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.

It’s game seven of the Stanley Cup Finals, and both teams are about to get on the ice. The camera hovers around them, and you notice that everyone has a complex array of fist bumps, arm movements, and rituals. Some even have smelling salts that they wave in front of them before the match starts. Superstition is rampant, and you roll your eyes as a scientist, knowing that it’s all nonsense.