Currently I am in the process of finding a PhD. Some potential supervisors are more didactical than others, some are nicer and warmer than others, and some are more famous mathematicians than others. Concerning this last point, I guess it is very fair to say that some professors are simply more talented at research. My question for you is: how important is this? When looking for a supervisor, how much should I weigh how famous and/or talented at research he/she is?
Potential answers I could give myself:
A supervisor talented at research will have very nice ideas and an inspiring way of thinking. From this I could learn a lot. So it is a good thing.
When looking for a postdoc, a reference letter from a famous mathematician is valued more. So again it is a good thing (yes, sorry, this is something we unfortunately need to care about these days).
The only thing that is important is his guidance. Any professor will be of much higher level than yourself, so what is important is how he manages to guide you through the research (this is a whole different thing than being able to do research yourself as well). So it doesn’t matter.
I am looking for people, preferably having finished their PhD or in the midst of it, that could give a personal opinion about this. Maybe with some anecdote?
P.S. I keep having Deligne and Grothendieck in mind. How much of Deligne’s development could be attributed to him being Grothendieck’s student?
P.P.S. Should I have asked this in academia stackexchange? I just feel this could differ A LOT among different research fields so it feels important to get answers from mathematicians.