Dual space of a vector space.
This is perhaps something that you don't hear very often (although would be some comfort to me if you have felt like this before). I've been studying mathematics for around 4 years now. At first, I enjoyed it - the concepts were explained, or at least easy enough to work out what they were getting at - there was enough intuition and motivation to me to see the point in why we are studying what we are. But now I feel completely different - I mainly study functional analysis now, and I find that most textbooks I come across are written "definition, lemma, proof, theorem, proof, end of chapter" - with little or no motivation. I am getting bored, I am seeing no reason why I should pick up a book any more other than the times that I have to. I just feel stupid when I tell someone I am interested in analysis, and yet I can't even tell you why Banach started looking at complete normed spaces (for them then to be named Banach spaces afterwards) because I seem to have to learn everything in some sort of backwards fashion.
Can someone give me some advice here?
Moderator edit: Moved from Chat room.