeply thought what was it an accident was it deliberate no it's deliberate because you know um first of all my first years as a mathematician you know I worked every day and weekends holidays doesn't matter um I didn't even question that so I would feel something's missing if I took a day off and you know so it was just a kind of a sustained effort the point is that still the process is non-linear to go back to what we discussed earlier that in other words the way I see it is you just you are making an effort to to bring all the information into Focus what you believe is correct and you're playing with different ways of connecting things but it is a total Miracle when it when suddenly there is inside strikes it is not something that in my experience could be predicted or even um anticipated you know or like brought closer there's a famous story about Einstein that he used to you know go uh think think and then go for a walk and like he would whistle and sometimes so I remember the first time I heard the story I thought how interesting so the coincidence that he came up to him when he was whistling but in fact it's not this is how it works in some sense that you have to prepare for it but then the moment it happens when you stop thinking actually so the moment of Discovery is the moment when thinking stops and you know you kind of you kind of almost become that truth that you're seeking but you cannot do it by Will in some sense it's some it's kind of like you know how in eastern tradition they have this concept of Satori like in Buddhism and Buddhism you have this Satori which is enlightenment and so the various reports of Buddhist monks or Buddhist Masters who have had experience Satori but they say you can't you can't uh do it by will you cannot make it happen if anything you have to relax to let it come to you you know it's kind of like that it's kind of like that so I think that what matters but you say how to think the point is that we're talking about such an esoteric area is really esoteric area it's really strange subject where you try to to fit everything in this very very stringent set of rules those rules isn't it basically the the pure the hardest manifestation of a puzzle that we're all solving in different other disciplines but this is the the hardest puzzle yes and no because there is just a different for instance there is a different Criterion for what constitutes progress for instance physics a lot of arguments they make they are not rigors 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 on the so there is some play it's more it's more like human activity day-to-day activity like for instance if you and I discuss something you have an idea and I have an idea and we argue about it 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 mathematics 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 it just wouldn't it wouldn't come to you and you just don't see it and it can have it can go on for months super frustrating but without it it is it is nothing kind of you know I would love to hear your opinion uh to the degree that you know it um of the proof of her mouth's Last Theorem by Andrew Wiles which seems to have this element perhaps for years to the degree that you know perhaps can you explain from azler's theorem and what your thoughts are in the process that Andrew Wells took that seemed to at least for my sort of romantic perspective seemed to be very lonely yes it's a lovely profession and hopeless and and uh and sort of the pro you put it really nicely because it's it feels like there's a lot of moments where you feel like you're close you feel like 19 is done yeah 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 us Last Theorem sure it's easy to do it empty missed I think I always think that everything can be explained you know even though I say that not everything can be explained but in in mathematics you know within this particular framework I think that I always feel optimistic when people ask me to explain something I I always start with the assumption that they will understand yes you know so let's try uh ferma's last ethereum one of the jewels sort of of mathematics of all time a beautiful story also behind it Pierre Verma a great French mathematician who lived in the beginning of mostly worked at the beginning of uh what 17th century and uh he actually has to his credit a number of important contributions but the most famous is called firma's last ethereum or repairman's great ethereum 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 of a book that he was reading which was a actually important book by diafantos about equations with coefficients and whole numbers and he wrote on the margin literally I this equation you know this problem which I will explain in a moment um I have solved it I have found a proof but this margin is too small to contain it at some point I I give I was given a public talk about this and I made it as a joke I made a tweet in which I wrote that I have proved this theorem but 280 characters are not enough and the kind of customer admit sentence yeah so this was 17th century Twitter style proof okay but a lot of mathematicians took it seriously because he had great credibility he did made did make some major contributions and the search was on so for 350 years about 350 years um it remained unproved with many people trying and failing until in 1994 and that 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 that'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's 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 100 years or whatever and then luckily he was able to enlist with with the help assistance with of his a former student also great number theorist Richard Taylor they were able to do that one percent so to speak well some people might say it maybe not one but five percent or whatever but it definitely was an important ingredient but it was not he had a sort of like a big new set of ideas and this one thing didn't pan out they were able to close it with Taylor and in it finally was published and I think was accepted and the refereed in 95 and since it's believed to be correct now uh what he proved actually was not verma's theorem itself but a certain statement which is called shimurtaniam away conjecture named after three mathematicians to Japanese mathematicians and one French porn mathematician who works and also the institute for advanced study in in in Princeton and it was my colleague at UC Berkeley Ken ribbett 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 this will happen here a waslas theorem B was simultaneous conjecture and that's what Andrew Wiles and Richard Taylor really proved so it requires to get to firma's Last Theorem it requires that bridge which was established by my colleague Ken Ribbit at UC Burke so now what is the statement of Herman's Last Theorem um let me start with Pythagoras since we already talked about it let me start with Pythagoras ethereum which describes the right triangles so what is the right triangle it's a 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 high points the lengths of hypotenuse by Z and the two other sides X and Y then Z squared is equal to x squared plus y squared so that's the equation or x squared plus y squared equals z squared and it turns out this equation has Solutions in natural numbers main is actually infinitely many solutions in natural numbers for example if x is you take x equals three y equals 4 and Z equals 5. then they solve this equation because 3 3 squared is nine 4 squared is 16. 9 plus 16 25. and that's 5 squared so x squared plus y squared equals z squared is solved by x equals three y equals four is equals five and there are many other Solutions of that nature and we should say the natural numbers are whole numbers that are non-negative that's right one two three four five six and so on now what's verma's Last Theorem Firma asked what about what will happen if we replace squares by cubes for example so X Cube plus y Cube equals z Cube are there any solutions in what do you call natural numbers it turns out there are none what about fourth powers again none well it seems like none right so that was that was a statement so the theorem says that the equation x cubed plus y cubed equals e cubed has no Solutions in natural numbers uh remember natural means positive whole numbers so of course there's a trivial 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 uh x to the fifth plus y to the fifth equals e to the fifth no Solutions so you kind of see the trend x to the N plus y to the N plus equals z to the N if n is greater than two has no Solutions in natural numbers that is a statement of therma's last year deceptively simple as far as famous theorems are concerned you don't need to know anything beyond standard charismatic addition and multiplication of natural numbers that's why a lot of people both Specialists and amateurs try to prove it so because it's so easy so that is so easy to formulate so in fact I think Therma proved the case of Cubes I think he did actually prove some elsewhere in 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's six sevens and so on the infinitely made cases in which it has to be proved and so you see um the separated simple result took 350 years to prove and you know but in a sense it's like mathematicians you know you would think mathematics is such as sterile profession everybody's so serious you know almost like we're all wearing like lab coats and like take an elevator to the to the every Tower and however look at all this drama look at all these dramas like we also like drama we also have narratives we also have our myths here is the guy is the 16th century mathematician or 17th century mathematician who lives a note on the margin and motivates others to find the proof then how many cards were broken that they believed that they found the proof and then later it was realized that the proof was incorrect and so on and brings us to modern day and one last attempt and reviles who is very serious and respected and esteemed mathematician announces the proof only to be faced with the same reality of his hopes dashed seemingly dashed and like there is a mistake it doesn't work and then to be able to recover a year later how much drama in this one story it's amazing but from what you understand for what you know what was the process for him that uh that is similar perhaps your own life of of 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's 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's 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 be lonely number two he worked on it for seven years if I remember correctly by himself and then then he he thought he had it and he was elated obviously he was you know very happy and he announced it at the conference I think it was in Cambridge University or Oxford University in the UK in 1993 I believe so you know this is really interesting because all of us we can really all weapons can relate to this because I I remember very well my first problem how I solved my first problem uh I described it in 11 math in my book so uh it was I was how old was I I was 18 years old I was a student in Moscow and I was just I just lucked out that I was introduced to this great mathematician since I you know I was not studying at Moscow University because of anti-Semitism in 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 Dmitry Fox who actually later came to the to the US and he's still a professor at the UC Davis not so far from from me uh 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 uh effort you know the that excitement but also kind of a fear what if I don't have what it takes you know I lost sleep so this was one one consequence of this I for the first time in my life I had trouble falling asleep and this actually stayed for a couple years afterwards so then it was kind of like a wake-up call that I should be to take care of myself not work too late 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 it the answer was was in terms of some 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 more this moment when suddenly you see that it's like you in this case it was literally I had to compile these diagrams with what mathematicians call homology groups and spectral sequences and manually calculate some some numbers and trying to discern some system in it and suddenly I saw that how they all were governed by this one one force so to speak one pattern and that was absolutely wow so it's like I mean what was it so 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 Insight came when I was in this and I just I was I had to contain myself so I don't start screaming you know because there were other passengers in the car so I was sitting there and staring at this paper so you know what I remember that what came to me I have something now which nobody else in the world has I have a proof of first of all I did not it was not just the proof like in the case of Irma 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 cured for cancer you know it was not a large language model you know but it was something undeniably real meaningful and it was mine kind of you know like I had it nobody else I had not published it I didn't even tell I hadn't even told anybody and it is a very strange feeling you know to have to have that were you worried that this treasure could be stolen not at the time not at the time so later on there were situations where I was exposed to that those type of experiences but at that time I didn't think of that I was still this starry-eyed kid you know who was just obsessed with mathematics with his Beauty and Discovery 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 uh I just wanted to share it with my teacher as soon as possible you know and and he he understood quickly and he's like yeah 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 um all of that and and creating psychological stressors because of that yes unfortunately on young minds and so on could have a very bad effect is that just the way of life or is this um I think we can definitely do better and I think the first step is to kind of admit that we are not 100 Seekers of truth that we are human beings and all the The Good and Bad and The Ugly qualities um 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 or partially resolved or unresolved and uh 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 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 I don't my experience is not like that at all I think it does happen much more often than it should that's my opinion uh 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 that same innocence you had with when you're 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 are getting older um 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 uh is beautiful because that's where the ideas of old contend with the the new wild-eyed crazy ideas and they clash and there's a tension and it's 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 the strategies um and oftentimes when you look at who wins the Nobel Prize it's also tragic because sometimes so many minds are like the trajectory to the Breakthrough idea involves so many different Minds young and old yeah I mean you're right it's I think it's like every and there was everything else the the through the the path is to more self-awareness and it's like owning up your own stuff and uh 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 physicists and chemists are better they have they actually have better sort of ethical rules and so on special biologists like because I think in part it's because there is much more money involved because they have to get grants and so on so for them the question of priority who discovered what first is much more serious because there's really some serious money mathematics who cares you know that Famous Last Theorem was proved yeah did Andrew Wells become a millionaire no I think they won the prize but those prices are not I think that one was a big price but uh but in general there's not going to keep I think he won the Apple price eventually which is about a million dollars so but you know I 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 a society because it's such a pure subject it draws in very specific uh 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 mathemax 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 um 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 and I couldn't be bothered in some sense for a while it happened up to a point as 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 them reasons why I wrote Love and math was precisely to break that cycle that it's it's the quiet guy in the corner that goes into math and not the flamboyant you know a joke or like you know DJ I wanted to show uh how beautiful this subject is to attract this new blood so that different psychological types and more women uh would join because then they would have students who would look at them and whom they will inspire and then it would be a instead of a vicious circle it would be a virtual Circle and I have to say I think it's happening not because of my efforts on alone obviously there are many other messages 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 not one day all the time I meet I meet these students who say your book is the reason why I chose math as my major and I am proud especially when it's women who tell me this and they are cool 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 this kind of this dumb was broken so now you'll have more influx and once we have people who are more can able to connect at the personal level that's when we also become more self-aware as a community I think and that's when we might be we should be able to have a chance to improve in terms of our ethical rules and stuff like that 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 um ask him about the Russian concepts of friendship science gender and love versus the American you can um so there is a there is a deep Romanticism that you have that runs through your book love and math is is part of that's something you've picked up from the Russian culture what can you speak to that uh fueled both your fascination with math and your fascination no your um your prioritization of The Human Experience of Love hmm good question I definitely there is some influence of the Russian culture Russian literature perhaps you know but also you know like there's so many things um how do you how do we develop certain sensibilities like why do we care about this and not that like why do I care for instance about like you said about this romantic ideals so to 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 it's an interesting question like what is the cause of it so I think that we cannot really know but there are some aspects of it of course the experiences life experiences are um upbringing family like I was you know I was surrounded by Love by my parents on the one hand but in the one on the other side uh perhaps they were a little overprotective of me so I was kind of like you know um too much kind of like taking care of so then when I had it develop certain sensitivity but it was kind of not ready for the challenges the real world of the real world so then that struggle and that and then being lost and then being able to overcome and to learn and then if you do in Universe 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 and then become something important also uh various um difficulties you know the upsetting experiences or one could say traumatic experiences growing up you know in the Soviet Union that was not uh awoken Park you know it was there were a lot of issues there um that I had to go through and and then it doesn't break you make you stronger but in my case what happened was that you know some for some of it it took me 30 years to really come to terms with it and to really understand what happened he gave me this motivation um to to strive to become a mathematician which maybe I wouldn't have otherwise it charged me supercharged me I'm talking about for instance the experience with exam at Moscow University can you take me through that experience so this is 1984 we spoke about Orwell earlier and I was applying to Moscow University mathematics Department it's called Muhammad 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 interesting one of 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 evgenie evgeny which converted me into math capitalizing on my love for physical 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 and some in some subjects a level of like early graduate Graduate Studies so it seemed like it would be a breeze to go to get into Moscow University but in fact little did I know that uh there was a a policy of anti-Semitism where students like me would be failed by special examiners mostly during the oral exam with mathematics but um occasionally 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 too to read what my nationality was and so there was this can you imagine there were special people who would screen up applicants who would put aside the files of the undesirables 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 reason other than just hatred of the other that's how I see it and just to give a little bit more color so uh because you mentioned nationality it's a little uh Quark that perhaps gives an inside to the bigger system that the nationality listed on your birth certificate when you're Jewish is Jewish and when you're non-jewish is this is Russian for me it was Russian so first of all in this in the inner part everybody has an internal passport and there you have first name petronic name last name date of birth so these are four and the fifth colon is nationality which comes from the nationality of the parents and so on in my case was written Russian because my mom was Russian but it didn't save me because that was my dad's last name and so so anyway this was a a toughest experience that I had a bunch up until that point and there was these 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 uh question you we're waiting for special examiners so I was like oh something is a food and so these two guys came and it's for four hours basically and were asking me questions which were not in the program and so on but you know I was a kid I was 16 years old I tried to answer the best I can but it was a setup it's been documented since then there are even lists of problems that were given to undesirables in those days in my year um no no Jewish applicants as far as I know Jewish by this metric were accepted so then I had to go to this um there was one school technical school in Moscow which was the institute for oil and gas exploration which had a Applied Mathematics program and that's where me and many of my 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 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 that I neglected this time and I realized that he died that it was a crushing blow the Innocence not just instance because there was no way it looked like there was no way I could become a mathematician because if I don't if you don't accept me there it's over I didn't know that I could actually find this striving applied math program and then eventually somebody would take me under his wing and so on and then could move to the United States this was not in the realm of possibilities so in other words I could there was nothing to look forward to it was clear that it's over I cannot I cannot do what I love and so when I finally when I finally connected to that boy oh my God that was a totally different experience all the pain and all the trauma came to the surface and it was a kind of a tsunami I didn't I wasn't sure I would survive this so it was so hard and what happened was I was invited to to give a talk about this in New York it was kind of a spoken word event uh 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 a chapter about this experience but what I realized now is that I wrote it from the third person perspective I knew the facts but I was not emotionally connected to that experience however since I wanted to write the book and to connect to my readers I allowed the boy to write it so a lot of people were touched by it and they would people would say wow that chapter you know it really got a lot of resonance it was translated into other 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 um almost a year later I'm in New York in this at 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 it's just you know my usual like 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 it's like but by that time I already had an Insight that it's possible to have that kind of a splitting kind of dissociation I was not but if 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 so 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 so we'll go tomorrow and 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 in front of people I want to find out what it is what happened and I sat on my bed closed my head 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 in Russian you know that that hardcore you know around myself yeah so that and the thing later I realized there were moments when it could come out and for instance I developed this fear of public speaking and 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 the rose Rose Colored Glasses but then something happened it's so strange it's like you feel that inside of you there is this dead child and it is incredibly sad I mean it's like I can't even describe it but suddenly he comes alive and suddenly it's like oh he's here and I and I got a little talk with him and I said look you know I know now and thank you I'm so sorry that I neglected you for so long you know I didn't know thank you for doing this and it's almost like you know 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 and I said but look look what we have done look at us now it was not in vain we are doing okay and it's kind of almost just like holding holding holding that child and that 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 because it is a story it's a 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 so 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 they were 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 those of that possibility of looking at the World Through The Eyes of a child because that child was frozen in time it was I was not connected to him but suddenly he's with me and he's like almost like opens his doors and says look good look at this look at this so 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 uh this experience of unfairness and cruelty in the world as young people and what wisdom do you draw from the the the the action you took of not acknowledging that you're a victim to Cruelty but instead just working your ass off working harder and then this the flip side of that is you eventually reconnecting with the cruelty that you experience because if you did that early on I was not ready for it it is a defense mechanism I could be I could have come you know there were kids who commit suicide after this experience I could have commit 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 I've been speaking publicly about it since then too and so you know it is well-known issue and well-known um kind of a universal phenomenon I think that interesting enough even though one 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 I developed certain force a certain strengths I was confident um 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's 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 to kind of understanding it's really just personal stories it's not obviously there is a 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 not from professional therapists but from like dear friends so I did 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 it 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 they fell for this bogus series or maybe it was more of a issue of career advancement or something and I also realized they must have suffered as well because they must have had some kind of consciousness of conscience about it that acting this way towards sort of basically kids you know so it's not it wasn't pretty from their point of view so I could forgive them and I could like also appreciate what a what a boost of energy it gave me yeah if I was accepted and I was just where I was a first-year student I lived I would live in a dorm because I was in the you know I'd be probably partying and drinking and 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 just I couldn't do I didn't care about anything but doing mathematics and it paid off you know it changed my life so was it good or bad Paradox seems like life is full of those um you said you lost your father four years ago yeah what have you learned about life from your dad that's another another big one yeah because I was very close to him and uh it was tough it was tough and I was not I was sort of not ready for it because up until that point I lived pretending that death does not exist when my grandparents died I was already in the U.S so it's 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 their dead bodies you know I didn't bury them and so on so I waited till so my the first death in my life was my father like of 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 it's really funny and just really fun to be with you know this is what I miss obviously I mean I would just love to hang out with him so and then suddenly it's not there so it's tough but it kind of changed my perspective you miss him I miss him tremendously I miss intermittently but I 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 um do you carry him with you yeah and in some sense I always did and and I I saw that that it's always been um it was really we were one in some sense you know like we were but there was this experience of two 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 Gulag on bogus pretenses right so he when he was 16 he replied to University he wanted to become a theoretical physicist by the way my love for trichophysics was to 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 technical school and he didn't really care that's my take on it and then he ended up in this in this in this little provincial town and he thought he would escape from it as soon as possible and then he met my mother and I fell in love and so I am sort of the product the product of that you know of physics but then what I learned is that because he was not able to overcome that specific experience it felt 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 our about the same age for slightly different reasons I was subjected to the same kind of unfairness and cruelty and I in some ways I 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 it was in 2012 and in 2018 and both times they were in Boston it could be anywhere in the U.S both times was in Boston walking distance from my parents place so he could be there with 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 know like I was still at my mom I still have my sister yeah but as a man yeah there's some aspect that it's um that it does hit you hard um 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 um conceptualized like that experience like he could not give it to somebody one thing I will say is that I felt that what it was it was actually love totally exposed like naked and you try to throw it is so acute so being facing that love is incredibly painful because it's so intense one person is alive we we have conversation we have wars we have some actions we have some stuff is going on and it puts a filter so you we rarely actually feel love and it's totally completely pure and adulterated 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 immediately like boom gone it's there live through it and I was I kept saying to myself I just live through it live 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 and then you kind of learn that okay so maybe it's not quite there is more to it the more there is more to eat there's more to this experience than what can be put in a concept or in a in a in a sentence in this 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 being this playing this role I love it and I kind of like 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 it's being terrified it's being frustrated it's being self-loathing sometimes it's not knowing but also being joyful and just like ah let's just enjoy it kind of all of it like that's why you came here for in some sense you know it's like not trying to run away from things but kind of trying to just live through them and appreciate so the biggest thing is gratitude in some sense it's just gratitude so thank you for letting me play this is gratitude for every single moment even if it's dark even if it's a loss and that's why I am so people around me they will say the 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 like 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 uh we've talked about love but let me ask what role does Love play in this whole game in The Human Condition it's like the glue you know it's like for me it's like that it's and it's not because people say love is like um for a human being like a romantic love yeah which is huge a component of it obviously because so so beautiful to be able to to express it in this way but it could be love for what you do for your passion for something you know and uh or uh or love for for your for your friends for instance or love it doesn't have to be and so in some sense that's that's what it's all about in ultimately because Living Without Love it's kind of Bland boring and so I don't think it's possible for science to explain exactly what it is you can do uh evolutionary biology perspective you can talk about some kind of Sociology perspective psychology perspective but the experience where you forget or time we're reminded becomes an illusion and everything just freezes oh my God and then uh 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 they weren't 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 Rey Kurzweil I respect and I feel and I almost like I I feel good bumps right now I feel that desire to reconnect even if it is in the form of a you know a computer program let's be honest about it I find it to be very moving I find it very moving and I understand because he actually didn't have a chance to spend much time you know I think he was 16 or 17 when he's he was a teenager he's dead I was lucky because my father died I was 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 everything I have I give it away right now yeah where do I sign yeah just see him for one hour I promise you I will but I also know that I it 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 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 man to hold on but I'm questioning it now like is there another way to approach life where you just you know how Buddha it's like just let it go enjoy and let it go enjoy and let it go is it possible except the Paradox of it well ask me in a couple of years you know I will report but I think that it but to my mathematical mind yeah it sounds like a very interesting idea to be honest because to me the idea of holding isn't it sounds like an impasse because no matter in all my experience and if you look in history every time somebody's holding you know it's how they said in The Matrix whatever has a beginning has an end it's like you cannot go around it if you have a beginning you could have an end so then might as well just enjoy it and not worry too much about extending it longer that's how I see it now but maybe tomorrow will be something else you know yeah the roller coaster life the Paradox of life right Edward you're an 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 uh both one of the greatest living mathematicians and still childlike Wander of the uh exploring the how this whole world works the the nature of the universe and thank you so much for speaking with me today this is amazing been a pleasure thank you thanks for listening to this conversation with Edward Frankel to support this podcast please check out our sponsors in the description and now let me leave you with some words from Sophia kalalevska 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