Contacting potential advisors before applying to graduate program - PURE MATH I have seen a few similar questions, but the answers are not usually specific enough to math, and it seems this is one of those things which varies heavily based on field. In many math programs, the student does not have an advisor until 2 or more years after being admitted to the program, so I'm really not sure how relevant contacting individual professors could be. Should I or should I not attempt to contact faculty with whom I would be interested in doing phd work? Do students who reach out to potential advisors generally have an advantage over those who don't in the admissions process, and are they more likely to actually end up working with the desired advisor?
Are there any cases known when contacting professors in this way has actually been harmful to a student's career? Suppose I have read some of Professor X's papers, and I like his style and the areas he works in, but I don't have specific questions about the papers -- then is there even a point in writing to him? Should I try to come up with questions for the sole purpose of writing?
If anyone knows of a post where these questions are addressed specifically for pure math, please let me know.
By the way, I am an undergrad in the US and applying to US math programs.
The expected behavior here is that you talk to faculty after you’ve been accepted to the program, not before.  That way you have more information to make your decision about where to go, but faculty aren’t spending a lot of time with students who aren’t going to be accepted.
Contacting a faculty member is unlikely to give you an advantage in admissions if you don’t already know them, what can give an advantage is if you have a mentor who knows faculty at the school you’re applying to and puts in a good word.  It’s not likely to hurt you either, as long as you’re polite about it, but you’re likely to get no reply or a short reply saying that they’re not on the admissions committee.  They’re more likely to be annoyed than to help, but in 9 cases out of 10 it just won’t amount to anything.