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