I love combinatorics, but do not really want to do pure math exclusively. I like the format of pure math (that is the theorem-proof-theorem-proof format), but would also like what to do research that immediately applies to something. I understand that lots of pure math eventually has applications, but what I'm looking for is research that is done in the pure math style of theorem-proof, but is an applied problem
Phylogenetics seems like such a field. I would like to know though of any other research areas where one is applying combinatorics (or discrete math in general) to a real world problem, but going about it in a "pure math style/format"