What are the prerequisites for learning math proofs?

Question

I am planning to self-study math proofs from "proofs form The Book". What are the prerequisites for learning it?

Answer 1

I have never read Proofs from The Book myself, but I understand it is a collection of proofs that are particularly simple and beautiful compared to what they prove. Most things one would like to prove don't have a proof that rises to that standard, so we have to make do with clunkier proofs with less "wow!" in them.

Therefore if you use Proofs from The Book as your only source of "what a proof is", you're setting yourself up for disappointment when you try to construct your own proofs and can't reach the same perfection. It is, by all accounts I've heard, an enjoyable and inspiring read for someone who already knows enough mathematics to appreciate the difference between the Book proofs and everyday pedestrian proofs, but it is not a textbook.

Really, there is no such thing as "studying math proofs" as a separate activity. That is simply the same as studying mathematics. The way to learn to do proofs is to do a lot of them, and you can't do that in a vacuum. The exercise has to go side by side with learning theories that you can prove things about. (There are texts such as How To Prove It that put particular focus on proof techniques, but putting that to work in practice still needs something to prove things about).

(Then there is proof theory which is a highly technical area of logic that aims to construct a mathematical theory about mathematical reasoning itself. It is pretty much impenetrable unless you already have a good familiarity with the kind of informally phrased proof that is actually used in ordinary mathematics. It's one of my favorite areas of mathematics, but learning it too early tends to produce a skewed and misleading view of what mathematics is or should be).