I love the rhetoric of maths. You have to write extremely simply, no letting the words get in the way of the concepts. You can talk about "climbing a peak" (getting to an important result). And sometimes unexpectedly, when you think you are halfway through the proof: "and now we're done." And it's like turning a corner and seeing the view. Or another thing: after some difficult proof in the book, they'll toss in some massively important result as a two-line lemma.
Lemma. Proposition. Theorem. Claim. Proof. Hah!
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