In today's post, she writes:
It's difficult to describe how or why math works. It's easier to just write the formula and say, "Do this." Several readers have commented on this blog that what's often missing from math education is more of a focus on why certain applications work. I agree. It's harder to remember what to do, if you don't have some sense of why it works.This is something that many mathematicians should remember. But there's a balance to be struck; if you spend too much time on the theory ("why" it works) and never apply it that's silly too.
As you may have guesed, I primarily view mathematics as a tool for solving various interesting problems; I'm often not interested in the theory for its own sake, but I do like that knowing "theoretical" things makes lots of problems more tractable. Often such problems involve lots of calculation, and as many of you know it's easy to get lost in a calculation if you don't understand why you're doing it. But if you never calculate, and you only prove general results, I feel like you're ignoring why this subject exists in the first place. (Mathematicians of a more theoretical inclination may, of course, disagree.)