For example, say I plan on studying Calculus. Calculus itself has many theorems and, as such, it has many proofs one should learn during his/her math career. But when is it recommended go and learn this proofs? I see three options:
- Go through the proof as soon you stumble upon a theorem/rule and learn how to apply it to some problems.
- Learn how to apply everything you learn from a subject such as Calculus I and then, after that, you go and learn every proof in Calculus I. And repeat the same for II and III.
- Like 2, but instead you learn Calculus I, II and III in a row and then you learn the proofs.
It seems option 1 would be the most rigorous, I wonder if it carries more benefits other than actually understanding why things work as soon as you see them working.