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Comment on Ask HN: Which books helped you gain mathematical maturity?

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I think a serious, difficult real analysis I course (sometimes they have I and II) or an equally difficult elementary number theory course will expose you to enough mathematical proofs.

That's not what OP is asking. OP is asking for an overall intuition for "all" of mathematics, not just what a proof looks like.

It takes a while undergrad degree worth of pure math study.

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