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I've been trying to start with mathematics from "scratch", but I do not rely on my foundations. I want to be a mathematician, so I picked this book "Basic mathematics" by Serge Lang and I picked up on that fact I requires proof-knowledge. So, if it's "Basic mathematics" that means that I would be highly encouraged to work through a book on proofs beforehand just start learning from there without stop reading arithmetic books or something. And then get on with Lang's book. What do you think?

NewSelfTaughtMathematician
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  • no joke: Donald Duck in Mathland – janmarqz Sep 26 '20 at 03:20
  • Can you just read Basic Mathematics directly? You don't need to read a book about proofs to understand proofs. Just read the proofs and see if you agree with the claims he makes or not. By the way, for developing proof ability, introductory number theory is a great subject. You could try reading a good introductory number theory book. – littleO Sep 26 '20 at 03:21
  • I think you'll need to tell us what you mean by "from scratch," as that doesn't tell us where you are now, but here's what I'd say initially. The earliest proofs you're likely to encounter are in high school geometry, and I feel these are the best way to learn the fundamentals of proof writing because the visual aid of the diagrams provides you with some sort of intuition for how you're going to reason through the proof. If you're still in high school or younger, focus on the concepts and reasoning as you gain basic knowledge. Other than that, basic logic is the main thing you'll need. – Stephen Goree Sep 26 '20 at 03:23
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    Don’t listen to @JCAA — I can’t imagine a recommendation that I could disagree with more. – Lubin Sep 26 '20 at 05:07

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