I think the biggest "aha-moment" (I believe the kids say "mind blowing" these days) in my entire education was the final few slides of the final class of "Introduction to Algorithms and Data Structures". Basically, if you're able to loosen the constraints of the problem, to solve for the specific case, not the general, by making assumptions about your input data set (perhaps it's almost sorted already) or accepting an only almost-correct solution (say, for travelling salesman, you just want a solution reasonably close to the best, it matters less if it is the best) you can make your algorithms orders of magnitude faster/simpler/better.