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" "[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.
(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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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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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.