Terence Tao: preference

Transcript context

…I mean, you’ve said that you can be both a hedgehog and the fox, depending on the context, depending on the collaboration. So can you, if it’s at all possible, speak to the difference between those two ways of thinking about a problem? Say you’re encountering a new problem, searching for the connections versus very singular focus. I’m much more comfortable with the fox paradigm. Yeah. So yeah, I like looking for analogies, narratives. I spend a lot of time… If there’s a result, I see it in one field, and I like the result, it’s a cool result, but I don’t like the proof, it uses types of mathematics that I’m not super familiar with, I often try to re-prove it myself using the tools that I favor. Often, my proof is worse, but by the exercise they’re doing, so I can say, “Oh, now I can see what the other proof was trying to do,” and from that, I can get some understanding of the tools that are used in that field. So it’s very exploratory, very… Doing crazy things in crazy fields and reinventing the wheel a lot, whereas the hedgehog style is, I think, much more scholarly. You’re very knowledge-based. You stay up to speed on all the developments in this field, you know all the history, you have a very good understanding of exactly the strengths and weaknesses of each particular technique. I think you rely a lot more on calculation than sort of trying to find narratives. So yeah, I can do that too, but other people are extremely good at that. Let’s step back and maybe look at a bit of a romanticized version of mathematics. So I think you’ve said that early on in your life, math was more like a puzzle-solving activity when you were young. When did you first encounter a problem or proof where you realized math can have a kind of elegance and beauty to it?…

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