The dirty secret of calculus is that most people who take and pass calculus don’t actually understand calculus. They just memorize the 100 or so common cases and formulae, recognize those in the problem sets, transform those into what they know, and solve programmatically without comprehending what they are doing even a little bit.

To be fair, I think the above is true of most of education, not math alone. But it’s kind of funny all the people who claim to be superior intellects because they can solve a canned problem — yet they can’t think their way out of a paper bag when it’s not pre-digested and can’t at all handle a real-world problem that has no answer in the back of the book.