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I'm choosing reference writers for my math PhD application this year, and need to decide between the 2 following professors:

  • Professor X is a young professor with whom I took measure theory and did a research project in my freshman year. The project went pretty well - we obtained some results earlier than he expected, and published a paper. He moved to another university and no longer worked with me, but we still keep in touch.
  • Professor Y is a fairly well-known professor whom I met at a 1-month summer workshop. I didn't interact much with her outside of the classroom, but she seemed to like me: after the workshop, she said she was really impressed by me and voluntarily asked if I want a recommendation letter from her.

Neither professor works in the field that I plan to study in grad school.

I often hear that "good at research" letters are way better than "do well in class" ones. However, in my sophomore year, I applied to some REU programs with professor X's letter (and another not so strong "do well in class" letter), and was rejected by all of them. Of course the recommendation is just one factor, but I think my course work was not bad - probably better than many of my junior friends who were admitted. My Putnam score was pretty good too, although I don't think it mattered. The following year I reapplied with both professor X's and Y's letters, and got first round offers from most of the programs.

Do you think this indicates that professor Y's letter substantially strengthened my application, or actually REU programs looked at some other factors I wasn't aware of? Do grad schools and REU programs look at recommendations the same way? Which letter would you recommend me to use? I can't use both because I have 2 other letters already, and many grad schools say they may not read more than 3 letters.

Thank you very much.

Edit:

  1. About the 2 other reference writers that I've already chosen: both did research with me, one of them also taught me several courses.

  2. The other letter I used in my sophomore year (along with professor X's) was probably not that bad. The reference writer said he was pretty impressed that my course grade was 95% or something, while everyone else got less than 60%. It's just that I didn't do research with him.

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My hunch would be to say what you already have heard. But given your history, it's also possible that professor X simply didn't write a very good letter for you, whereas professor Y did. Writing good recommendation letters is also a skill that improves with practice ... –  Sverre Jun 4 at 15:26
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All else being equal: A reference from someone I've heard of is probably of more weight than one from someone I've not heard of; even more so if I personally know the referee (and hence their standards). And a reference from someone who 'didn't need to offer to write one' would seem to carry more weight than one from a professor at your school who is more-or-less obliged to agree to write something. –  avid Jun 4 at 17:23
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It would help to know if the other two letters that you already have are in the "good at research" or "do well in class" category. –  Federico Poloni Jun 4 at 19:04
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Most places I have seen ask you for a minimum of two letters, so you don't have to choose! And even if they ask for only one, submitting two will probably not hurt. –  Davidmh Jun 4 at 21:12
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If the admission committee sees that you did research with X but doesn't get a letter from him, that omission might be glaring: they might assume the project went poorly or he doesn't have a good enough opinion of you to write a letter. I don't know for sure, but maybe someone with admissions experience can chime in. –  Nate Eldredge Jun 4 at 21:15

2 Answers 2

up vote 12 down vote accepted

Your REU evidence that X wrote you a weak letter is not very strong. I run an REU, and we accept less than 3% of our applicants. Our target participants are either legendary at small colleges (best in a decade), or excellent at top universities (top 25% this year at Harvard). Plenty of excellent people get turned away for essentially random reasons. Maybe one of your letters was submitted late. Maybe you forgot to list a course on your application that was considered essential that year. Maybe I had a bad burrito for lunch and hated your essay when I read it. Maybe there were just lots of really good applicants that year. And yes, maybe professor X (or professor Z, the other letter-writer) said or implied something negative about you.

In addition, Professor Y offering to write on your behalf after a one month course says more about her than it does about you. This does not guarantee that she will write a strong letter, and if she does she may write strong letters for a lot of people, which might be known by the people reading her letters.

Here is my advice. Go to Professor Y and tell her that you did research with Professor X and published a paper together. Then, ask her whether you should ask for X's recommendation or hers. If she really feels that you are spectacular, she will insist on writing the letter herself.

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Great answer. Love the first paragraph. –  Behacad Jun 4 at 18:07
    
Thank you. Could you tell me whether PhD and REU programs look at recommendation letters differently? (e.g. REUs may put more weights on course work because they have less time to educate the participants). I understand that many REUs are very competitive, but the fact that all of them rejected me bothers me a little bit. –  Ben Jun 4 at 20:05
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There is high variance in REU and PhD selection policies. There is a lot of randomness in both -- you could have sent the exact same application the second year and gotten very different results. –  vadim123 Jun 4 at 20:16
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Also, I plan to discuss this with professor Y, as you advised. There's a thing: she read professor X's letter, as she decided who received funding for the workshop. I don't think I can give her (meaningful) information about professor X without letting her know who that is. Is it inappropriate to ask her about professor X's letter? –  Ben Jun 4 at 20:19
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You should not ask about professor X's letter, but you shouldn't hesitate identifying this person. Her knowledge of what he wrote will only cause her to make a better decision about whose letter you should use. –  vadim123 Jun 4 at 20:21

The standard wisdom about getting letters from people you worked with rather than those who merely had you in a class is only approximate, of course, and it doesn't mean that every recommendation you get from someone you worked with will be better than every recommendation from someone who you took a class with. To me, the fact that professor Y voluntarily asked if you wanted her recommendation is more important in your case. She wouldn't offer to do that unless she was confident that she could write you a good recommendation. So I think there's a decent chance that her recommendation letter actually helped you more than the one you got from professor X.

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