TITLE: What do you do when you are completely lost during a proof?
QUESTION [9 upvotes]: We've all been in the sort of situation where your professor is doing a proof/derivation, and the whole thing goes completely over your head (if you don't know what I meant, I envy you). And when they ask for questions at the end (or in the middle, even), no one else speaks up, and nobody wants to feel like the only confused one, so your questions go unasked.
I think it's also sometimes the case that your "question" would be "I have no idea what you're doing, or why", and that would feel a bit silly to say in class.
This has been happening to me a lot lately in my real analysis class; we have no assigned text, and my professor is very busy and has only two office hours during the week, so it's hard to ask them questions sometimes.
Anyway, in such a state of confusion, what is the best way (in your experience) to get a firm grasp on difficult proofs? Sometimes it seems that certain parts of proofs are pulled from nowhere, and I cannot imagine myself being clever enough to come up with such an argument, which deeply upsets me.
Perhaps some people would suggest I forget about the proof and accept the theorem as true, but this isn't a mathematical way of thinking to me.

REPLY [2 votes]: You can always ask for an intuitive explanation of a proof. For example, the proof that the real numbers are uncountable is actually quite easy if you understand the intuition behind the standard proof. Also the proof that an isometry $f:X \to X$ for a compact metric space $X$ must be surjective also has an intuitive explanation. (It must be "volume preserving" and hence onto because it's an isometry and thus distance preserving). There is often an intuitive explanation behind a proof, some key idea or something, and it can do a great deal toward you understanding the entire proof.