If you... came back from a very nice trip... Lots of adventures and lots of wonderful experience... and... relaxing one evening... with your family, … - 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.

You can Google my name, and ... There are lots of videos that they put out online... and you can watch these. However, even that is only a substitute. There's nothing that replaces your own touch. Trying things yourself, and indeed noticing curiosities in nature itself.

[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.