I transcribed this excerpt starting at the 22-minute mark, of Okinawa Institute of Science and Technology’s May 19 2020 podcast with Professor Tadashi Tokieda:
For example, this is a bit too technical, but there's a definition.... a very very precise way of thinking about the limits and continuity and so on, which is goes on the name of Epsilon and Delta. So for every epsilon there exists a delta such that and blah blah blah. And this is a stumbling block for almost everyone. But when I came into mathematics as an adult already (you know I taught myself mathematics), and when I came to Epsilon-Delta, 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. And so, the idea that, you know, if you change the order quantifiers, of course, the meaning changes completely. It's comp. It was trivial, of course, I mean, compared with the task a difficult task of taking apart the syntax of, say something somebody, like Thucydides you know whose sentence can continue for a page, with subordinate clause upon subordinate clause. By the way, he writes really clearly, but in a complicated syntax. Well compared with that kind of thing, language in mathematics was very very easy. I mean there's nothing to it. I think the fact of the matter is, most people don't have a sufficient mastery of their native language. They never had the experience, they don't have had enough, shall I say a bit more gently, enough practice of careful use of their own native language. You know, do you speak really carefully and making sure that you understand absolutely everything that you are saying and every word and every phrase counts? The answer is no. The people just blah blah blah, just talk away. So, if you have a really careful habit of careful use of language, it's my personal belief that most of the difficulties in mathematics will go away. And it's just that mathematics is an unforgiving subject, where any misunderstanding any lack of understanding shows immediately, whereas in the rest of human endeavors, you can keep going by faking for quite a long time. So in that way, yes the language frames how you understand mathematics, but in that very very practical way. I think the best way to improve your chance of your future advancing mathematics is to practice and improve your native language.
Does research on students’ difficulties with the δ-ε definition of limits and continuity substantiate Tokieda’s asseveration that a primary cause is insufficient mastery—or at least lack of a habit of careful use—of their native languages? Does empty-headedness of linguistic syntax bedevil undergraduates on, and thwart them from, δ-ε definitions?