[oatmealsnap]

I remember letting wolfram|Alpha solve some problems, then reading the steps it took to get there. They weren't always the most "human" approaches, but there was something to learn from it as well.

Poor-man's (student) tutor.

[neutralid]

If you know how to formulate the problem well (which is typically half the problem anyway), Mathematica is great for providing closed-form solutions, if there is one. In CS graduate school, it would provide general closed-form solutions that I'd never have thought of. Most everyone else brute-forced a solution numerically or simplified the problem to specific cases, which is fine but you get so much more insight from the general analytical solution, if one exists.