Who will write the better letter? Also, can your econ prof brag about your math abilities?
I always have this question: should I use a math prof as my third letter writer? I have heard very contradictory opinions and successful stories in both cases. Personally, I have two set letters, one econ and one finance. If I add a math rec, then I only have one econ. Does it look bad when I apply to econ departments?
I'm sure many applicants are pondering this question. If the experts from this forum can give an "official" answer to this question, it will be great!
If both will write an equally good letter, then different situations call for different protocol. If your math background is weak on paper, but in fact very strong, then your math professor would be able to attest to this (for example, if you did some independent study or something). Otherwise, it may be better to get the economist's letter, since he/she can compare you with others he/she has sent to top programs, and say whether or not you have everything it takes to make it through and be a good researcher (as opposed to just whether or not you have the math skills).
Take this advice with a grain of salt, as I am essentially just regurgitating information I've heard on these boards. (I myself had 3 economists)
There are basically two things that they're looking for: mathematical ability and research potential.
Mathematicians are the best judge of your mathematical ability, and economists are the best credible judge for your research potential. However, both things can also be signaled through other means. Having completed an independent thesis and won an award for it is a signal of your research potential; and having taken math courses with high grades is a strong signal for mathematical ability.
I think in most cases I've seen on this forum, mathematical ability has been adequately signaled through courses. It's the research potential signaling that's lacking. That's why most people use economists for reference letters. I've seen your profile and it seems that the same reasoning applies to you.
I should add: how good are you at math? If you're one of the top guys in your class at mathematics--i.e. you're so good at math that your math profs will remember you in six years and all wish that you were applying to mathematics graduate programs instead--then I would say get a math rec letter. Otherwise, I would say get an econ rec letter since. From looking at your profile, your econ profs are well known, so there is a higher opportunity cost to selecting a math rec.
Yiisheng, I would happily go to whatever schools you get into ;-). Our profiles are actually pretty similar, but you have better known rec writers.
Well-knownness of math profs doesn't really matter. I imagine that because economists aren't part of the math academic community, the adcom will probably only have three tiers for math recommenders:
Tier 2: Math professor at a B/C-tier school.
Tier 1: Math professor at an A-tier school.
Tier 0: Terry Tao or some similarly well-known fields-medalist.
I'm sure your math prof qualifies as Tier 1, which is as good as anyone because someone who can impress Terry Tao doesn't need a rec letter... they need to start polishing a case to put their fields medal in.
If you've published with the math prof and feel that his recommendation will be much better than that from the back-up economist (and that the rec you're already getting from the economist is absolutely stellar), then it might be wise to go with the math prof.
the tl;dr is: you have a tough choice, but I'm sure that you'll do well either way. You may want to consider asking one of your profs what they recommend.
I think you ought to go with the letter from the math prof you RA'd with. Research experience is invaluable -- the signals they're looking for there are broad. "Research Assistant" can mean so many things, that I imagine it's taken to mean "this student was exceptional enough that a Professor took a break from not answering 80% of his email and working on his next book or paper to personally tutor this student and hand-hold them through some nominal research." That's a big deal, not because of the content of what you've done -- because what you've done as an undergrad RA is maybe clever, maybe arduous, but rarely a forceful, invaluable contribution. It's a big deal because it shows that someone with a sixth-sense gained from watching thousands of students roll through a program identified you as someone with genuine aptitude and promise and ambition.
I won't speak for anyone else here, but my contribution to my mentor's work has been 0 in the limit, while hers to my learning has been infinite in the limit. And I've been RA for three years (that's not to say I don't see my ideas creep into her work, sometimes directly, but the overall effect is sort of like a six year old reminding her Dad he forgot his wallet before walking out of the house: "thanks honey bun").
It sounds like the math prof knows you extremely well, and I think it would be silly to ditch that signal because you're afraid adcoms won't recognize his last name. Can you imagine how damning a mediocre letter from a well-known economist would be? Someone sits down to skim your package, notices a letter from Kenneth Arrow that says little more than "so and so was a very capable student." How does that get interpreted? I imagine: "Wow, Ken is so-so about this kid -- the kid must be so-so. Don't need to read further if that's how Ken feels." Just a conjecture.
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