I tend to think of Haskell as a language designed by mathematicians but not for mathematicians. Not even to say that it's not useful for doing math but simply that it's not structured to explore ideas via proofs. Consider Coq or Mathematica which are definitely designed with that goal in mind.

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.