Jews From France

"In establishing the tasks to be undertaken by Bourbaki, significant progress was made with the adoption of the notion of structure, and of the related notion of isomorphism. Retrospectively these two concepts seem ordinary and rather short on mathematical content, unless the notions of morphism and category are added. At the time of our early work these notions cast new light upon subjects which were still shrouded in confusion: even the meaning of the term "isomorphism" varied from one theory to another. That there were simple structures of group, of topological space, etc., and then also more complex structures, from rings to fields, had not to my knowledge been said by anyone before Bourbaki, and it was something that needed to be said. As for the choice of the word "structure," my memory fails me; but at that time, I believe, it had already entered the working vocabulary of linguists, a milieu with which I had maintained ties (in particular with Émile Benveniste)."

"The major classic texts in analysis (Jordan, Goursat) which we had at first set out to replace aimed to set forth in a few volumes everything a beginning mathematician should know before specializing. At the end of the nineteenth century, such a claim could still be made seriously; by now it had become absurd. ... it soon became apparent that there was no alternative but to give up any idea of writing a text for college-level instruction. Above all it was important to lay a foundation that was broad enough to support the essential core of modern mathematics..."

"Otto Schmidt] called together the principal mathematicians in Moscow and Petrograd (later known as Leningrad) and spoke to them more or less as follows: "Whatever the regime, the work of mathematicians is too inaccessible to laymen for us to be criticized from the outside; as long as we stick together, we will remain invulnerable.""

"Awaiting me upon my return to Strasbourg were Henri Cartan and the course on "differential and integral calculus," which was our joint responsibility. ... One point that concerned him was the degree to which we should generalize Stokes' formula in our teaching. ... In his book on invariant integrals, Elie Cartan, following Poincare in emphasizing the importance of this formula, proposed to extend its domain of validity. Mathematically speaking, the question was of a depth that far exceeded what we were in a position to suspect. ... One winter day toward the end of 1934,1 thought of a brilliant way of putting an end to my friend's persistent questioning. We had several friends who were responsible for teaching the same topics in various universities. "Why don't we get together and settle such matters once and for all, and you won't plague me with your questions any more?" Little did I know that at that moment Bourbaki was born."

"I had also, unsuccessfully, looked for the works of Saint John of the Cross. The flashing beauty of his poems would probably have moved me more than did Saint Theresa, but it was not until much later that I came to know his work. I read a little of Saint Theresa and became quickly convinced that mystic thought is at bottom the same in all times and places: reading Suzuki's popular works on Zen was soon to confirm this conclusion. ... Speaking of a saint whose behavior was somewhat eccentric, one of the monks remarked gently: "But Christianity is madness" ("el cristianismo es una locum"). This perfectly orthodox statement often comes to mind when I think about my sister's life."

"[On meeting Raymond Paley] At first, we seemed to be on completely different wavelengths. Finally, it became apparent to me that he worked fruitfully only when competing with others: having the rest of the pack at his side spurred him to greater efforts as he tried to surpass them. In contrast, my style was to seek out topics that I felt exposed me to no competition whatsoever, leaving me free to reflect undisturbed for years. No doubt every scientific discipline has room for such differences of temperament. What does it matter if a given researcher is motivated primarily by hopes of winning the Nobel prize? Sometimes it seems to me that Ganesh, the Hindu god of knowledge, chooses the bait, noble or vulgar, best suited to each of his followers."

"Both the Jews and the brahmins of southern India are communities that, for twenty centuries, have devoted themselves tirelessly to the most abstract subtleties of grammar and theology. For the Jews it was the study of the Talmud, a task often passed down from father to son; for the brahmins, it was the Brahmanas and the Upanishads. It is hardly surprising that the younger generations, when their time came, turned toward the sciences, and preferably the most abstract among them: this trend was merely the natural extension of millennial traditions."

"Is it mere coincidence that in India Pāṇini's invention of grammar had preceded that of decimal notation and negative numbers, and that later on, both grammar and algebra reached the unparalleled heights for which the medieval civilization of the Arabic-speaking world is known?"

"I began to combine this ordinary form of touring with a specifically mathematical variety. I had formed the ambition of becoming, like Hadamard, a "universal" mathematician: the way I expressed it was that I wished to know more than non-specialists and less than specialists about every mathematical topic. Naturally, I did not achieve either goal."

"Hopf, back from Amsterdam, was teaching Brouwer's topology. He had helped arrange lodgings for me quite close to where he lived, rather far from the center of town, and together we would take the long tram ride to the university. One day I asked him what he would do when he got tired of topology. He replied in all seriousness: "But I'll never get tired of topology!""

"In comparison with the wise man, the saint is perhaps just a specialist - a specialist in holiness; whereas the wise man has no specialty. This is not to say, far from it, that Dehn was not a mathematician of great talent; he left behind a body of work of very high quality. But for such a man, truth is all one, and mathematics is but one of the mirrors in which it is reflected - perhaps more purely than it is elsewhere."

"In mathematics, perhaps more than in any other branch of knowledge, ideas spring fully armed from the creator's brain; thus mathematical talent usually reveals itself at a young age; and second-rate researchers play a smaller role than elsewhere, the role of a sounding board for a sound they do not contribute to shape."

"Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously, and in which the unconscious (however one interprets this word) seems to play a role. In a famous passage, Poincaré describes how he discovered Fuchsian functions in such a moment. About such states, Gauss is said to have remarked as follows: "Procreare jucundum (to conceive is a pleasure)"; he added, however, "sed parturire molestum (but to give birth is painful)." Unlike sexual pleasure, this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do so at will, unless perhaps by dogged work which it seems to reward with its appearance. It is true that the pleasure experienced is not necessarily in proportion with the value of the discoveries with which it is associated."

"‘[…] his correspondence with Digby, and, through Digby, with the English mathematicians WALLIS and BROUCKNER occupies the next year and a half, from January 1657 to June 1658. It begins with a challenge to Wallis and Brouckner, but at the same time also to Frenicle, Schooten “and all others in Europe” to solve a few problems, with special emphasis upon what later became known (through a mistake of Euler’s) as “Pell’s equation”. What would have been Fermat’s astonishment if some missionary, just back from India, had told him that his problem had been successfully tackled there by native mathematicians almost six centuries earlier!’"

"We should ask our fellow physicists to invent a principle of anti-interference, which would bring light out of two obscurities (Leray and Grothendieck)."

"About ancient mathematics (whether Greek or Mesopotamian) and medieval mathematics (Western or Oriental), the would-be historian must of necessity confine himself to the description of a comparatively small number of islands accidentally emerging from an ocean of ignorance, and to tenuous conjectural reconstructions of the submerged continents which at one time must have bridged the gaps between them."

"It is hard for you to appreciate that modern mathematics has become so extensive and so complex that it is essential, if mathematics is to stay as a whole and not become a pile of little bits of research, to provide a unification, which absorbs in some simple and general theories all the common substrata of the diverse branches if the science, suppressing what is not so useful and necessary, and leaving intact what is truly the specific detail of each big problem. This is the good one can achieve with axiomatics (and this is no small achievement). This is what Bourbaki is up to."

"An important point is that the p-adic field, or respectively the real or complex field, corresponding to a prime ideal, plays exactly the role, in arithmetic, that the field of power series in the neighborhood of a point plays in the theory of functions: that is why one calls it a local field."

"First rank scientists recruit first rank scientists, but second rank scientists tend to recruit third rank scientists, third rank scientists recruit fifth rank, and so on. If the director of the Department is genuinely interested in preserving the high quality of his Institute, he must exercise all of his power to put things in their right place, otherwise the deterioration process is destined to diverge indefinitely."

"God exists since mathematics is consistent, and the Devil exists since we cannot prove it."

"If you say to someone who has ears to hear: "What you are doing to me is not just," you may touch and awaken at its source the spirit of attention and love. But it is not the same with words like, "I have the right..." or "you have no right to..." They evoke a latent war and awaken the spirit of contention."

"Ca va faire, je pense, 23 ans que tu as fait ton entrée dans le monde phénoménal pour le plus grand emmerdement des recteurs et des directrices."

"I knew her very well, I have had long discussions with her. For a period of time she was more or less in sympathy with our cause, but then she lost faith in the proletariat and in Marxism. It's possible that she will turn toward the left again."

"Light for the spirit and nourishment for the soul, Simone Weil’s work does not have to be brought "up to date," since it emanates from that summit of being which overhangs all times and places. How could one put a date on a particular thought by Plato or Marcus Aurelius, a verse by Aeschylus, or the utterance of a Shakespearean hero ? The same is true, and in exemplary fashion, for Simone Weil. True light does not fade, and a true fountain need never be replenished. To speak of what is timeless is also to speak of what is universal. The undeserved privilege of presenting Simone Weil’s first book to the public has brought me countless favourable comments from the four corners of the globe. What strikes me most about these is that they come from individuals of such diverse backgrounds, social status, cultural milieu, etc, and that reading this work has left a deep impression on all their souls, as they found in it the revelation of an inner truth for which they had, up until then, been waiting in vain. At the twilight of a century whose accelerated history has led to the rise and fall of so many idols, this book increasingly appears like a message from eternity, addressed to eternal man, this "Nothingness capable of God," who is enslaved by gravity and liberated by grace."

"Most sins can be traced back to the social element. They spring from a thirst to appear and to dominate. It is not that Simone Weil rejects the social element as such; she knows that our environment, roots and traditions form bridges, metaxu between earth and heaven; what she repudiates is the totalitarian city — symbolized by the ‘Great Beast’ of Plato and the Beast of the Apocalypse — whose power and prestige usurp God’s place in the soul. Whether it shows itself under a conservative or a revolutionary aspect, whether it consists of adoring the present or the future city, social idolatry always tends to stifle and to replace the true mystic tradition. All the persecutions of prophets and saints are due to it; through it Antigone and Joan of Arc were condemned and Jesus Christ crucified. The social Beast offers man a substitute for religion which allows him to transcend his individuality without surrendering his self and so, at small cost, to dispense with God; a social imitation of the highest virtues is possible by which they are immediately degraded into pharisaism: "The pharisee is he who is virtuous out of obedience to the Great Beast.""

"Although a few commentators have noted the influence of Simone Weil on the thought of Albert Camus, their relationship has never been fully explored … I shall examine several aspects of that influence in … Weil's critique of Marxism which Camus adopted in L'Homme Révolté… the conception of the rebel as an artisan which Camus also used in L'Homme Révolté, and … Weil's mysticism, to which Camus was reluctantly though definitely drawn. … I shall consider more fully the different conceptions of freedom and justice which appear in their writings and argue that their contributions to political thought here lay with their appreciation of the impulse in modern man to seek and impose absolute values. In this context, we shall see that Camus and Simone Weil provide different routes to individual authenticity and integrity in an absurd world."

"Simone Weil was one of the most remarkable women of the twentieth, or indeed of any other century. I have great sympathy for her, but sympathy is not necessarily congeniality. It would be easier to write of her if I liked what she had to say, which I strongly do not. …I think Simone Weil had both over- and under-equipped herself for the crisis which overwhelmed her — along, we forget, immersed in her tragedy, with all the rest of us. She was almost the perfectly typical passionate, revolutionary, intellectual woman — a frailer, even more highly strung Rosa Luxemburg. … She made up her own revolution out of her vitals, like a spider or silkworm. She could introject all the ill of the world into her own heart, but she could not project herself in sympathy to others. Her letters read like the more distraught signals of John of the Cross in the dark night."

"[By 1939] Simone Weil had developed a social and political awareness which it took the war and the German occupation to awaken in many French intellectuals and beyond which many of them, including Sartre, have never progressed."

"I have read everything by Simone Weil, who was an extraordinary woman gifted with immense empathy. But I think she might have profited from some better advice. She was not physically strong and yet, in order to directly experience the struggle of working people, she undertook factory work that was too much for her. And she also fought in the Spanish Civil War and, being somewhat clumsy, stepped into a pail of boiling oil, was severely burned, and went to Portugal to recuperate. Later, she would eat only the minimal portion of food she believed was available to people in occupied France—a few potatoes perhaps. She had been diagnosed with tuberculosis, and this may well have contributed to her death. (Then, as you see her, she is more of an inspiration than a model.) EP: Yes, an inspiration. She could not have been a model for me because I am neither a genius nor a mystic and, like Leonora, I had children I loved and for whom I was responsible, so that even if I had discovered a vocation of this sort in myself, I could not have lived such an extreme life."

"By saying Simone Weil's life was both comic and terrible I am not trying to reduce it, but mean to be paying her the highest tribute I can, short of calling her a saint, which I don't believe she was. Possibly I have a higher opinion of the comic and terrible than you do. To my way of thinking it includes her great courage and to call her anything less would be to see here as merely ordinary. Of course, I can only say, as you point out, this is what I see, not, this is what she is — which only God knows."

"Her life is almost a perfect blending of the Comic and the Terrible, which two things may be opposite sides of the same coin. In my own experience, everything funny I have ever written is more terrible than it is funny, or only funny because it is terrible, or only terrible because it is funny. Well Simone Weil's is the most comical life I have ever read about, and the most truly tragic and terrible."

"I went through a stage in life when I was thirty-two or thirty-three years old-when I was very fascinated by the writings of Simone Weil. In the end, her religious philosophy left me where I was. But I felt that there was something there that answered to a need that I felt, my "need for roots" that she wrote about so marvelously. I couldn't find the same solution."

"What she cared about was human souls. Her study of human rights and human obligations exposes the falsity of some of the verbiage still current which was used during the war to serve as a moral stimulant."

"In her political thinking she appears as a strong critic of both Right and Left; at the same time or truly a lover of order and hierarchy than even most of those who call themselves Conservative, and more truly a lover of the people than most of those who call themselves Socialist."

"The reader of her work finds himself confronted by a difficult, violent and complex personality; and the assistance of those who have the advantage of long discussions or correspondence with her, especially those who are under the peculiar conditions of the last five years her life, will be a permanent value in the future. … After reading Waiting on God and the present volume I saw that I must try to understand the personality of the author and that the reading and re-reading of all her work was necessary for this slow process of understanding. In trying to understand her, we must not be distracted … by considering how far, and at what points we agree or disagree. We must simply expose ourselves to the personality of a woman of genius, of a kind of genius akin to that of the saints. … I cannot conceive of anybody's agreeing with all of her views, or of not disagreeing violently with some of them. But agreement and rejection are secondary: what matters is to make contact with a great soul. Simone Weil was one who might have become a saint. Like some who have achieved this state, she had greater obstacles to overcome, as well as greater strength for overcoming them, then the rest of us. A potential saint can be a very difficult person. I suspect that Simone Weil could be at times insupportable. One is struck, here and there, by contrast between an almost superhuman humility and what appears to be an almost outrageous arrogance."

"The assimilation of algebra by mathematical physics, a process spanning the eighteenth and extending into the nineteenth century, exacerbates the implicit thoughtlessness of classical science by subordinating scientific cognition to symbolic formulae increasingly devoid of insight. In the process, a genuine encounter with natural necessity, revelatory of divine providence, is lost to science, Symbolic or algebraic physics represents the collectivization of thought, as it were, where science itself is rendered a technique of knowledge production and thought ceases to be the activity of any responsible individual. … This process reaches its logical conclusion in twentieth-century physics, where science is reduced finally to a form of symbolic manipulation the only value of which is predictive success and technological domination of nature."

"Weil’s critique of modern science consists of two parts, the first directed at classical (Newtonian) science, the latter at contemporary science, especially twentieth-century relativity and quantum mechanics. In each, Weil detects a species of thoughtlessness or failure of that prayerful attention that marks all genuine study and intellectual accomplishment."

"In the last years of her life she worried that all beliefs, even religious ones, risk idolatry. Her insistence upon "a convention ratified by God" is another example of the thoroughly personal knowledge of God that she sought, and one gathers, believed herself to have attained. She seemed persuaded that under the auspices of the Church such personal knowledge simply does not come about; on the contrary, parishioners turn idolatrous and mistake a ritual, a habit, and alas, a social custom (to go to church on Sunday, say) for such a convention."

"Simone Weil, je le sais encore maintenant, est le seul grand esprit de notre temps et je souhaite que ceux qui le reconnaissent en reçoivent assez de modestie pour ne pas essayer d’annexer ce témoignage bouleversant. Pour moi, je serais comblé si l’on pouvait dire qu’à ma place, et avec les faibles moyens don’t je dispose, j’ai servi à faire connaitre et à répandre son oeuvre dont on n’a pas encore mesuré tout le retentissement."

"Given that only the religion of pervasive kenosis can be truly universal, no single historical individual can exhaust its fullness by virtue of his redemptive acts, and no religious institution can grasp and articulate its meaning by means of dogmatic or doctrinal teachings. In the last resort, it is in the name of religious universalism that Simone Weil calls for a reversion of historical Christianity to its origins as a religion of kenosis."

"Simone Weil's intellectual and existential search encompassed several of the major religious and sapiential traditions. Since her religiosity was imbued by Greek thought, Gnosticism, Chinese wisdom, Christian mysticism, and Indian philosophy, it is not surprising that scholars have been especially attentive to her perceptive elaborations on the universal truths informing these — at first sight — hardly compatible spiritual world views."

"In her relatively short life, Simone Weil … created a body of work whose intellectual scope and acuity are remindful of religious thinkers such as Blaise Pascal or Søren Kierkegaard. Since no book by Simone Weil appeared in her lifetime and only a few of her writings were intended for publication, a noteworthy reception of her ideas took place only when selections of her notes, diaries and fragments began to be published posthumously after World War II."

"In the interest of public security it would be advisable that this person be distanced from Le Puy, where she has never ceased to preach revolt."

"There is a certain kind of morality which is even more alien to good and evil than amorality is."

"In a general way, the literature of the twentieth century is essentially psychological; and psychology consists of describing states of the soul by displaying them all on the same plane, without any discrimination of value, as though good and evil were external to them, as though the effort toward the good could be absent at any moment from the thought of any man."

"Such words as spontaneity, sincerity, gratuitousness, richness, enrichment — words which imply an almost total indifference to contrasts of value — have come more often from their [the surrealists’] pens than words which contain a reference to good and evil. Moreover, this latter class of words has become degraded, especially those which refer to the good, as Valéry remarked some years ago. Words like virtue, nobility, honor, honesty, generosity, have become almost impossible to use or else they have acquired bastard meanings; language is no longer equipped for legitimately praising a man’s character."

"Dadaism and surrealism … represented the intoxication of total license, the intoxication in which the mind wallows when it has made a clean sweep of value and surrendered to the immediate. The good is the pole towards which the human spirit is necessarily oriented, not only in action but in every effort, including the effort of pure intelligence. The surrealists have set up non-oriented thought as a model; they have chosen the total absence of value as their supreme value. Men have always been intoxicated by license, which is why, throughout history, towns have been sacked. But there has not always been a literary equivalent for the sacking of towns. Surrealism is such an equivalent."

"The essential characteristic of the first half of the twentieth century is the growing weakness, and almost the disappearance, of the idea of value."

"It is not only in literature that fiction generates immorality. It does it also in life itself. For the substance of our life is almost exclusively composed of fiction. We fictionalize our future, and, unless we are heroically devoted to truth, we fictionalize our past, refashioning it to our taste. We do not study other people; we invent what they are thinking, saying, and doing. Reality provides us with some raw material, just as novelists often take a theme from a news item, but we envelop it in a fog in which, as in all fiction, values are reversed, so that evil is attractive and good is tedious."

"When, as a result of what was called Enlightenment in the eighteenth century, the priests had in fact almost entirely lost this function of guidance. Their place was taken by writers and scientists. In both cases it is equally absurd. Mathematics, physics, and biology are as remote from spiritual guidance as the art of arranging words. When that function is usurped by literature and science it proves there is no longer any spiritual life."