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When it comes to postdoc positions in mathematics in the US, does it make any difference for the hiring committees if your thesis adviser is a big name (say, someone like Gromov or Milnor)?

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    It doesn't just make a difference. Assuming they write you a good letter, the name recognition of your advisor is (perhaps unfortunately) the single most important factor in getting a good postdoc. – user37208 Nov 18 '15 at 18:46
  • I assume you have a PhD and since you have no longer an alternative for your thesis adviser, what is the relevance of asking if it make any difference if your thesis adviser is a big name or not? – Sathyam Nov 20 '15 at 23:15
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    @user37208 Wow - "the single most important factor" does not involve at all the quality of your research work? If it is really so, it is disappointing. – Federico Poloni Nov 21 '15 at 4:18
  • Presumably, getting a good letter from a well known person is about the quality of your research work, @Federico Peloni. – Oswald Veblen Nov 23 '15 at 2:26
  • @OswaldVeblen Of course, a student with a good letter from a top-level advisor has the best opportunities. There is no arguing against that. But "the single most important factor is your advisor" to me means "a bad student from a well-known professor has better chances than an excellent student from University of Nowhere", and that bothers me. – Federico Poloni Nov 23 '15 at 7:54
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I'm surely not the most qualified person on this site to answer, but I have been on a postdoc hiring committee in pure mathematics and I quite disagree with the existing answers. The single most important factor is going to be your letters of recommendation (with second on the list being your publications and preprints). I think having a famous advisor is going to be of minor importance in comparison; most people understand that also great mathematicians sometimes have students that are just mediocre, so that it's no great predictor of future success. In fact I heard in a sense the opposite argument being made, that if an applicant from a smaller university with a less famous advisor has strong letters from big names, then this is more impressive than if a student at a "top" university had the exact same letters.

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In spite of the obsession with objective assessment and quantification that supposedly governs science, personal recommendations often still matter the most during the hiring process. Hence, if you have a big shot PhD advisor, you'll probably have an easier time finding a good postdoc in a group that your advisor has good contacts with.

If you don't have the big shot backing, you can (partly) make up for it by approaching potential postdoc advisors in person (e.g. at a conference) and convincing them that you're not only a scientist with high potential but also a nice person.

The point is, when you apply for a postdoc in a good group, your application is likely to go to the "meh" pile if neither your nor your advisor's name ring a bell with the group leader.

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    I downvoted this answer because it does not (in my opinion) reflect the situation in mathematics, which the original question asked about; for example, postdocs in mathematics are not usually in a "group", good or otherwise, but rather in a good department. However it might be more applicable in other fields. – Tom Church Nov 21 '15 at 1:47
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Yes, it makes difference. However, your personal relationships with the prospective advisor make even more difference.

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    I downvoted this answer because it does not (in my opinion) reflect the situation in mathematics, which the original question asked about; for example, postdocs in mathematics may not have a single "prospective advisor", or any particular advisor at all. However it might be more applicable in other fields. – Tom Church Nov 21 '15 at 1:48
  • I agree with Tom Church. Of course, no department wants to hire a postdoc that nobody can work with. But apart from specialized applications (e.g. the NSF postdoc in the US), math postdoc applications don't really require pre-existing relationships with anyone in the target department. – Oswald Veblen Nov 23 '15 at 2:30

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