If have just finished the first year of my PhD studies in mathematics at a German university. After my master's, which I have done in representation theory, I had started a PhD in a more applied field, partly because my current supervisor pointed to the necessity for knowledge in representation theory in his field. However, I have been feeling disappointed since almost the beginning. The reasons are as follows:
- For the problems I work on, my supervisor can barely act as an advisor. He has almost no expertise in what he asks me to do. If I talk to him about a point where I have no clue how to proceed, I have to explain basic material to him instead of obtaining useful hints.
- He is unwilling or unable to provide me with suggestions on what to try, whom to ask, what to read etc. Probably, I should be able to do all these things on my own. In the case that the expectation is that I should state my research questions, find helpful material, and solve them completely without any advise, I am suspecting that I am not apt for pursuing a PhD.
- There is also no vivid exchange between me and the other PhD students. This is mostly due to the fact that my supervisor has hired students from completely different backgrounds to work on very unrelated problems, which only have in common that he is no expert in any of the fields he has hired students from. However, when talking to my colleagues, it seems that I am the only one suffering from this isolation.
- It is hard for me to spot and solve problems completely on my own. When starting my PhD, I had hoped for an opportunity to learn new things. Until now, I haven't learned anything. That I have my background in a different field does not make things easier, but I think that I would also struggle in my original field if I constantly have no one to talk to.
- The social climate in the group is quite cold, also apart from talking about mathematics. Again, my colleagues seem to be fine with this solitude. This is fine, and, to be honest, I actually envy them for not needing exchange, company or just some chatting about what they do. I have the impression that I cannot live that way, which more and more seems like a deficiency to me.
These are the reasons why I have applied for two opened PhD positions I have found in January, both in representation theory. Contrary to my expectations, both have offered me the position. However, I hesitate to accept one of these positions because:
- How can I be certain that I am good enough for these positions? Yes, they have judged my application, based on a talk I gave there and based on what I wrote in my master's thesis, they are experienced professors, but how can I be certain that I am good, creative, persevering etc. enough?
- How can I be certain that the reason for my distress is not my working group, professor etc., but my lack of aptitude for doing a PhD? Shouldn't I be able to work independently, without the need for talking to others about what I do? Shouldn't I know of my own which questions I want and can work on?
- How can I be certain that I will feel better if I start a new project?
Apart from these work-related questions, other aspects that make me hesitate are:
- If I quit, I will be 31 or 32 when I finish the new project.
- Exchanging a PhD on applied questions from a well-known university for a purely abstract PhD at some less-known university does not sound like a good thing to do with your CV.
- For a PhD, the salary and other benefits I obtain know are perfect. This could not be any better and would certainly degrade if I quit.
- Arriving in a new town, getting to know new people etc. has always put a lot of pressure on me. It has always taken me monthsto get to make new friends after having moved to somewhere else.
I am aware that I should try not to take these aspects into account, but I have mentioned them for completeness.
Question: How can I take a good decision?