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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.

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closed as primarily opinion-based by Najib Idrissi, Willie Wong, graydad, quid, Krish Mar 18 '15 at 16:03

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I think this really depends on your needs as a student. I am a very independent person, and I picked none of the projects my advisor suggested. Instead I came up with my own problems and my own ideas. I know other people that their Ph.D. is in some sense an extension of their advisor's work. I know people who need close work with their advisors and I know people who only come from time to time to report progress or discuss specific problems that come up. I don't think there's some "formulated answer" here. $\endgroup$ – Asaf Karagila Jan 25 '15 at 23:44
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    $\begingroup$ Absolutely critical. $\endgroup$ – André Nicolas Jan 25 '15 at 23:45
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    $\begingroup$ "When looking for a supervisor, how much should I weigh how famous and/or talented at research he/she is?" This isn't my own experience. I have a friend whose adviser is friends with (whom I was led to believe is) THE guy on his field. He has met him and told me stories that make it clear that it's very useful to have a knowledgeable adviser. The guy seemed to know everything that was done and where to find it, had always good ideas to solve problems, etc. There is no getting stuck with him as an adviser. $\endgroup$ – Git Gud Jan 25 '15 at 23:46
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    $\begingroup$ 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. If you ask it at A.S.E. the question will still reach mathematicians. You can even ask there and link both questions to each other. It already has decent exposure here so whoever wishes to answer on A.S.E. can go there to answer. $\endgroup$ – Git Gud Jan 25 '15 at 23:48
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    $\begingroup$ I have nothing to add to my comment, sorry. My thoughts are mainly with my research this evening. Trying to hammer the final, and most annoying of nails into the proof for couple of weeks now. (Here is an example where my own creativity is important, by the time I meet my advisor for advice, I come up with the next approach and just get validation that it's a good idea, or some plausible pitfalls to avoid; both important and I'm grateful for having such a quick witted and sharp advisor that can give them in real time, since my research is quite far from his. (But now I'm really done! :-))) $\endgroup$ – Asaf Karagila Jan 25 '15 at 23:51
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I have a PhD and have served as direct advisor for a few PhD students and on committees for several, though in physics and electrical engineering and computer science, not mathematics. A few thoughts:

First, look deep into yourself and review your career so far and understand your strengths and weaknesses, and choose an advisor accordingly. Some of my friends and colleagues in math are superb math problem SOLVERS, but not question POSERS. If you're such a mathematician, choose an advisor who can help you identify great problems, and also teach you how to do so yourself (essential for a productive career).

Next, choose someone with whom you can work productively. He or she need not be a close friend, or agree on politics or religion or sports teams or whatever, but when you spend an hour in his or her office, you should feel like you're making progress, that the advisor hears your challenges and helps you along. Most good students doing world-class work hit stumbling blocks, and you need to know that your advisor can help you. (He or she won't be travelling the world or is such a recluse or has so many students that it will take weeks to seem him or her, etc.)

Understand within yourself whether you know precisely the field and class of problems you'd like to address (topology, number theory, differential equations, ...) and choose accordingly. But if you're still unsure, try to find an advisor who will support your exploration throughout a range of fields.

All other things being equal, a more famous, better connected advisor may help you land a job, but notice who is a rising star and will be making a name for him or herself in the three or four years it will take you to finish. Being the first advisee of such a rising star can be a great help when you graduate, especially if potential employers want to move into the field pioneered by your advisor. (My own boss was the first PhD student of just such a rising star at a major university, and their joint work has been cited many thousands of times.)

Importantly: talk honestly to current PhD students and graduates of a candidate advisor, and see where they've found jobs, whether they would work again with that candidate advisor.

Most importantly: talk to candidate advisors and ask about their advising methods. You can get this person's views on previous students and compare these views to those from the students and former students with whom you've corresponded.

Good luck!

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  • $\begingroup$ Your second paragraph is spot on about knowing if you a solver or poser. $\endgroup$ – dustin Jan 26 '15 at 0:31
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    $\begingroup$ I can think of only one thing that you’ve missed: the OP should also think about how he works. There’s a very good reason that the list of things for which I thanked mine in my thesis ended ‘... but, above all else, for letting me emulate “the cat that walked by himself” in matters mathematical’! $\endgroup$ – Brian M. Scott Jan 26 '15 at 4:48
  • $\begingroup$ Thanks this is great. Just one question, when you said "notice who is a rising star", do you mean that you recommend working with someone who is a rising star, or..? But then I don't understand why there is a "but" in between the two parts of that sentence. Could you maybe clarify this a little? $\endgroup$ – Joachim Jan 29 '15 at 10:17
  • $\begingroup$ @Joachim: My point was that the student might be attracted to an already famous mathematician, BUT should anticipate who is not yet—but may soon *become*—a famous mathematician. That is, a "rising star." Clear? $\endgroup$ – David G. Stork Jun 2 at 16:22

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