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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 besi… - Tadashi Tokieda
" "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.
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About Tadashi Tokieda
(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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Tokieda Tadashi
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Additional quotes by Tadashi Tokieda
[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.
[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...
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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.
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