As it happens, I was wondering whether or not I should buy the latest version of Mathematica
when I discovered a fantastic free tool tool that does most of the things I want from Mathematica. Maxima
and it's predecessors have been around longer than I've been alive, but I had no idea that there were usable GUIs for it. I find it damn near impossible to see what's going on in a mathematical expression unless it's typeset properly.
So, I've always avoided Maxima because it doesn't have an interface, or so I thought.
There is a fantastic little emacs lisp module called Imaxima
that renders Maxima output in LaTeX and embeds it into an interactive emacs mode. So far, I like it much more than Mathematica 5's bizarre, ugly and schizophrenic Motief interface. Admittedly, I haven't yet tried Mathematica's new QT interface, but I suspect it will probably be nicer-looking but more complicated. I prefer simple and direct, and Imaxima is just that.
And yes, after doing a bunch of machine-assisted algebra, you can make interactive 3d color plots directly from emacs. Yes, emacs really does do everything.