I like to think that CS is just a different approach to math. Of course, I say this as somebody who likes Haskell where the programmers work really hard at pretending to be mathematicians :) However, even when I'm writing in other language, I think about things in terms of math. Additionally, my CS courses so far have all been heavily influenced by math, except for systems that was much more heavily influenced by EE.…
I think programmers aren't doing math at all, but I think what programmers do is better, more adroitly, done when its guided strongly by math. For that reason I think programmers should learn lots of math, even if they don't spend much time proving things for their own purposes.