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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?

  • On prestige: See this answer to a related question. (It's about theoretical CS instead of math, but I don't think the cultures are all that different.) – JeffE Jan 26 '14 at 4:08
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    The advisor matters more than the school. – David Ketcheson Jan 26 '14 at 6:41
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    It is the number of articles in prestigious journals in the end that matters, and the results. If you are a good match research-wise, then this is obviously better; I (hope) that journals do not accept to publish results based on the university ranking, but based on the result, so yeah.. – Per Alexandersson Jan 26 '14 at 16:57
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    @Paxinum: Not the number of papers. What really matters is the quality of the work. – JeffE Jan 28 '14 at 4:10
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    @JeffE Hm, ah ok. But I have the (cynical, inherited from my advisor, I guess) view that people in the first selection only look at journal first, and then at the actual article. – Per Alexandersson Jan 28 '14 at 12:49
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nagniemerg is absolutely right that at the end of the day, your results will be much more important than a name on your CV. I think being at a prestigious institution is very useful for getting a first look at your application (which is a f***ing valuable thing, as Rod Blagojevich would say); if the rest of what's there doesn't stand up, getting that look won't help much.

That said, I would think carefully about how sure you are that institution Y really will provide a better research environment. Prestige tends to correlate (far from perfectly) with having an active department with a lot of seminars and visitors, which can often be more valuable than day-to-day contact with a single advisor. Having higher-quality students and colleagues can make you a better researcher.

I also think there's a lot to be said for the uncertainty of life. Maybe you'll go somewhere and whoever you were going to work with will get a job somewhere else, or have a baby, or go on sabbatical. Maybe you'll start a collaboration with someone you don't even know exists yet. It's all very hard to predict, and on some level you have to go with your gut. You could do a lot worse than just going with the most prestigious option, but if other factors seem to point another direction, I don't think you should just ignore them.

EDIT: I wrote this is a bit of hurry last night, and I realize it might be a bit unhelpful. However, it's honestly quite difficult to say anything general, and you indicate that senior mathematicians who know you and know what your options are cannot come to a consensus. To me this indicates that probably you will not be able to conclusively figure out where is the better choice. This is not to say it doesn't matter, but once the uncertainties are sufficiently large, one might as well flip a coin (or at least flip a coin until you get the answer you want).

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At the end of the day, the quality of your research is more important than prestige. I would go with the university that is a better research match.

As for what makes a good postdoc supervisor. I think this depends completely on the individual and how one conducts research. The two extremes are: hands off -- I have plenty of ideas and give me something to work on.

The best is a combination of the two. This shows you are able to work independently and work well with others.

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