Japanese mathematician
(Japanese: 時枝正; born 1968) is a Japanese mathematician, working in mathematical physics. He is a professor of mathematics at Stanford University; previously he was a fellow and Director of Studies of Mathematics at Trinity Hall, Cambridge. He is also very active in inventing, collecting, and studying toys that uniquely reveal and explore real-world surprises of mathematics and physics. In comparison with most mathematicians, he had an unusual path in life: he started as a painter, and then became a classical philologist, before switching to mathematics.
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Nature is doing everything in perfect harmony... [W]herever you see and whichever [way] you look, there is something fundamental happening, and there are thousands and tens of thousands of laws of nature that are being satisfied at the same time... [M]any 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 you close your books, and your professor leaves the room, and go into vacation time, and your internet is down, and so on, you think science stops existing and it stops existing for humans, but Nature keeps going.
In science we... tend to be interested in things that have been already labeled "interesting." ...[W]e ...think science happens in institutionalized contexts, and that the latest fashions and the "cutting edge" ...is where science occurs... [P]eople who get interested in science often read... books that tell you about the cutting edge... and they get excited, but it's not that they have had an intimate contact with science and got excited. It's rather that sociologically they have been told to be excited about something that's supposed to be exciting. ...They haven't had any exposure to "theory X" but they... are told hero stories... romantic stories... But those... "sciences in flower"... are already blossoming. ...[T]hey have lots and lots of intricate structures up there and [are] connected to lots and lots of things. But at the same time, as with plants, we should look at "sciences in sprout." ...We have the impression that when we stop doing science and go on holiday, or close up our offices and shut down the laboratories for the weekend, science stops happening. And when you close the textbooks and the professor says, "OK, end of class!" you can forget about science... and it stops happening. But that's not true. There's something that keeps practicing science 24 hours a day, 7 days a week, nonstop everywhere in the world, everywhere in the universe, and that's called Nature! If you take... even this blob of air in front of me... there are so many beautiful and intricate and unbelievably complicated, complex s that are dancing together and trying to satisfy one another, and succeeding and satisfying this huge... network of patterns. That is science! It's amazing, and conversely, there is nothing easier to discover than science. ...Everywhere I look, there must be science, because we live in this universe. We cannot even escape living in this universe. We need... imagination and a little bit of patience because you often fail, but especially... we need to look, imagine and maybe a willingness to be trained in acquiring better vision, which is called scientific education. ...It's wonderful that people get interested in science because they're supposed to be interested in science and read... and so on, but that they also try in daily life, phenomena around them, however modest. It would be nice if they started noticing sciences in sprout.
I don't believe that I'm a good communicator. I believe that lots of other people are simply very bad communicators... 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, and if you think this passionately, and if your agenda is not some of the other things I described earlier... [I]f your agenda is to share surprises and to share, if possible, some of the joy to make people understand, there are obvious things that you can do... I'm very surprised that people aren't doing it... [I]t's absolutely obvious to anybody.
[J]ust as many people... correctly worry about biodiversity, I get... emotional and upset... whenever linguistic diversity in particular, and cultural diversity in general, decreases... is threatened... [T]he history of evolution tells us that... you get interesting diversity and... life forms because of . Whenever diversity decreases and one single species or... idea or... way of doing things starts taking over, usually the world is headed for destruction. ...Monkeys that call themselves humans might do some optimization calculations... in their foolishness, and they say, "Oh, ...we have times this ...and that means we have to do it this way. Everyone should be behaving this way..." and so on... [T]hen they end up doing this and in some sense the invention of money doomed us to go in that direction. But I do believe that that way lies madness. ...[F]or me, madness means you abandoned diversity and ...everyone started running in the same direction, and that's really dangerous. So I am... 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.
If you... came back from a very nice trip... Lots of adventures and lots of wonderful experience... and... relaxing one evening... with your family, and you tell your stories, your family are drawn in... I can already...imagine hearing... laughter and... clapping hands and gasps of breath... [Y]ou're communicating very well... [Y]ou do the same thing with science. It's not difficult at all. Absolutely not! In fact the onus is on the other side. Why are people so incompetent? ...[B]ecause their agenda is somewhere else and... who can blame them? ...As humans you want to have a comfortable life. You want to have some... socially recognized position and... security... and the society requires that you communicate in a certain way, which is not at all the way science should be communicated, if your agenda is not one of those.
[T]here are lots of things that one does which are essential, indespensable for survival and which is foundational for everything else, about which people never ask... "What's exciting about it?" What's exciting about breathing for example. ...[I]f you stop breathing, you are no longer. ...You're aware of breathing sometimes. It's not that you're completely unconcsiously invisible, but you don't ask that question. What's exciting about... 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 and 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... [S]cientists, 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 on. If they are doing science where they do science because, almost, they have to, because that's their existence... If I lost my job... I have to be able to live somehow, but let's assume that I have some kind of income, and I have to move to and live in isolation. I think after... the initial period of being really depressed... "Why am I stuck here?" and so on, I think I'd end up doing science, because that's... who I am.
Draw pictures, draw pictures! As a guideline, when I do research in any area (fluid mechanics, geometry, dynamical systems, topology, combinatorics, representation theory), I always draw pictures when I'm doing research. I'm drawing one picture every few minutes, so by the end of the day, after maybe six or seven hours, I have maybe 30, 40 pictures, if not more. So in a week that's hundreds. You should be drawing lots and lots of pictures, trying lots of pictures. Some of these pictures can be in your head, but you should start by drawing lots of real pictures, on paper. But not a few pictures. Not tens of pictures. Hundreds of pictures, please, hundreds. Because that's how we can, eventually, listen to Mozart's music - in mathematics!
I'm fortunate enough to be friends and personally acquainted with some of the leading mathematicians of our age, but... I have never met a genius. They are all understandable. They are wonderful, wonderful people, and they really love what they are doing, and their creations... open up a whole world for you... but I don't think... I ever met a genius. ...In practical terms, it's much more useful to ...focus on other things. So that's why I'm skirting around your question on innate ability.