I hope it is appropriate to ask this type of question. I'm in my second year as an undergraduate right now. While my problem solving skills have improved tremendously, I almost never tried to actually remember what I learned. I always had the attitude: "If I don't remember it, I will simply look it up." While this might be legitimate to a certain extent (especially when it comes down to definitions), I'm not sure where this leads to in terms of being able to see various connections much faster.
Would you say that it is necessary to remember most of the things that you learnt so far? Of course it wouldn't do any damage at all, but one has always think about it in terms of efficiency, I guess. I mean, it's hard enough to learn mathematics itself - but remembering all of those things just to gain the ability of solving some problems faster? I'm not sure about that and would like to hear your opinion on it.