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?