I'm a math PhD who considered himself to be a physicist at heart, and as soon as I was exposed to a lot of the research-level stuff, I found a lot of it incredibly obscure and uninteresting. It gets to a point where there are very extravagant levels of abstraction and complication. So, on some level, I can relate, but I also wonder if you are looking at some of it in the wrong way. Personally, I am kind of fond of graph theory, and I see it as one of the less boring math subjects out there, though to some degree, it suffers from the same extreme over-formality and stuffiness of presentation as many other subjects.
Whether it's boring or not is pretty subjective. What I would say is that it's a pretty diverse subject, and you might find subjects more compelling. For a lot of it, you have to look at it in just the right way to see why it's interesting.
As I've said before, what I enjoy most about math is making things obvious to myself that were initially far from obvious. That might go some way towards explaining the point of coming up with better proofs of the same result. If you just view it as a way to establish a fact and forget why it's true, then who cares? But if you view it as a way to understand the fact, to know the why and intuition behind it, not just establish it, then it becomes crucial what proofs you use. So, it seems you are missing something fundamental to the appreciation of mathematics, though I do have some sympathy for resenting the lack of hands-on calculations, which is one thing that many mathematicians seem to neglect these days.
Some general criticisms I have of the state of the mathematical culture, particularly in regards to being boring:
1) They love to give incomprehensible talks. They need to come to their senses about this, ASAP. Here's a fun little opinion from Doron Zeilberger, a professor at Rutgers, who shares my opinion here:
http://www.math.rutgers.edu/~zeilberg/Opinion104.html
2) Their writing is too formal. Here is an article from a Fields Medalist, exposing some the issues here:
http://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-00502-6/S0273-0979-1994-00502-6.pdf
3) Not only is their writing too formal, but sometimes, their other forms of teaching as well (and even their thinking, as Thurston points out).
http://www.math.fsu.edu/~wxm/Arnold.htm
My favorite line from the whole article points out that it is impossible to understand an unmotivated definition. That's probably the number one thing that I see wrong with the way higher-level math is being taught these days.
4) Not enough thought is given to the purpose of what they are doing, including practical applications. Up to a point, math for math's sake is a worthy goal, but when you look at how hard mathematicians have to work, it seems as though many of their lives are just getting consumed by it, which completely defeats the purpose of enjoying math for its own sake. If the purpose is enjoyment, why would you drown your whole life in it? Moreover, drowning your whole life in it is almost a requirement for success, given the current competitive, rat-race conditions.Many mathematicians might try to insist that the writing needs to be so formal in order to be rigorous. This is quite obviously complete nonsense because adding additional intuitive commentary need not have any effect on the rigor.
There's some distinction between math as a subject and math as a research topic. As a subject to study, at the graduate level, I would disagree that it's boring, although the way it is presented is often very boring. It's not the subject's fault, though. It is the way it is presented.
Of the stuff that people do research on, however, 95% seems to be completely boring and obscure to me. Of course, that's fairly subjective, but I am not alone in my opinion. I quit math research, but I remember someone who continued with a postdoc saying that everything people are studying these days is ugly. Her husband, also a graduate student in algebraic geometry would have agreed. He quit research, too. In fact, 90% of us math PhDs quit research, and I'm willing to bet, in lot of cases, it doesn't have much to do with their lack of ability.
I think it's sort of out of control. Too much information out there, too many papers, too much pressure to publish, too much crap. We need precisely the sort of consolidation (better proofs, and more importantly, better explanations) you are objecting to to get it more under control. Who cares about producing billions of obscure results if no one can understand them?
