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 th

At the heart of maths is the desire to understand things rather than just know them.

Mathematics is the science of imagination. Between those who allow themselves to imagine, observe, and manipulate mathematical objects and those who don’t, there’s an enormous divide. Over the years, this divide becomes monstrous, obscene, almost as monstrous and obscene as the divide between children with a room full of toys and games, and those w

Mathematicians don’t have this option and it’s a huge problem for them. In their minds, the ideas are luminous, simple, and powerful. On paper, they become stunted and sad. The mathematicians’ curse is that they can only play math in their own heads. If you taught children music by giving them the written scores for Mozart or Michael Jackson to dec

This geometric intuition has been the secret weapon in my mathematical career. I began to see things that no one else had seen, to solve problems that no one else had been able to solve. It was only much later, talking with other mathematicians and reading the stories of famous mathematicians, that I found out my experience was not at all unique. W