Mathematica: A Secret World of Intuition and Curiosity
Mathematics shapes our world. It is an instrument of power and domination. But for those who live it, math is above all an inner experience, a sensual and spiritual quest.
A 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 to get used to feeling your body in a new way. Finding the solution means thinking what had been unthinkable.
I don't think I've ever seen anyone explain mathematical discovery as a somatic process!
understanding a discovery is almost as challenging as making the discovery itself. In order to reproduce unseen actions, you can’t avoid introspection. You have to listen to yourself, and reinvent the actions _within yourself_ and _for yourself_.
The ability to associate imaginary physical sensations with abstract concepts is called _synesthesia_. Some people see letters in colors. Others see the days of the week as if they were positioned in the space around them. There’s a widespread belief that synesthesia is rare and associated with certain mental conditions. In reality it’s a universal phenomenon and a core building block of human cognition. Here’s a little test to see if you’re capable of synesthesia: looking at the word _chocolate_, are you able to sense a sound, a color, a taste? Looking at “999,999,999,” do you get the feeling of something large? 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.
Some mathematicians even think that the comparison with Einstein isn’t fair to Grothendieck. They find Einstein’s work beautiful, elegant, brilliant, admirable. They say that it’s the work of a genius. As for Grothendieck’s work, they find it extraordinary, staggering, sublime, terrifying. They say that it can’t be the work of a human being.
Grothendieck had a different explanation: “The quality of the inventiveness and the imagination of a researcher comes from the quality of his attention, listening to the voice of things.”
But it’s obviously a metaphor. Grothendieck is alluding to the child who is present “within us” and with whom “we have lost contact.” His book is actually addressed not to us but to the lost child within us, as he makes perfectly clear from the onset: “It’s to the one within you who knows how to be alone, to the child, that I wish to speak, and to no one else.”
Grothendieck explains his uncommon creativity by the proximity he maintains with his inner child: “In me, and for reasons I have not yet dreamed of exploring, a certain innocence has survived.” He describes this as a “gift of solitude,” the capacity to find himself “alone and listening to things, intensely absorbed in a child’s game.” “Seeking and finding, that is to say, questioning and listening, is the simplest, the most spontaneous thing in the world, that no one has sole rights to. It’s a ‘gift’ that we all received in the cradle.”
Harvests and Sowings often reads like a yoga manual, and in a way that’s exactly what it is. Behind the metaphors and personal anecdotes, the text describes a certain way of holding your body, a peculiar physical attitude, an unusual relationship to language and truth.
When I’m curious about a thing, mathematical or otherwise, I interrogate it. I interrogate it, without worrying about whether my question is or will seem to be stupid, certainly without it being well thought out. Often the question takes the form
wasn’t afraid of failure. He was even certain that he would be wrong, and that’s exactly what he was looking for. Grothendieck actively sought out the error as a young child actively seeks mischief.
Fear of mistakes and fear of the truth is one and the same thing. The person who fears being wrong is powerless to discover anything new. It’s when we fear making a mistake that the error which is inside of us becomes immovable as a rock.