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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
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!
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.
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[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.
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