Sublime

It’s not surprising if you couldn’t find the words to describe how you tie your shoes. Most likely, you didn’t even try. Writing mathematics, that is, transcribing mental images with enough clarity and precision to allow others to understand and reproduce them, is an art.

For Thurston, as for most creative mathematicians, mathematics is a sensual and carnal experience that is located upstream from language. Logical formalism is at the heart of the apparatus that makes this experience possible. Math books may be unreadable, but we nevertheless need them. They’re a device that we rely on in our quest for the true math

Physics basically says we’ll understand the universe because we’re going to extremize a function. That’s what physics does—optimization, some least-action principles. So, we’re going to minimize the time, we’ll minimize the energy, we’ll minimize the distance. We’re looking for those functions that we’re trying to extremize and we’re going to repre