I basically wanted to do mathematical physics when I entered the program but I ended up having to change my focus since I was mistaken about the level of the department's involvement in that area. I chose math originally because it was the safer route, which I now see was a poor reason to make a decision. Anyway, I'm basically in a bad research area with no way out at the moment. My advisor won't let me switch topics and I hate what I do as much as person can hate an abstract idea lol. I considered that possibly after graduate school I could become involved with something I enjoyed, but that's looking very unlikely given how isolated and specialized I've become. As far as I can tell, there are no promising jobs or research opportunities coming after graduation. All of that aside, I am frustrated daily by the "frame of mind" I have to be in order to work in pure math. That's the best way I can describe it. There is a lot of obsessing over minute details (of course, this is math) and for the most part, my work involves generalizing theorems that work in "nice" spaces to not-so-nice spaces. It's like reinventing the wheel but only having the rock to work with.
I've done a lot of thinking about how I got to this stage. In other words, I've wondered why I got into math in the first place. I've come to the realization that it wasn't the math alone that I enjoyed but it was the whole process of doing physics of which math is a large part. It's not that I can't stand research period: I'm actually rather desperate to become a research academic which isn't shaping up right now. Long story short, I miss physics and want to get back if I can. There's a strong possibility that I will finish my dissertation soon and it would perfect if I could enter the physics program at the university I'm already at. If I had to go to another school, I would be very open to that too.
Thanks for your interest!