38. Math Isn’t About Working Hard, It’s About Being Cleverly Lazy
(Epistemic status: a time-worn explanation I used to give my undergrads, fancied up a little.) Math isn't about working hard to get the right answer. It's about being cleverly lazy. Let me explain. For most of your life, you've probably been afraid of math, or burned out by it, or intimidated. There's a single right answer, and everything you need to do to get that answer is hard and weird and abstract. Surely as you keep going in math, as you learn harder math and are asked to do more difficult things, you'll also need to keep putting in more and more effort? Surely you need to work yourself to the bone doing it "the right way" just to keep up? No! Absolutely not! If you try to pull that garbage you will end up doing a literally infinite amount of work! For a good example of this, consider something like the sum of negative powers of 2: 1, 1/2, 1/4, 1/8, and so on forever. You could spend a lifetime adding those up by hand and not get anywhere, and if you...