Alexandre Grothendieck > Quotes

“Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.”
― Alexander Grothendieck

“In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone.”
― Alexander Grothendieck

“If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size,’ but always form.”
― Alexander Grothendieck

“One should never try to prove anything that is not almost obvious.”
― Alexander Grothendieck

“It's to that being inside of you who knows how to be alone, it is to this infant that I wish to speak, and no-one else. I'm well aware that this infant has been considerably estranged. It's been through some hard times, and more than once over a long period. It's been dropped off Lord knows where, and it can be very difficult to reach. One swears that it died ages ago, or that it never existed - and yet I am certain it's always there, and very much alive.”
― Alexander Grothendieck

“It is in this gesture of "going beyond," to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one-it is in this solitary act that one finds true creativity. All others things follow as a matter of course.”
― Alexander Grothendieck

“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: Réflexions et témoignage sur un passé de mathématicien.

“The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps...”
― Alexandre Grothendieck

“Comme toute activité purement intellectuelle, l’activité mathématique intense et de longue haleine a un effet plutôt abrutissant.”
― Alexandre Grothendieck, Récoltes et semailles: Réflexions et témoignage sur un passé de mathématicien.

“Et je sais aussi qu’il n’y a récoltes qui ne soient aussi semailles d’autres récoltes, plus amères souvent que celles qui les avaient précédées. Il arrive encore que quelque chose en moi se serre devant la chaîne apparemment sans fin de semailles insouciantes et de récoltes amères, transmise et reprise de génération à génération.”
― Alexandre Grothendieck, Récoltes et semailles: Réflexions et témoignage sur un passé de mathématicien.

“I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise, you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marble, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.”
― Alexandre Grothendieck

“Je pourrais illustrer la ... approche, en gardant l’image de la noix qu’il s’agit d’ouvrir. La première parabole qui m’est venue à l’esprit tantôt, c’est qu’on plonge la noix dans un liquide émollient, de l’eau simplement pourquoi pas, de temps en temps on frotte pour qu’elle pénètre mieux, pour le reste on laisse faire le temps. La coque s’assouplit au fil des semaines et des mois — quand le temps est mûr, une pression de la main suffit, la coque s’ouvre comme celle d’un avocat mûr à point! . . .

L’image qui m’était venue il y a quelques semaines était différente encore, la chose inconnue qu’il s’agit de connaître m’apparaissait comme quelque étendue de terre ou de marnes compactes, réticente à se laisser pénétrer. ... La mer s’avance insensiblement et sans bruit, rien ne semble se casser rien ne bouge l’eau est si loin on l’entend à peine... Pourtant elle finit par entourer la substance rétive...

I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! . . .

A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.”
― Alexandre Grothendieck, Récoltes et semailles: Réflexions et témoignage sur un passé de mathématicien.