Hello,
Yes, the "symbolic-program-x" I referred to above was Macsyma as well (I thought the general rule here was not to mention other software by name? Or, perhaps that was the mathgroup newsgroup?)
Back towards the original topic. I am thinking about the ways that I use Mathematica. They don't fit easily into a single category. Mathematica is something of a swiss army knife.
Academics have less time on their hands than many people think--most of my faculty colleagues work long (and thankless) hours seven days a week. And, I believe that, in most cases, the time is not spent on research or teaching. So, I was wondering why I am able to open Mathematica at all?
From a research perspective, I use Mathematica:
1) derive stuff
2) simulate stuff
2) keep track of stuff that I've derived
3) visualize things that I've learned.
It serves as workbench and as scratch paper. As much as I agree with David Park's viewpoint about using Mathematica to publish, I can't afford for the research community to catch up or adopt. It's a battle that I can't win and I'm either too afraid or too lazy to fight. However, It is easy and eye-opening to give presentations with Mathematica--hopefully this might help get the ball rolling to archival publication.
From a teaching perspective, I use Mathematica:
1) To show students that they can understand a physical phenomenon much much better by coding it and visualizing it.
2) to reduce the barrier for physical scientists to learning maths that they should know (the documentation and electronic communities are excellent modules for math as well as mathematica).
3) simulating physical systems for pedagogy.
I believe that being able to code is integral to scientific literacy. For physical scientists, symbolic computing languages like Mathematica threads together many educational goals.
From a recreational perspective,
1) It is fun just to play with new ideas by coding them up.
2) I have collaborated on pieces that have been exhibited at MoMA, the Pompidou, the Paris Fashion Show, and other places that we created with Mathematica.
Finally, while we are quoting about death and revolution, there is a nice one by Henry Ford, "“Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young.” Just playing with Mathematica is a good strategy for staying young.