I am trying to decide between some math postdoc offers, and I can't decide what is important for a postdoc position. I have talked to several senior mathematicians including my advisor, but they all seem to have different opinions. I just want to hear some more opinions on the following:
How important is prestige? Suppose that I have an offer from school X, which is fairly prestigious (something like top 10, which isn't a well-defined notion). Also suppose that I have an offer from school Y, which is not as prestigious but a better match research-wise. Suppose that the ranking of school Y is approximately n (again, not a well-defined notion). For which values of n should I choose school X over school Y? My goal is to become a tenure-track professor in a PhD-granting institution.
What makes a good postdoc supervisor? I can think of the following criteria: compatible research interests, being well-known in one's field, compatible personalities, generous with time, etc. Am I missing anything else?