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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 definit… - Tadashi Tokieda
" "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.
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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
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.
[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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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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