TITLE: Recalling Proofs
QUESTION [13 upvotes]: When I am able to follow a proof presented in class or in a textbook, I usually can prove the same corollary or theorem a couple days later using the same arguments. But after a week of seeing the proof, I have no idea how I should prove it and get stuck especially if it is a long proof. Is there anything I could do so I don't keep forgetting proofs?
Thanks in advance.

REPLY [5 votes]: Depending on the subject area and texture of the proof, one thing I might do is memorize what I would call the "milestones" in the proof, so that later I only need to figure out how to go from one milestone to the other instead of retrace the entire proof from hazy memory. This doesn't always work though, especially when the pieces of the proof are not in-and-of-themselves interesting or easy to remember, when the number of suppositions and hypotheses needed between each mile-stone is large in number, or when the route from one milestone to another involves gymnastics whose validity you can't vouch for or whose a priori derivability you don't see on your own. These latter issues can be ameliorated for the most part simply by become more familiar and well-versed in the particular subject area so that tricks "stick" conceptually and can be understood intuitively.