TITLE: How to learn without looking at solutions? (real analysis)
QUESTION [12 upvotes]: I have 2 weeks to do real analysis HW set, I work on them everyday, but many questions I spend hours on and cannot figure out. In the end, I google them (and feel horrible), read the proofs, and think there was no way I could've come up with that proof. I know I need to not google solutions to learn, but I can't learn without googling solutions. What to do? Or at what point is googling ok?
And in an ideal world I'd spend all the time in the world on a question, but reality is my hours are limited in college. I literally count the hours I have each day, and spend them accordingly, and at some point not googling a solution is simply shooting myself in the foot for other classes.

REPLY [9 votes]: I also agree that objectively is not bad to look up solutions per se. I already agree a lot with the answers given so far. Maybe let me add this point. 
Studying mathematics is no a sprint but a marathon. So what happens on the first 20 km doesn't really say much about what happens after 30 oder 42km, as long as you stay true to yourself and keep trying. I study mathematics for a couple of years now and every single new semester I am amazed of the new mathematics that I am exposed to and in the beginning it is always quite hard and I feel lost. It gets a bit easier because I went through this experience a lot that you described where one is simply shocked what a certain solution to a problem looks like. And even though I think I am not that talented in mathematics through a lot of effort I became quite decent at it. 
And maybe to stay in the metaphor: "This kilometer is quite nasty but hey, so was the one 10 kilometers ago and then it became a bit better again. So this might past as well".
So here I wanted to tell you, pull trough! Don't give up. You learn this stuff for you, don't get jealous or frustrated because this or that person seems to have it much easier. Everyone can contribute and again for that it really doesn't matter when or if you struggled, because in this everyone does.
Let me also stress this point about the learning curve. I have some experiences with other fields and I can say that mathematicians are a super nice and relaxed and a smart bunch. But when it comes to the pedagogy of how to teach this field I feel many instructors lack a bit of inspiration!
Finally, here is something a professor of mine told us that I found super helpful:
"There are (at least) three types of students: Some very few students look at a homework sheet and solve it within a few hours. Those people exist. Then there are students who work on the homework the whole week and struggle but in the end they get most of it. And then there are those who struggle for a week and don't quite get there on there own, but when they see the solution they understand. I think all of these types can be very successful students."