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nonequilibrium

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I'm currently taking a course in number theory, and I usually enjoy every branch of pure mathematics, but somehow number theory is not really exciting me. It's hard to pin-point why exactly... Perhaps the following two feelings:

- It's hard to see a real structure when trying to tackle a given problem (i.e. a certain exercise). It seems to be rather dependent of accidentally thinking of a certain trick.

- The theorems are often awfully concrete (talking specifically about certain numbers), not giving off an aura of blissful generality through abstraction (as opposed to any other field of pure mathematics, really).

Am I perceiving things the wrong way? Or is it correct and do I simply not appreciate these characteristics enough whilst others do? Or does it simply take some time to get into the right atmosphere for these things? (For example I remember first struggling with Abstract Algebra, I wasn't connecting with it in the beginning either, but now I do; maybe the same thing must happen with Number Theory?)

What is Number Theory to you? And was it love on first sight? What is your stance towards is?

PS: I'm in first place a physicist, so if anyone knows of relevance for number theory for physics, do share, but I'm pretty confident that there isn't (not that relevance for physics is necessary for me to enjoy math!)

(Note: I realize that it is very useful for cryptography, but those things don't interest me and probably never will, so I can't really turn to that for motivation.)

EDIT: It might matter, or it might not, but my "favorite" area of pure math is analysis. Then either algebra or topology. And then geometry. I might like the foundations of math (I like foundations, generally), but I haven't really been exposed to it formally yet. At the bottom I would

*currently*place number theory, but hopefully this will change somewhat...