Hello everyone, this is my first post here. I'm happy to find a forum catering specifically to graduate students.
I've been a Ph.D. student in mathematics at my university since fall of 2007. I completed the introductory classes and exams well within the alloted time, and chose my advisor. Well, chose may not be the best word for it; the professor I originally wanted as my advisor was apparently very busy with other students, as well as with just becoming chair of the department. He referred me to who my advisor is now (partly, I suspect, because this professor needed an advisee, because I can't imagine anyone willingly seeking him out for this).
Don't get me wrong; my advisor is brilliant. Perhaps too brilliant. I've learned a ton of things under him in the areas of abstract algebra, specifically algebraic geometry. The entire time, though, I've had an enormous problem communicating with him. About pretty much anything. I guess he's so smart that any of the stuff I'm trying to learn is already trivial to him, and it is nearly impossible to get him to explain or help me understand something with which I'm struggling. More often than not, I find myself going to other professors in the department with questions.
If it were just that, I would deal with it and move on. That's frustrating, but manageable. Another, perhaps larger, problem is the difficulty in communication when it comes to matters of progression through the Ph.D. program. On the way to the degree, after choosing an advisor, I had to pass two preliminary exams. I did accomplish that, but about a year later than most Ph.D. students do here. Not because I struggled with them; I passed both easily on the first attempt. My advisor just didn't seem to be aware of the proper timeframe, and very rarely listens when I ask questions about this sort of thing. He usually goes into a monologue about there being "too many rules and procedures; people around here are too concerned with paperwork when they should be concerned with math".
I'm really beginning to worry (well, maybe not beginning; I've been worried for a while) that I may never come anywhere close to actually finishing this degree. Technically the only thing left for me to do is a dissertation. While he has had me working on this and that, there's never been a sense of "okay, this is really interesting, this is worth really working on". I guess what I'm trying to say is it feels like I'm doing a bunch of exercises to keep me busy. Not that they are worthless... I am learning a lot of things, but whenever I get to the end of something, whether I come up with an answer or not, he seems to write it off and move on to something else.
I don't really know what to do at this point. I mean, I can keep going on like this... well, until the day the university informs me that I've been there too long and they can't pay me anymore. I've tried asking him about a dissertation, or even just specific things that would be worth researching, but I always end up working on whatever he's working on. Which I don't mind, but I feel like I'm being used just to test some theories out as opposed to being set on a course for something major.
Maybe I could take some of the blame; I can be very timid, and that only amplifies the difficulty that is had when trying to communicate with him. It's not just me; the entire department, students and professors alike, have as little communication with him as possible. He doesn't attend staff meetings, students that are taking is classes are terrified to go to his office for help. I've tried asking other professors, even those on my Ph.D. committee, about the track I'm on, but the answer is always "that's a conversation you need to have with your advisor". Which is exactly the issue.
Sorry for the wall of text... I would really appreciate some advice, but it was also nice just to get that off my chest.