[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.