Mathematica is a very powerful Lisp-based programming language(without user-visible s-expressions). It is (to an extent) designed for numerical/symbolic math; there are a lot of libraries available for that.
However, they've added a lot of other libraries, for things like image processing, etc.
It is a very powerful system, however somewhat limited by poor market penetration (nothing else uses it, so only people with Mathematica could use it).
A friend of mine who's a physicist claims that he's so used to Mathematica that he uses it for everyday scripting tasks, the way other people use Tcl or Perl.
Yeah - I met a chap at an openbase conference in 2005 that was using it for professional web-application development. I've been intrigued by the idea ever since. I'd be interested to hear more stories from people who really leverage it like this.
However, they've added a lot of other libraries, for things like image processing, etc.
It is a very powerful system, however somewhat limited by poor market penetration (nothing else uses it, so only people with Mathematica could use it).