First, a little background: I hope to go to graduate school in mathematics, but for financial reasons I will be unable to go back to school any sooner than the fall of 2016. However, since I feel quite sure I would like to undertake further studies in math, and because I really enjoy the subject, I have been self-studying on my own in my free time.
The issue I am having is this: When I tackle a problem, I am very determined, and I don't mind spending a long time working on any given problem. But, sometimes I get stuck on a difficult problem, and I work on it for days, only to end up frustrated by not finding a solution. Then, I find it difficult to skip that problem and move on to other problems, because the skipped problem keeps nagging at me. I worked nearly all the problems in Blue Rudin, chapters 1-8, but there are a few problems I never got that are still bothering me. Sometimes, I think there must be some fact that I didn't absorb well enough for that particular problem, and it seems like a problem I "should" be able to solve.
Does anyone else feel frustrated or dismayed when there is a single problem in a chapter's exercises that you just can't seem to get no matter how long you work on it? During my undergrad math studies, I did very well, so I don't think it is that I have a lack of ability. Does this sort of thing even happen to great mathematicians? I feel that I should somehow come to terms with this experience, as I am sure it will keep coming up as I continue to study math. I would very much like to hear others' thoughts and experiences with this sort of thing.