What is rare, and what our culture doesn’t push you to do, is to be aware of your capability for synesthesia and to try to develop it systematically. Secret math is a mental yoga whose goal is to retake control over our ability for synesthesia.

When I look at a bridge, I see stress lines. I see which parts of the bridge are subject to compression, and which ones are subject to tension. I can call up these perceptions on command, with a bit of concentration. They help me experience and understand the world. You have similar sensations. You can “see” that a rope is stretched too tightly and

Logic doesn’t help you think. It helps you find out where you’re thinking wrong. When Grothendieck sends out “probes” to interrogate objects he wants to understand, he gets his answer by writing: Often, you only have to write it down for you to see it’s incorrect, whereas before writing there was a vagueness, a bad feeling, instead of this evidence

If you open Discourse on Method looking for a glorification of System 2, you’ll be sadly disappointed. Descartes’s great innovation was to put intuition and subjectivity at the heart of his approach

This feeling is part of their everyday life. Mathematicians at research conferences know that things will probably fall apart in the first five minutes. They know that it won’t do any good to continue on, that it will just be sad and humiliating, because the words will simply have no meaning. But they know that getting lost is a normal stage in the

The only way to get there is to go beyond words. Replacing “the sum of whole numbers from 1 to 100” with “1 + 2 + 3 + . . . + 98 + 99 + 100” is a good start. You might have the impression of seeing the sum in a more tangible and concrete way. But that’s only ever an illusion. In reality, you’ll be missing most of the numbers, those hidden by the el

and objects are positioned in space, their actions and movements. Describing what you see and feel as simply and faithfully as possible. Capturing the moods, the music, the smells, the textures. If you can do that, you can do anything. Writing down dreams, in my experience, is the closest you can get to mathematical writing.

discovery always begins with the simple and innocent desire to understand. You invent new actions not because you want to do something new and original, but because you can’t get where you want to be with the existing techniques. Without any reference point, without someone to guide you, you have to listen to what your body is telling you. You have

The ancient Greek philosophers granted a special place to mathematics. They made it the prerequisite of all philosophy and science. Legend has it that the following phrase was engraved at the entry to Plato’s Academy: “Let no one ignorant of geometry enter.”