You ever try changin' break shoes without that little tool to pop those springs on an off? Yeah, knuckle-buster for sure. Same dif with Mathematica and mathematics: I personally cannot see how anyone can do mathematics in the 21st century without having Mathematica to pop "springs" on and off. Take for example a recent problem in here in the DE forum:

whatta' gonna do with such a thing? Solve it I guess. How do you know it's right though? Easy to check it Mathematica. Easy to experiment with, and study. Others too. How about all those triple integrals with volumes? Hard to visualize sometimes unless you draw them first, and again how do you know your manual answer is right? Easy to check in Mathematica. And if you're into Complex Analysis, then Mathematica 6 and 7 was made for that subject in my opinion. Lots of other things too. If you're gonna' do mathematics, then learn how to use Mathematica and stop bustin' ya' knuckles.