One important thing about proofs is that you will never be able to appreciate them, and therefore to learn from them, if you are not capable of reading the statement to be proved with a sceptical attitude, and to try to imagine it is untrue (What's this nonsense they are claiming, it cannot be true! Certainly it must be possible to satisfy the hypotheses without subjecting to the obligation to accept the conclusion!). Once you have some mental idea of what a counterexample to the statement would look like, you can interpret the proof as an argument that systematically talks this idea out of your head, convincing you that it really really is not possible to ever come up with such a counterexample. Then you will have acquired a feeling of what the proof is really about, and you will be far more likely to retain it, and to come up with similar arguments when you need to prove something yourself. But if you take a docile attitude and accept the statement to be proved from the onset, you will never be able to understand what all this reasoning was needed for in the first place.

Такие дела.