 You're listening to the OIST podcast, bringing you the latest in science and tech from the Okinawa Institute of Science and Technology Graduate University. My name is Andrew Scott. It's a rare treat to be able to share this interview with one of the most engaging mathematicians around today. Tadashi Tokyeda is currently a professor in the Department of Mathematics at Stanford University in the United States, but he started his fascinating career as a painter in Japan. He then moved on to France to study philology, and by the early 90s he'd earned a bachelor's degree in mathematics from Oxford University and the PhD from Princeton a few years later. Professor Tokyeda visited OIST at the start of November, where he gave an excellent talk about the strange physical properties of a collection of otherwise everyday looking objects. As an example of informative and entertaining science communication, his lectures are well worth seeking out, or failing that, his collaborations with the YouTube channel Numberphile. If you're looking to spark a bit of fascination with the world, you won't go disappointed viewing them. I sat down with Professor Tokyeda after his lecture for an enthralling chat that would take in mathematics, child prodigies and how language frames science amongst many other subjects. I hope you enjoy it. Can you tell me a little bit about the lecture that you gave us? I'm not going to tell you anything about the lecture that I gave you for the good reason, and in fact this is an important point, that you see it's like telling the punchline of a joke and then trying to explain the joke without actually telling the joke. Life is very short and the universe is a wonderful place, and there is so much to see and so much to experience and so much to become more intelligent about. And the only way you can do it is to have your personal, however modest, your personal experience of various phenomena, various happenings, and various events. And telling about something, this is a meta comment about something, instead of doing the actual thing is the worst way to approach science. And I'm not going to tell anybody about this and deprive them of the pleasure of seeing the phenomenon themselves. If you want to, this is a kind of replacement substitute. You can Google my name and the number file, there are lots of videos that they put out online, thanks to the number file, of various phenomena and really magical effects of those curious objects and so on, and you can watch this. Even that is only a substitute. There's nothing that replaces your own touch, trying things yourself and indeed noticing curiosities in nature yourself. So okay, watching videos is much better than a stupid person like me telling you about this, that's really the worst possible way to proceed. But even watching videos is no good, you should really try those things yourselves and indeed discover some things yourself. There is so much out there. And let me add something that I didn't say last time. People say, well, discovering things difficult and extracting science from everyday life and in the mundane effects and so on that requires talent and special aptitude and so on. I believe that's wrong for the following reason. The reason presupposes a certain belief and outlook on the universe. My outlook is, well, people say, well, I don't like science. That's fair enough. Some people don't like science. And I like science, but I get tired after a while and I can't continue for some. That's very, very reasonable. All, I try very, very hard, but I can't get through some difficulties. Well, that's more human than that, sure. But it's true that however fragile and however weak humans are, there is actually one, shall I say, creature, a sort of morphically speaking creature who keeps practicing in science very, very successfully. In fact, with 100% success, 24 hours a day, seven days a week with no stop and has been doing it for ages and ages and everywhere you go. And that's nature herself. Nature is doing everything in perfect harmony. And in fact, wherever you see, whichever you look, there's some phenomenon that happening. And there are thousands and tens of thousands of laws of nature that have been satisfied at the same time. And many of those laws of nature are yet unknown to humans. But it's amazing how coordinated nature is. It's working all the time. So even when you are fed up and when you close your books and your professor leaves the room and you go into vacation time and your internet is down and so on, you think that science stops existing and it stops existing for humans. But nature keeps going. The other side of this observation is that therefore, whichever you look, as I said, and whatever you listen to and wherever you cast your mind to, and in that part of the universe that you are observing, nature is doing something. So nothing is easier than to discover than science because science is happening all around you. It's just a matter of opening up your mind a little bit and making a little bit of effort. And indeed, you have to have an eye for surprises, but humans are born to be surprised and programmed by mother nature to be curious about things. So you just pay attention and pause and then you relax. And especially you shouldn't worry about what other people think and what your social standing is. If you are interested in something, it's interesting. And if you're not interested in something, it's not interesting, but you should just keep looking and everywhere you look, you reach out with your right arm, you reach out to your left arm, you stick out your left foot and right foot. Everywhere you reach, there is a bit of science in there. And so you just meet science all over the place. It's very easy. So starting your career as an artist and then going on to philology and then coming into mathematics obviously is not the standard path into science that most people in the career do. But I think it gives you a very different perspective from a lot of people who have taken a more traditional path. Is there any lessons that you've learned along that way that has changed your approach to science? I should mention one thing. Maybe not everyone knows the word philology. People used to know this, but it means the level of languages. But more specifically, the study of languages. Some people call it linguistics, but the nuance is quite different. Linguistics, especially Chomsky and that school, became very analytical and almost mathematical. I'm absolutely not interested in universal grammar or analytical study of languages. Absolutely not. I'm a mathematician and if I want to do that kind of thing, I'll do just mathematics, straight mathematics. Instead, philology in the glory days of the 19th century meant primarily the reconstruction of the Indo-European family. So people knew lots and lots of languages and their peculiarities and their accidental evolution in Greek, Latin, Sanskrit, and that kind of thing. And of course, he was practiced outside this Indo-European family for his notably Semitic family, especially languages that have a lot of written records that go way back. You can do science. So that's what philology means and that's what they used to do. But I do emphasize that I'm not at all, absolutely not interested in mathematical aspects of linguistics. I'm interested in the languages themselves and I still am. Okay, that's the explanation of philology. Well, what about the unusual background? Okay, you say unusual background, but I do believe that the unusualness or usualness is in some sense the eyes of the beholder or to be precise of the external beholder. What I mean is, it's a bit to try to say, but every human life is unique, especially seen from the inside. You might look like a boring doldrums and the standard kind of path to somebody else, but for each individual, that person is living only once and they're unique experiences and the experiences are not replaceable by anything else. And so I'm not sure that my experience is qualitatively different from other people's experience in that way. I mean, people struggle through various difficulties and have moments of joy and moments of discovery and sometimes they get fed up and they want to leave and then sometimes they come back and so on and so on. Okay, so I don't think it's that different. And the reason I'm telling this is, people should realize that their experience is unique and it's interesting if you make it interesting. I mean, if you decide that, oh, I'm a boring person, I'm a boring person, of course you become ifsofactor a boring person and other people will not help you out. They'll say you're boring, but you live only once and you have, I'm sure that there's lots going on in your brain that the rest of the world cannot see naturally and you should cherish it and that's unique. But one lesson that I drew from coming in from perhaps lots and lots of details, well, I'm not gonna tell you any lesson because I think it's up to you to discover, but let me kind of describe the other side of the coin. So clearly I started doing mathematics seriously quite late in life because I used to do something else. And that had interesting consequences. And again, I'm sorry to keep doing this, but I'm not going to describe those consequences, but let me describe the other side of the coin or the other side of the coin which sounds like the initial side of the coin. Most people in mathematics came into mathematics early. They say, well, typically in your teens, maybe age 13, 14, 15, you get really interested in mathematics and you start doing it. And the important point I'm going to raise and something that is for all of you to think about is that the phenomenon of child prodigy exists as far as I can see only in music and in mathematics. It's very difficult to think of child prodigies in other fields of human endeavor. For example, it's absolutely, it's clearly ridiculous to think about child prodigy in history, right? I mean, of course, no such thing exists. Or indeed in even in sports, I think the only sport where child prodigies can be argued exist is gymnastics. But that's not quite the same because now there's gymnastics for various reasons, not all of them desirable, started lowering the age. That means that young children perform very, very well. But when they grow up, they stop being able to perform because of various physical reasons. So that's not really a child prodigy phenomenon. It's just saying that the optimal age is low. And the child prodigy should mean, for example, like violinists and so on, that a child can do something that adult performers who are also professionals can do and even sometimes better and that's amazing and so on. And those child prodigies can continue to grow. And then when they become adults, they are also very competent performers and so on. I used the word performer. That's because I think child prodigies exist primarily as performers and the mathematical equivalent is problem solvers rather than theory builders and the music equivalent would be composers. It's truly Mozart was a child prodigy in composition. But on the whole, I think performers and problem solvers, the dominant types of child prodigy. And it's interesting, I think, that this phenomenon of child prodigy exists only in music and mathematics and correspondingly, people tend to come in quite early into music and mathematics. So that's a very interesting phenomenon to describe, which I would appear to suggest that these abilities to decode the structures behind music and mathematics might be innate in us or at least an evolved trait. Yeah, it's interesting. So I have no idea. One thing that is true, however, is that innate or not innate involves a lot of training. And the child prodigies are in some sense, well, maybe there's such a thing as talent, you know? But one necessary condition for a child prodigy to exist is the, shall I say, the temperament that could bear with long, long, long hours of enormous amounts of training. And sometimes it becomes an obsession. Well, by the way, in case somebody is going to raise an objection, yes, yes, I'm aware that the child prodigies exist in chess and Shogi, there's in fact a very famous Shogi player, Fujii, who's a high school student now in Japan and who's beating all the masters and then go and so on. But that's if you like a small variation on mathematics, right? I mean, in some sense. So that's part of what I'm describing. So I don't know about inertness and in fact I'm not entirely sure about what people call talent. You know, of course, I think human brain is a very complicated machine and it would be very surprising if there is no innate difference between one brain and another brain. After all, there are lots and lots of innate differences between one body and another body, right? But it's true, I have seen lots and lots of mathematics students in my own field and who are very talented and so on, so on by the standard judgment of the society. But ultimately, it seems to me that, again, on the whole, I'm simplifying. But ultimately, it's really the effort and how much you really like the subject that made the difference as to ultimate success. So I'm not such a great believer in talent. Maybe I'd rather use the word temperament. You see, because I found the, I'm digressing from your question but that's kind of the point of this interview. I find that people talk too much about genius and correspondingly to the phenomenon I mentioned of child prodigy in music and in mathematics, they talk about genius all the time. That's a dangerous word and I'm not sure that it's socially beneficial to talk about genius whether it exists or not, yeah? So I'm saying, well, maybe scientifically you can discuss the concept of genius but it certainly does more damage sociologically than it does good. For example, it's possible to argue and please don't shoot me that, well, you know, of course there are wonderful musicians and let's talk about Western classical music but wonderful musicians nowadays, obviously but they're all performers. Okay, okay, they're wonderful composers but don't we agree that compared with the time of Bach, Mozart and Beethoven, a composition in classical music has gone down, right? On the whole. I think it's a fair assessment. I'm a lover of classical music but I think that's the assessment and it's possible to argue that the concept and the belief in genius killed classical music composition. It's extremely discouraging to be told, oh, you shouldn't compose unless you can be Beethoven, yeah? Because the basic, the concept of genius is an invention of the German idealistic philosophers. People didn't talk about genius before and people simply didn't have the concept and it wasn't part of people's thinking. So look at, for example, Italian baroque composers. You know, they didn't care about talent or genius but they're creating wonderful music just on the spot and, you know, they don't have to be tragic, they don't have to have a dramatic life. No, no, no, you just do it because you like it and the same with mathematics. I can say, you know, I'm fortunate enough to be friends and personally acquainted with some of the leading mathematicians of our age but I can say that I have never met a genius. They are all understandable. They are wonderful, wonderful people and they really loved what they're doing and their creations really, you know, open up a whole world for you and so on. But I don't think I ever met a genius. So it's, anyway, in practical terms it's much more useful to focus on other things. So that's why I'm skirting around your question of innate ability. So Oist, to go on on to a different track a little bit. Oist is by definition a very, very multicultural, multidisciplinary institution. And I'm wondering, as someone who has kind of done the opposite and sought out the world and worked in science across it, have you noticed a universality to the science that you see or is there like local variations and if so, how does that affect the approach to science in these different places? I think it's fair to state my predilection, let's say, my position in this kind of thing. Because I have lived in many countries and some of you might have heard the rumor that I know an insane number of languages and so on. And you might think I'm an internationalist but it's the contrary. You see, just as many people quite correctly worry about biodiversity, I get really emotional and upset about the whenever linguistic diversity, in particular, and cultural diversity in general, decreases, is threatened. And I do believe also that the history of evolution tells us that evolution happens and you get interesting diversity and interesting life forms because of speciation. Whenever diversity decreases than the one single species or single idea or single way of doing things that's taking over, usually the world is headed for destruction. Well, it might be because monkeys that I call them humans might do some optimization calculations because in their foolishness. And they say, oh, you know, we obtain this. And that means that we have to do it this way. Every one should be behaving this way and so on and so on. And then they end up doing this. And in some sense, invention of money doomed us to go in that direction. But I do believe that that way lies madness. And in fact, for me, madness means that you abandoned diversity and you started doing every one started running in the same direction. And that's really dangerous. So I am actually a great partisan of people doing things their own cultural ways. And I don't want, for example, English to take over the entire world. And of course, you know, people say, but unless you write in English, you don't get much readership and then that's necessary for your tenure and for your promotion. Ah, yes, yes, we are talking about the same problem, right? Okay, so who can blame the young people for worrying about this kind of thing? But after I got the permanent position, I decided, and I always wanted to do this, to publish in languages other than English. It puts me in mind a little bit of some philosophy I read quite lightly, I have to admit, that said, something along the lines of that, language frames our perception of reality. Would you think that is true for our perception of science? Does language give a certain bent to the approaches that certain people speak? Well, on a superficial level, yes. In the sense that the different cultures, at least until recently, used to do science in different styles. Let's say, mathematics, which is supposed to be the most universal of these, because of course, if you do zoology or geology, things like that, which are geographically constrained, different countries might do things differently, but mathematics is indeed as universal as any human endeavor can get. But nonetheless, if you read, and apart from, of course, the language in which it was written, it's a giveaway, but the Russians write mathematics in a very, very different, write and think mathematics in a way very different from how Americans thought and wrote, and then French wrote mathematics and thought mathematics in a way very different from how the Japanese did and so on. And you could tell instantly which school, which culture it came from. And so much later, I would say. Another thing that I would say about language and mathematics and how the former friends later, it's a bit of the topic that you have in mind is pedagogical. Many people say, oh, mathematics is very difficult to learn, and sure it is, and it's probably one of the most difficult things that you can say. Besides, human brains are not really well adapted to mathematics, it's designed for doing other things. But a lot of mathematical difficulties that people encounter in mathematics are actually linguistic. For example, this is a bit too technical, but there's a definition, very, very precise way of thinking about the limits and continuity and so on, which goes under the name of epsilon and delta. So for every epsilon, there exists a delta such that, and blah, blah, blah. And this is a stumbling block for almost everyone. But when I came into mathematics as an adult already, you know, I taught myself mathematics, and when I came to epsilon delta, I felt no difficulty whatsoever. In fact, I didn't even notice that if it was supposed to be difficult. That's because I had been very rigorously trained in the use of languages as a linguist. And so, the idea that if you change the order quantifiers, of course the meaning changes completely. It was trivial, of course. I mean, compared with a task, difficult task of taking apart the syntax of, say, somebody like Fusilides, you know, whose sentence can continue for a page with subordinate clause upon subordinate clause. By the way, he writes really clearly, but in a complicated syntax. Well, compared with that kind of thing, the language of mathematics was very, very easy. I mean, there was nothing to it. I think the fact of matter is most people don't have sufficient mastery of their native language. They never had the experience. They don't have had enough, shall I say, a bit more gently, enough practice of careful use of their own native language. You know, do you speak really carefully, making sure that you understand absolutely everything that you are saying, and every word and every phrase counts? The answer is no, the people just blah, blah, blah, just talk away. So, if you have a really careful habit of careful use of language, it's my personal belief that most of the difficulties in mathematics will go away. And it's just that mathematics is an unforgiving subject where any misunderstanding, any lack of understanding shows immediately. Whereas in the rest of human endeavors, you can keep going by faking for quite a long time. So in that way, yes, the language frames how you understand mathematics, but in that very, very practical way, I think the best way to improve your chance of future advancing mathematics is to practice and improve your native language. I'll say, having viewed your lecture earlier today, it's that you're a very, very skilled science communicator. You ever make your subjects very accessible and exciting for an audience. What is your kind of approach to coming up with your communications philosophy? Again, I don't believe that I'm a good communicator, and I believe that lots of other people are simply very bad communicators. And the reason is I don't think other people are thinking. It's completely common sense. I have no intention of claiming any credit for what I do. If you think this passionately, and if your agenda is not some of the things that I described earlier in the interview, but if your agenda is to share surprises and to share, if possible, some of the joy and to make people understand, there are obvious things that you can do. And I'm very surprised that people are not doing it. And it's absolutely obvious to anybody. Well, think of it this way. If you just came back from a very nice trip, lots of adventures and lots of wonderful experience and so on, and you are relaxing one evening, shortly after you return with your family, and you tell the stories. Your family are drawn in, OK, they're on your side. And then you tell stories very well. And I can already hear, imagine hearing laughter and then clapping hands and gasps of breath and so on. Well, you are communicating very well because you have a certain agenda. And as an intelligent human being, you are communicating properly. Well, you do the same thing with science. It's not difficult at all. Absolutely not. It's, in fact, the onus is on the other side. Why are people so incompetent? Well, I can answer that question. I have answered the question a long time for myself, and I'm going to repeat myself. That's because their agenda is somewhere else. And now I'll be much gentler and compassionate. Who can blame them? Because as humans, you want to live a comfortable life. You want to have some position of socially recognized position, and of course, security and all that kind of thing. And this society requires that you communicate in a certain way, which is not at all, not at all the way science should be communicated if your agenda is not one of those. What still excites you about the work that you do? Now, that's also a curious question. You probably have been finding it unsatisfactory that I never give a straight answer. But you see, lots of people talk about, oh, that's a common question. What's exciting about your work? For example, when you write a research grant or something like that, you're supposed to describe what's exciting about your project and so on. On the other hand, there are lots of things that one does, which are essential, indispensable for survival, and which is foundational for everything else, about which people never ask, well, what's exciting about it? What's exciting about breathing, for example? You breathe every day, every hour, every minute, every second, you breathe. And if you stop breathing, you are no longer. What's exciting about it? It's not exciting, but I do breathe. And then, if there's fresh air, I enjoy breathing. And if it's all smoky, as it happens in California when there are wildfires, then you don't enjoy breathing. So you are aware of breathing sometimes. It's not that you're completely unconscious, you're invisible, but you don't ask that question. What's exciting about indeed living itself? Of course, there are ups and downs. There are dramas in life. But people don't live because it's exciting. People live because it's natural for them, because that's what they want to do, despite everything sometimes, or in some lucky cases, because of some things. But people live because it's a basic and natural way of existing as humans, as indeed biological creatures. And I would say that the scientists, when they are unhampered and unencumbered by those dictates of sociology, where you have to publish in certain ways because you want to enhance your career, because you want to achieve some status, because you want to ensure you have a certain standard of living. And so if they are doing science, where they do science, because almost they have to, because that's their existence. And for myself, I would say, I'm sorry to be a bit sentimental, but if I lost my job and I have to be able to live somehow, but let's say I assume that I have some kind of income, and I have to move to Antarctica and living in isolation, I think after, of course, the initial period of being, I'm really depressed and so forth, and why am I stuck here and so on, I think I'll end up doing science, because that's who I am. That's a question you've always wanted to be asked, but never have, and what's the answer to it? I would say it's a good question, I have the exact answer to that once. The question I wanted to be asked, and which I have never been asked, is what is the question you have been wanting to be asked, but you have not been asked? Professor Tokiira, thank you very much. Thank you for listening to the OIST podcast. Special thanks this week to Professor Takashi Tokiira. If you enjoyed the podcast, why not let the world know about it by leaving your rating or a review, and don't forget to subscribe to be updated whenever we release a new episode. Thank you for listening and see you next time.