I'm going to be applying for postdocs in the immediate future in either physics or pure mathematics (preferably the latter, though my focus won't change). Assume for the sake of argument the following two letters are strong: (1) my PhD advisor (a physicist by training) and (2) a lesser-known mathematician whom I've been collaborating with recently but haven't produced anything yet. Now, suppose I need a third letter.

My interests have often brought me into collaboration with people in a different disciplines. Do I choose the third letter based upon how well the third person knows me or based upon the discipline of the job I'm applying for?

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    The writer should be able to speak with authority on your accomplishments and potential in the field in which you propose to work. Generally, letters from anyone outside your target discipline (or disciplines, in case your thesis work and/or proposed postdoc work is interdisciplinary) will not help your case. – Anonymous Sep 8 '15 at 20:50
  • @Anonymous: could there be some exceptions? For example, a recommendation letter from the PhD advisor can attest of the ability to cope with hard work and to bring new ideas. – Taladris Oct 22 '15 at 2:52
  • @Taladris, I think working hard, etc, is taken for granted. In fact, if I read in the top part of a letter that someone "works hard", I wonder whether it it is a coded insult. Everyone works hard. Everyone is pretty bright. Subject-specific things, background, training, talent, ... matter. – paul garrett Oct 22 '15 at 14:28

Ideally you want someone who is well known to people on the hiring committee.

It sounds like you already have letters from two people who are very familiar with your work. If you can get a STRONG letter from a "big shot" in the field (math?), you should go for it. That person doesn't need to know you very well, but he/she should be able to put your work in context and explain why it is important/interesting.

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    Perhaps you can expand a bit? As it, this doesn't really provide much of an answer. – jakebeal Oct 22 '15 at 4:05
  • If there's no personal connection, it is unlikely that a letter created in such a context would be helpful... unless one is already a rising star, in which case I'd think this question would not have arisen in the first place. There needs to be a substantial personal connection or the "big shot" will not want to write a letter at all. – paul garrett Oct 22 '15 at 14:25

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