I am about to become a Ph.D student in mathematics. I am having some doubts about where I should do my Ph.D and I would appreciate some advice, or anything really.
- I could do research with a very competent professor that is internationally well-known and is also very interested in me succeeding, having helped me with much already. He is also a really kind person. The area he is working in is one of the most fascinating areas in all of mathematics to me. However, it is in a different city from where I live now. As I live now, I have a really good apartment and a girlfriend too who lives here. She would be OK if I moved, although a bit sad. I am afraid of moving to a new city, and more than that, also somewhat scared that if I am not as good as my advisor belives me to be, it will all go terribly wrong.
- I could do research where I live. However, the advisors are not as competent as he is, nor as interested in me (so far, I am not their student yet). Further, the areas are not as fascinating (although very fascinating!). I could continue with living my life as of now.
So, what should I think about regarding these choices when it comes to making a future career? I am a bit vague here, since I want general advice to think about.