Stepping back from all this, what’s most astounding is how invisible mathematics is to most of the world. And how a huge part of mathematics isn’t just solving equations, but rather taking some invisible pattern you discovered in your head, and getting that insight into another person’s head so they can understand it just as lucidly as you do. That’s how mathematics grows in practice. It’s this evolving network of conversations, drawings, and gesticulations. Mathematics is like this thick underbrush that takes a machete to get a peek inside. It grows and expands while some branches whither and die. But a select few offshoots slowly but surely pierce through the canopy into the sunlight, and their fruits change the world.