And every science, when we understand it not as an instrument of power and domination but as an adventure in knowledge pursued by our species across the ages, is nothing but this harmony, more or less vast, more or less rich from one epoch to another, which unfurls over the course of generations and centuries, by the delicate counterpoint of all the themes appearing in turn, as if summoned from the void.
- Alexandre Grothendieck, Récoltes et Semailles, pg. 20
If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it neither “number” or “size”, but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.
- Alexandre Grothendieck, Récoltes et Semailles, pg. 27
Grothendieck suggested, “All right, take 57.”
He likens his approach to mathematics to as sea: “The sea advances imperceptibly and without sound, nothing seems to happen and nothing is disturbed, the water is so far off one hardly hears it. But it ends up surrounding the stubborn peninsula, then an island, then an islet, which itself it submerged, as if dissolved by the ocean stretching away as far as the eye can sea.”
- Alexandre Grothendieck, Récoltes et Semailles, pg. 553
Today I am no longer, as I once was, the prisoner of interminable tasks, which so often prevented me from leaping into the unknown, mathematical or otherwise. The time of tasks for me is over. If age has brought me anything, it is lightness.
- Alexandre Grothendieck, Esquisse d’un Programme
As if summoned from the Void: The Life of Alexandre Grothendieck:
Maybe I was only then becoming aware of the weight, the inertia, the opacity of the world—qualities that stick to writing from the start, unless one finds some way of evading them. At certain moments I felt that the entire world was turning into stone: a slow petrification, more or less advanced depending on people and places but one that spared no as- pect of life. It was as if no one could escape the inexorable stare of Medusa. The only hero able to cut off Medusa’s head is Perseus, who flies with winged sandals; Perseus, who does not turn his gaze upon the face of the Gorgon but only upon her image reflected in his bronze shield.
- Italo Calvino, Lightness, Six Memos