I am getting ready to apply to mathematics graduate programs this semester. As far as I know most school require 3 letters of reference. I've secured two letters but for my third letter I have a couple of options. I can simply ask another professor whose class I have done well in, but I am not confident in the strength of the letter. As for my other option, I have just finished a summer research program under the supervision of a grad student and I feel as if he has more helpful things to say. However, it seems like in general it is not the best idea to get references from people who do not have PhD's. I was wondering what the best course of action would be.

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    As a grad student, I would NEVER write a letter for graduate admission for a student I worked with. I have none of the qualifications that a professor (and thus an experienced academic letter writer has). From Harvard's admission page "Letter writers should be faculty or others qualified to evaluate the applicant's potential for graduate study in mathematics. " It should be quite clear why grad students fail that qualification. – PVAL Aug 3 '15 at 20:51
  • I wrote one just after I got my PhD for a friend. It worked. Our mutual supervisor was a bit shocked, however, that they were satisfied with a letter from me. – Mark Joshi Aug 4 '15 at 3:29
  • A very related question, asked from the PhD student side: Is it appropriate for a PhD student to write reference for a PhD applicant? – Ooker Sep 21 '15 at 8:59
  • academia.stackexchange.com/questions/34631/… – user131132 Oct 30 at 3:23

There are a couple of major dangers in asking a graduate student for a letter:

  1. A typical grad student has never actually read a letter of recommendation and has very little idea of how they are written or what the standard of comparison is. It's easy to completely misjudge the style or miscalibrate the letter, in which case a letter that's intended to be helpful can turn out to be useless, or even counterproductive. No inexperienced letter writer should ever send a letter without first running it by a mentor, so you would need to make sure the grad student plans to do that.

  2. Graduate students automatically write from a position of somewhat less credibility, just because they lack experience. Someone with more experience can compare a student to past students whose later career trajectories are known, but grad students generally can't do that.

One possibility is for the grad student to write a letter jointly with his/her advisor. That may or may not be feasible, but it's worth checking.

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    Indeed... Again, as in my other comment, and, apparently not so obviously to students, the point of these letters is not just to "say good things", or even "glowing" things, but to say good things and have considerable credibility in saying them. – paul garrett Aug 3 '15 at 21:25
  • If the PhD student is not someone I will not be my labmate but a leader of a volunteer organization, would he has the credibility to saying that? The letter doesn't say much about my research ability (of course), but written pretty well about my other abilities (teamwork, eager to learn, etc) – Ooker Sep 16 '15 at 12:44
  • That won't help much with credibility, since it's a matter of sustained experience. The problem is that a graduate student has typically not worked with many students and has not done so over a long enough time period to find out what actually became of them later. So they've got a small sample size to compare with, and all they can do is guess about what this predicts for later success. – Anonymous Mathematician Sep 16 '15 at 14:08
  • In contrast, jakebeal has an opposite thinking about "situations where the graduate student is the right person to recommend" – Ooker Sep 21 '15 at 9:06

I don't recommend to ask a reference letter from another student. From my experience, the persons who will evaluate your application will most likely not trust a letter written by a student. In general, a referee is a professor, researcher or a person working in the industry. This person should have supervised you, collaborated with you or you should have taken their course.

So in your situation, you should ask the professor who is supervising the grad student instead of asking the grad student. Otherwise, you may always ask the other professor that you mentioned.

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    If I have never talked to his supervisor, how would this work out? – Memeozuki Aug 3 '15 at 21:03
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    The professor is certainly aware that you have worked for his student, so you could talk to him and he should at least know that you exist, or if you don't feel comfortable with that, you can ask the grad student to talk to the professor for you. – Phil Aug 3 '15 at 23:35
  • Ok, I wasn't aware that this sort of ghost writing was an option. Thank you. – Memeozuki Aug 4 '15 at 0:41

It is common for graduate students or postdocs to have a better grasp of the work that you've done on a project as generally they are the ones supervising and providing mentorship to research assistants/fellows. Generally, a lot of the text of the letter will be written by your direct supervisor (grad student or postdoc) who will provide this to the professor in charge of the lab, who will provide some additional comments and put it on their letterhead & sign it. Thus, you will need to ask both the grad student and the professor to combine forces on the letter. Sometimes the graduate student can facilitate this communication for you and sometimes you'll need to be more proactive. But this is extremely common and expected--the graduate student will provide concrete examples of your work & work ethic that the professor can then use.

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  • Your answer applies to STE fields but not very well to mathematics: there is no lab, there are no research assistants, most undergraduates (even the best) do not do research during the academic year, and so forth. In mathematics, undergraduates are expected to make contact with faculty sufficiently meaningful so that they can write strong letters for them, usually unassisted. – Pete L. Clark Aug 4 '15 at 16:24

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