I am currently applying to graduate school in mathematics. In the last year of undergraduate study I have read many papers and books by experienced mathematicians, and with the help of my honours advisor, I have a list of potential PhD supervisors at universities in the USA and Europe.

I am wondering if it is good form to email mathematicians (or more generally any faculty) at graduate schools you are applying to, just to assert your general interests and/or goals to work with them.

I'm definitely not planning on spamming hundreds of mathematicians with a generic email, but there are a handful who I think I can say a few words to.

Is this type of think considered annoying? Does it help the application process in anyway? Does anyone else do this?