Reflection and testimony on a past as a mathematician
Récoltes et Semailles — Harvests and Sowing (1986). Notes from source. An internal race of two horses — of mathematics and of meditation. The former which is “not personal to me, they are meant to be communicated” whereas the latter “knowledge that arises from the work of meditation is “solitary” knowledge, knowledge that cannot be shared[partagée], let alone “communicated””.
- ”The little child discovers the world as he breathes - the ebb and flow of his breath make him welcome the world in its delicate being, and makes him project himself into the world that also welcomes him. The adult can also discover, in those rare moments when he has forgotten his fears and his knowledge, when he looks at things or himself with eyes wide open, eager to know, new eyes - the eyes of a child.”
- ”When I am curious about something, mathematical or otherwise, I question[interroge] it. I question it, without caring if my question is perhaps stupid or if it will appear so, without it being carefully weighed. Often the question takes the form of an assertion - an assertion which, in truth, is a knocking probe. I will then believe more or believe less in the assertion, which depends of course on where I stand in the comprehension of the things I’m looking at. Often, especially at the beginning of a research, the assertion is completely false - but this still had to be done to convince yourself. Often, it suffices to write it down for it to become obvious that it is false, whereas before writing it down there was a vagueness[flou], like an uneasiness[malaise], instead of obviousness."
- "One who fears to be wrong is powerless to discover. It is when we are afraid of making mistakes that the mistake inside us becomes immovable like a rock. Because in our fear, we cling to what we have decreed to be “true”, or what has always been presented to us as “true”. If we are moved, not by the fear of seeing an illusory security vanish, but by a thirst for knowing, then error, like suffering or sorrow, will cross us without ever becoming frozen, and the trace of its passage will be a renewed understanding."
- "This fundamental inertia of the mind, suffocated by its ‘knowledge’, is certainly not specific to mathematicians. I am straying somewhat away from my subject: the prohibition imposed upon the mathematical dream, and through it, anything that does not present itself under the usual appearance of a finished product, ready to be taken in. The little I have learned about the other natural sciences is enough to make me realise that a similarly rigorous prohibition would have condemned them to sterility, or to progressing like a tortoise, a bit like in the Middle Ages when there was no question of cadging[écornifler] the letters of the Holy Scriptures. But I am also well aware that the deep source of discovery, as well as the process of discovery in all its essential aspects, is the same in mathematics as in any other region or thing of the universe that our body and mind can know. To banish the dream is to banish the source - to condemn it to an occult existence.”
- See also: epistemic play
- ”Much more than I did, he had retained a sense of the simple and essential things - the sun, the rain, the earth, the wind, the song, the friendship…"
- "My vocation is to learn, to know this world through myself, and to know myself through this world. If my life can bring any benefit to myself or others, it is to the extent that I am true to this vocation, that I am true to myself."
- "My principal guide in my work was the constant search for a perfect coherence, a complete harmony that I divined behind the turbulent surface of things, and which I patiently strove to uncover, without ever being tired of it. It was a heightened sense of “beauty”, surely, that was my flair and my only compass."
- "It is not so much, it seems to me, a so-called “brain power” that makes the difference between this mathematician and another, or between one piece of work and another of a same mathematician; but rather the quality of finesse, of the greater or lesser delicacy of this openness or sensitivity, from one researcher to another or from one moment to another in the same researcher. The most profound and fruitful work is also that which attests to the most delicate sensitivity in apprehending the hidden beauty of things."
- "Once the work is done, the “result” appears obvious, and can be formulated in a few words. But if someone perceptive had said these words to me before or during the work, it would probably not have helped me at all. If the work took so long, it is because the resistance was strong, and deep."
- "In maths, the “obvious” things are also the ones that sooner or later someone has to come across. They are not “inventions” that you can or cannot make. They are things that have always been there, that everyone walks by without paying attention, even if it means taking a long diversions around them, or tripping over them every time. After a year or a millennium, inevitably, someone finally pays attention to the thing, digs around it, unearths it, looks at it from all sides, cleans it, and finally gives it a name."
- "To put it another way: meditation is a solitary adventure. It is solitary in nature. And not only is the work of meditation a solitary work - I think this is true of any work of discovery, even when it is part of a collective work. But the knowledge that arises from the work of meditation is “solitary” knowledge, knowledge that cannot be shared[partagée], let alone “communicated”; or if it can be shared, it is only in rare moments. It is a work, a knowledge that goes against the grain of the most inveterate consensus, consensus which concerns[inquiètent] each and everyone. This knowledge is certainly expressed simply, in simple and clear words. When I express it to myself, I learn in the process of expressing, because the expression itself is part of a work, carried by an intense interest. But these same simple and clear words are powerless to communicate meaning to others when they come up against the closed doors of indifference or fear."
- "The most immediate meaning of this work has been that of a dialogue with myself, therefore of a meditation”