My dissertation will be an expansion of a paper I am writing with my PhD advisor, Dr. C. It's an unusual approach. Normally, the dissertation comes first and then must be trimmed down from 100+ pages to only 20 or so to be fit as a journal article. The best part of this is that we don't have the usual problem of trying to decide what stays and what goes. We already know what is most important.
Contrary to what most PhD students experience, I enjoy this process. I enjoy the writing, even if the programming aspects are tedious. I think this is partially because I write (as a hobby and hopefully for publishing). However, the main reason is that I have someone to work with, to bounce ideas against, to take my observations and ideas and help me decide if they are worth pursuing. We catch each others mistakes. With the camaraderie and the sharing of ideas that occurs, I doubt I'll ever do solo research. It has made me infinitely glad that I took that step, went to Dr. C's office, and asked if he'd have me for a PhD student. It also makes me long for his equivalent in the realm of my fiction writing.
We're spinning our wheels right now, not because we're stuck but because we're in the process of collecting the proper definitions for the objects we're examining. Filling in the details, so to speak. Definitions in this branch of mathematics seem to change yearly, so it's important to keep track of all the tweaks. After searching online and printing papers yesterday, we finally found one elusive definition. It turns out that a proof I had already written and planned to discard is almost the exact proof we need.
Sometimes, things just click. Dr. C and I mesh well. The property we invented is Baby Bear, just right. Dr. C warned me not to expect this sort of thing from research. More often than not, it painfully tedious and leads to dead-ends instead of further down the rabbit hole. We got lucky in a sense.
We've reached a point along the way where we can stop and say, "There is more to this tunnel, but we're stopping here for now. Look for more in the sequel." This is one of the bonuses of creating your own property. You are the first to define it and explore it. Everything you do is new and better.
I just hope it continues to go smoothly. I've come too far this time to screw it all up. If something bad is going to happen, I pray it waits until after May of 2012.