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I hope this question isn't considered too strange.

Gowers argues in "The Two Cultures of Mathematics" That mathematicians can be broadly categorized as those interested in understanding mathematics and those interested in solving problems.

I have quite a few books that I would consider to be in the "problem solving" tradition, Polya's "How to Solve it" and Knuth's "Concrete Mathematics" illustrate this style of thinking beautifully.

I'm curious if there are canonical books that can be considered representative of the "understanding" tradition. What sorts of books did the Heroes of understanding math read when they were young (Like Grothendieck)? Or is this question too broad, In that any book which proves a theorem could be a valid candidate?

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  • $\begingroup$ It's a profound misquote to say that Gowers's theory builders are the only people who want to understand math. $\endgroup$ – user4894 May 7 '17 at 5:52
  • $\begingroup$ "So when I say that mathematicians can be classified into theory-builders and problem-solvers, I am talking about their priorities, rather than making the ridiculous claim that they are exclusively devoted to only one sort of mathematical activity" Perhaps I remembered this incorrectly. I don't like the term "Theory building". I prefer Atiyah's framing "I have never started off with a particular goal, except the goal of understanding mathematics". I don't mean to suggest Problem solvers aren't trying to understand Math. $\endgroup$ – Polymer May 7 '17 at 15:44

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