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The study of languages, some... call it linguistics, but the nuance is quite different. Linguistics, since especially Chomsky and that school, became… - Tadashi Tokieda
" "The study of languages, some... call it linguistics, but the nuance is quite different. Linguistics, since especially Chomsky and that school, became very... analytical and almost mathematical, and so I'm absolutely not interested in or... an analytical study of languages. ...I'm a mathematician, and if I wanted to that... I'll just do... straight mathematics... [I]nstead, philology in the glory days of the 19th century meant primarily the reconstruction of the Indo-European family. So people knew lots and lots of languages, and their peculiarities, and their accidentals and evolution in Greek, Latin, Sanskrit... [I]t was practiced outside the European family, for notably the Semitic family, especially languages that have a lot of written records that go way back, and you can do science. So that's what philology means and that's what they used to do, but I do emphasize that I'm... absolutely not interested in mathematical aspects of linguistics. I'm interested in the languages themselves.
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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
[W]hen I did my PhD, it was in very very pure mathematics and I still love that field, ...algebraic topology ...but then ...I started moving into more physical subjects and... started doing experiments... I thought this was an opportunity. Until then I had lots of... friends and family who were not scientists, and who didn't have any mathematical background, but... with pure mathematics it's very difficult to convey the excitement of computing s... [W]ith physics I decided that every time I finish a project, write a paper or even figure out something, I should design a toy that... captures... joy that I have had, and can share it with people... [T]hen it became quite successful, and it became the other way around. Now I look around and... realize that there's science all around and so I start from the toys... I try to... discover one every month... I was given most of them because my good friends send me toys... but I have... stumbled on... 1/3 of them myself, and... depending on the public lecture... I got... maybe a dozen and... try to tell a story. ...[S]ome of the collections are more cohesive stories than others, but ...whatever I take, I start seeing connections ...And as with the larger nature, so with my toy collection, there are lots and lots of inner connections that I'm waiting to discover; and I usually can.
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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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!
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