Programming for a mathematician?

I have started studying Haskell. I expect the type system and monads to be the most interesting things to learn (I know common lisp and have already seen many cool features). Though the days of general programming are long gone. I am interested in writing math apps though. Should I continue learning Haskell or should I start studying Mathematica (or some other alternative like matlab/maple) instead?

>>2
Terminology has little to do with the question.
>>6
I am not sure what I mean by math program. But I sure do like the 3D visualizations they make. A math program for example:
Let S be any 2 dimensional surface with some gravitational field F defined on it, and m₁, m₂, ... m_k be the mass of spheres of some radius. I'd like to work out how they'd 'roll' on that surface and hit each other. Ideally the input would be the surface, gravity field and spheres, and then there would be an animation of how things would roll out. I think it'd be best to write this in Mathematica/matlab/maple.

Coq is not what I have in mind, I'm talking about fancy 3D stuff that is not mathematically trivial (For example, this video http://www.youtube.com/watch?v=9gRx66xKXek )