Just as an aside, I dual-majored in both pure math and C.S. I found the types of thinking for both subjects to be very, very similar. In fact, finding a constructive proof for a math theorem was almost like writing code.
I started programming fairly young, about 12, so the "constructive" mathematical approach was the most natural to me. By my third year at university it had worn off and I was much more comfortable with things like existence proofs and thinking in terms of relations rather than constructions (a very vague description, but it will suffice for now), but programming always felt like it emphasized the constructive part of mathematical thinking. It was like I went to a math class and thought one way, then a C.S. class and emphasized a large subset of that thinking.
I started programming fairly young, about 12, so the "constructive" mathematical approach was the most natural to me. By my third year at university it had worn off and I was much more comfortable with things like existence proofs and thinking in terms of relations rather than constructions (a very vague description, but it will suffice for now), but programming always felt like it emphasized the constructive part of mathematical thinking. It was like I went to a math class and thought one way, then a C.S. class and emphasized a large subset of that thinking.