Learning to write math is learning to have clear ideas. Wouldn’t it be a shame to deprive yourself of that? By writing math yourself, you’ll get to understand why it is written in such a bizarre formalism, in this language made for robots: there’s really no other choice. To demonstrate, we’ll return to another of our favorite examples: the concept

It is beautifully expressed in these striking lines written by Thurston in 2011: “Mathematics is commonly thought to be the pursuit of universal truths, of patterns that are not anchored to any single fixed context. But on a deeper level the goal of mathematics is to develop enhanced ways for humans to see and think about the world. Mathematics is

The secret techniques of mathematicians aim to facilitate and accelerate this intuitive understanding. Mathematicians use logic and language as an apparatus for learning to see.

Official math can be found in textbooks, where it is presented in a logical and structured manner, in an esoteric language that relies on indecipherable symbols. Secret math, also known as mathematical intuition, can be found in the heads of mathematicians. It consists of mental representations and abstract sensations, often visual, that are for