Do you feel like you’re not getting enough out of what you do in class? Does mathematics feel boring, just a bunch of rules that you follow without more or less knowing why?

When mathematics makes sense, each piece seems to fit together. There’s no question about how to do things, because it’s all natural. This is what happens when you become good at algebraic manipulations. No matter how hairy the expression, you’re able to deal with it. Double-decker fractions aren’t frightening. Sure, it might be tedious to work through, but it’s doable. It’s sort of like strolling through a path in a meadow. Nothing is blocking you, and the way forward is clear.

There’s no doubt that writing is a useful tool. If anything, I’m biased towards writing. I write every day, so I know what it means to use words to craft an explanation. If you can use the right words in the right arrangement, almost everything becomes clear.

As a student in science, you’re taught how to understand the details, the gory bits of an argument or a concept. When you learn about Kepler’s law of equal areas being swept out in equal times, you’re not just told that fact, but you prove it. Each part of the argument is explained, and you get a full explanation.