Tadashi Tokieda Quotes

[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.

It's possible to argue... [T]here are wonderful musicians, let's talk about... western classical music... nowadays... but... compared with the time of Bach, Mozart and Beethoven, composition in classical music has gone down. ...It's possible to argue that the concept and the belief in genius killed classical music composition. It's extremely... discouraging to be told, "You shouldn't compose unless you can be Beethoven." ...[T]he concept of the 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. ...[L]ook at ...Italian Baroque composers... They didn't care about talent or genius but they're creating wonderful music... just on the spot. ...[T]hey didn't have to be tragic. They don't have to have a dramatic life. ...You just do it because you like it, and the same with 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.

When you learn mathematics, you learn a lot of definitions. And let's say that you have a certain number of definitions - maybe you learn 100 definitions. Also, there are a number of theorems, and a number of examples to which the theorems apply. Now, a good piece of mathematics should have many more theorems than definitions. And you should have many more examples than theorems - that's a good situation. Unfortunately, everywhere in the world, it happens that in textbooks, in classrooms - You learn 100 definitions (you have memorize definitions!) And then you learn 10 theorems;
And then there is only one example.
It should be that you have one definition, ten theorems, and 100 or even 10,000 examples to which the theorems apply.

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.

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.

[E]very human life... is unique, especially seen from the inside. ...You might look like the boring doldrums and the standard... path to somebody else, but for each individual... that person is living only once, and unique experiences... are not... replaceable by anything else... I'm not sure that my experience is qualitatively different from other people's... [P]eople struggle through various difficulties and have moments of joy and... discovery and sometimes... get fed up and... want to leave... [T]hen sometimes they come back and so on... I don't think that it's that different. ...People should realize that their experience is unique and it's interesting, if you make it interesting. ...[I]f you decide that, "Oh, I'm a boring person..." of course you become, , a boring person... [O]ther people will not help you out. They'll say you're boring, but... you live only once, and... I'm sure there's lot's going on in your brain that the rest of the world cannot see, naturally... [Y]ou should cherish it...

Watching videos is much better than a stupid person like me telling you about this, so that's really the worst possible way to proceed, but even watching videos is no good. You should really try those things yourself and... discover things yourself. There's so much, so much out there.

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.

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]t'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. ...[T]he best way to improve your chance of future advance in mathematics is to practice, and improve your native language.

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.

[L]ife 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... [T]he only way you can do it is to have your personal (however modest)... experience of various phenomena... happenings and... events. ...[T]elling about something (this is a meta-comment about something) instead of doing the actual thing, is the worst way to approach science... I'm not going to tell anyone about this and deprive them of the pleasure of seeing the phenomenon themselves.

Different cultures... until recently, used... science in different styles... [M]athematics, which is supposed to be the most universal of these... If you do zoology or geology or things like that which are geographically constrained, different countries might so things differently, but mathematics is... as universal as any human endeavor can get... [N]onetheless... the Russians... write and think about mathematics in a way very different from how Americans thought and wrote, and the French wrote... and thought mathematics in a way very different from how the Japanese did, and so on... [Y]ou can tell instantly which school, which culture, it came from.

Many people say mathematics is very difficult to learn, and so it is, and it's probably one of the most difficult things that you can learn, and 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... are actually linguistic. ...[T]here is a definition, a 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... [T]his is a stumbling block for just about everyone, but when I came into mathematics as an adult... I felt no difficulty whatsoever. In fact I didn't even notice that it was supposed to be difficult. That's because I had been very rigorously trained in the use of languages, as a linguist. ...[S]o the idea that if you change the order quantifiers, of course the meaning changes completely. It was trivial, of course... Compared with the task of taking apart the syntax of somebody like Thucydides... whose sentence continued for a page, with subordinate clause upon subordinate clause... By the way, he writes really clearly, but in a complicated . ...[C]ompared to that kind of thing, the language of mathematics was very very easy. ...[T]here is nothing to it.