A truth: I do not care about all of mathematics.
Some questions are immediately exciting. I see a paper on the arXiv, get a little tingle when I read the abstract, download it extra-quick, start skimming. Oh, how exciting! That's so cool! I go to a talk and can't stop taking notes. The ideas are so beautiful. I can envision switching to this question and spending hour, weeks, years learning its intricacies.
Some take some introduction: I am cajoled into seeing the coolness by a convincing conversation, a slow unfolding of ideas, a string of relationships. Wow. Now that I spend some time thinking about it, that's awfully cool. Often these are the big ideas -- they take some time to digest.
Some I just can't get into. Why is that so interesting to people? Why do you care about that question? How is that important, other than as a stepping stone to (something actually cool)? Yawn.
I guess I'm happy with being selectively interested. If I got carried away by every current I'd probably never get anywhere. I've noticed that I like certain things -- geometry, dynamics, big pictures -- and am not immediately interested in technicalities, clever tricks, counting things, and algebra that I can't imagine.
While I use my interests to motivate myself and keep awake, the things I don't love turn out to be important. I have to push myself to care about the technicalities and appreciate them for the foundational issues they often turn up. It's ironic how often I need the unloved mathematics to answer the questions that make me happy.
For instance, I now care (a little bit) about counting things :)