So I'm not such a great believer in talent. Maybe I'd rather use the word ... because... I find that the people talk too much about the genius, and... correspondingly to the... in music and... mathematics... That's a dangerous word, and I'm not sure that it's socially beneficial to talk about... whether it exists or not. ...Maybe scientifically you can talk about the concept of genius, but it... does more damage sociologically, than it does good.
Japanese mathematician
(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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[T]he one lesson that I drew from coming in from... lots and lots of detours. ...[T]he other side of the coin. ...I started doing mathematics seriously quite late ...That had interesting consequences. ...Most people in mathematics came into mathematics early ...typically in your teens ...[T]he phenomenon of exists ...only in music and mathematics. ...[C]hild prodegies exist primarily as performers, and the mathematical equivalent is problem solvers, rather than theory builders, and the music equivalent would be s. It's true that Mozart was a child prodigy in composition, but on the whole... performers and problem solvers are the dominant types of child prodigies... [T]his phenomenon only exists in music and mathematics, and correspondingly, they come in quite early... Innate or not... it involves a lot of ... Well, maybe there is such a thing as talent... but one necessary condition for a child prodigy... is... the... that could bear with long long long hours of enormous amounts of training, and sometimes it becomes an obsession. ...I'm aware that child prodigies exist in chess and in ... and in go and so on, but that's... a small variation on mathematics... I don't know about innateness and... I'm not sure about... talent. ...[T]he human brain is a very complicated machine and it would be very surprising if there is no... innate difference between one brain and another... after all, there are innate differences between one body and another... I have seen lots and lots of mathematics students... who are very talented... by the standard judgement... But ultimately... on the whole, I am simplifying... it's really the effort, and how much you really like the subject that made a difference as to ultimate success.
[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...
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.
The other side... of this observation is that.... whichever [way] you look, and whatever you listen to, and wherever you cast your mind... in that part of the universe that you are observing Nature is doing something. So nothing is easier... to discover than science because science is happening all around you. It's just a matter of opening up your mind a little bit, and making a little bit of effort, and... you have to have an eye for surprises, but humans are born to be surprised, and programmed by Mother Nature to be curious... So you just pay attention, and pause, and relax... [E]specially, you shouldn't worry about what other people think, and what your social standing is. If you are interested in something, it's interesting, and if you're not interested in something, it's not interesting. But you should just keep looking, and everywhere you look, you reach out with your right arm, you reach out your left arm. You stick out your left foot and right foot. Everywhere you reach, there is a bit of science in there... [S]o you meet science all over the place. It's very easy.
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.
People say... discovering things is difficult and... extracting science from everyday life, and the mundane facts... requires talent and special aptitude and so on. I believe that's wrong for the following reason. The reason presupposes a certain belief and outlook on the universe. My outlook is... people say... "I don't like science." That's fair enough... and "Oh, I like science, but... I get tired after a while and I can't continue for so long"... [T]hat's very very reasonable. Or, "I try very very hard but I can't get through some difficulties." Well, what's more human than that? Sure, but... however fragile and... weak humans are, there's... one... creature (anthropomorphically speaking)... who keeps practicing science very very successfully, in fact with 100% success, 24 hours a day, 7 days a week with no stop... and has been doing it for ages and ages... everywhere you go, and that's Nature herself.
[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.