It’s hard to defend Cauchy’s stance on pedagogical grounds. But I’m sympathetic with him anyway. One of the great joys of mathematics is the incontrovertible feeling that you’ve understood something the right way, all the way down to the bottom; it’s a feeling I haven’t experienced in any other sphere of mental life. And when you know how to do something the right way, it’s hard—for some stubborn people, impossible—to make yourself explain it the wrong way.
