I am accepted to a math PhD program and have a visit in a few weeks. I only have a few days to tell the university which professors I would like to meet.
Problem: I also still don't know what I would like to work on (which I stated explicitly in my SOP) and the departments has ~100 faculty members. I started to go one by one and see if I like what they do but what would make a good topic?
Reading the papers from professor A things look "easy", I don't know the solution to the problems but I'm in familiar territory: it is number theory, a junior high school could understand the problem, and maybe high school could understand some solutions.
The vast majority of the time, for other professors, I don't understand anything at all. Sometimes I have a clear disgust (seeing lots of integrals/computations), sometimes I feel it is too hard (Langland related algebra), ...
I wonder how discomfortable I should be with a subject? I would be sad to end a PhD with seemingly "no additional knowledge" (if I choose prof. A) but conversely I would also be sad if I struggle on something too hard for me or for which I have no appetite even after spending time understanding it. Finally I don't have enough time to spend hours on each professor's topic to see if I would like it.
What is a good way to approach this?