Agnostics

"Rather than words comes the thought of high windows: The sun-comprehending glass, And beyond it, the deep blue air, that shows Nothing, and is nowhere, and is endless."

"What are days for? Days are where we live. They come, they wake us Time and time over. They are to be happy in: Where can we live but days?"

"His general thesis, a return to the human values of early jazz, is acceptable enough, but the waspish relish with which he attacks everything outside his own tastes is hysterical and in the end alienating, even to those of us who more or less agree with him."

"I thought of London spread out in the sun, Its postal districts packed like squares of wheat."

"Give me your arm, old toad; Help me down Cemetery Road."

"The trees are coming into leaf Like something almost being said; The recent buds relax and spread, Their greenness is a kind of grief.Is it that they are born again And we grow old? No, they die too. Their yearly trick of looking new Is written down in rings of grain.Yet still the unresting castles thresh In fullgrown thickness every May. Last year is dead, they seem to say, Begin afresh, afresh, afresh."

"I våldets Sverige så får hederliga medborgare flytta åt sidan. I rädsla för att vara nästa som drabbas av våldsverkaren, med vapen i hand, med drogögon mitt i ansiktet, så vet vi inte vad den här personen är kapabel att göra"

"Ursvenskt är bara barbariet. Resten av utvecklingen har kommit utifrån. [...] Det kan ibland vara bra att ödmjukt påminna om att väldigt mycket av det som är Sverige har skapats i utveckling, just för att vi varit öppna för att ta emot andra människor och andra erfarenheter"

"We have a strong economy but we don't have the job creation we need. We want more job creation."

"The Nordic welfare model is in many aspects a good model but it needs more of a choice for individuals."

"Om alla liknar Carl bekräftas vanföreställningarna av moderaterna. Det blir ett parti för Carl Bildt-kopior."

"Ska vi vara ärliga så är en hel del av jobbproblematiken kopplad till utrikes födda."

"For our genius of a father did not limit himself to math. His brain was an octopus, the tentacles of which extended in all directions. He could scan Latin verse and Greek verse as well, and it was as if he were hearing Homer or Theocritus in person. Not to mention the fact that he read Greek from volumes filled with characters which in no way resembled the ones in our Greek grammar or book of excerpts from Greek literature. He also read Sanskrit, with its truly bizarre letters. He spoke Italian like Dante, Spanish like Cervantes, and so for almost every living language."

"When he was not busy doing math, he reads fat books covered with rough leather, on the pages of which can be seen very old, perfectly round holes dug out by medieval worms. Or else he passes through a museum while devoting himself to unbelievably profound notions about Van Gogh's paintings or Greek amphorae."

"Yes, but there is the problem. It would have been banal. Mediocre. We had been trained to despise everything which was not excellent. How disgusting to see the father of one of our classmates or friends on vacation playing cards or, even worse, sitting on the sofa watching television. We blush with shame for our unfortunate little friend."

"(April 7) My mathematics work is proceeding beyond my wildest hopes, and I am even a bit worried - if it's only in prison that I work so well, will I have to arrange to spend two or three months locked up every year? In the meantime, I am contemplating writing a report to the proper authorities, as follows: "To the Director of Scientific Research: Having recently been in a position to discover through personal experience the considerable advantages afforded to pure and distinterested research by a stay in the establishments of the Penitentiary System, I take the liberty of, etc. etc.""

"One day it occurred to me to measure the speed with which such rumors were propagated. All I had to do was to start one - the more preposterous the better - at one end of the stadium, and then hasten to the other end to await the results."

"Already while at the Ecole Normale, I had been deeply struck by the damage wreaked upon mathematics in France by World War I. This war had created a vacuum that my own and subsequent generations were hard pressed to fill. In 1914, the Germans had wisely sought to spare the cream of their young scientific elite and, to a large extent, these people had been sheltered. In France a misguided notion of equality in the face of sacrifice - no doubt praiseworthy in intent - had led to the opposite policy, whose disastrous consequences can be read, for example, on the monument to the dead of the Ecole Normale. Those were cruel losses; but there was more besides. Four or more years of military life, whether close to death or far away from it - but in any case far from science -, are not good preparation for resuming the scientific life: very few of those who survived returned to science with the keenness they had felt for it. This was a fate that I thought it my duty, or rather my dharma, to avoid."

"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.""

"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)."

"Alexandre Grothendieck was very different from Weil in the way he approached mathematics: Grothendieck was not just a mathematician who could understand the discipline and prove important results—he was a man who could create mathematics. And he did it alone."

"Kantian ethic, or what passes for it today, has always seemed to me to be the height of arrogance and folly. Claiming always to behave according to the precepts of universal maxims is either totally inept or totally hypocritical; one can always find a maxim to justify whatever behavior one chooses. I could not count the times (for example, when I tell people I never vote in elections) that I have heard the objection: "But if everyone were to behave like you..." - to which I usually reply that this possibility seems to me so implausible that I do not feel obligated to take it into account."

"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."

"[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."

"Mozart's music, even at its most beautiful, often gives an impression of some being who, though very far above us in his incomprehensible serenity, nevertheless stops to remember us for a brief instant and comes within our reach, with gentle mockery and tender pity, to transcribe a fleeting message for us. But sometimes, in certain quartets and quintets, and in certain parts of The Magic Flute, this same being, without a thought for us, communicates with his fellow beings, and what we hear then is a world unknown to us, a world of which we are allowed only a furtive glimpse."

"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."

"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 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."

"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."

"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."

"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 his thesis, Weil generalized Mordell's theorem on the finite generation of the group of rational points on an elliptic curve, to abelian varieties of any dimension. Weil then hoped to use this finite generation result for the rational points on the jacobian of a curve to go on to show that when a curve of genus > 1 is imbedded in its jacobian, only a finite number of the rational points of the jacobian can lie on the curve. Not finding a way to do this, he decided to call his proof of finite generation (the "theorem of Mordell-Weill") a thesis, despite Hadamard's advice not to be satisfied with half a result!"

"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."

"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."

"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."

"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."

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

"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."

"... the geometry over p-adic fields, and more generally over complete local rings, can provide us only with local data; and the main tasks of algebraic geometry have always been understood to be of a global nature. It is well known that there can be no global theory of algebraic varieties unless one makes them "complete", by adding to them suitable "points at infinity," embedding them, for example, in projective spaces. In the theory of curves, for instance, one would not otherwise obtain such basic facts as that the number of poles and zeros of a function are equal, of that the sum of residues of a differential is 0."

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

"‘[…] 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!’"

"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."

"Sometimes my sister and I dream of having a run-of-the-mill father. He would make coffee and toss salads. He would not prefer his work to us, and he would tell us instead: "How pretty you look, my dear, tell me what you did today." He would speak to us with words of affectionate banality."

"Twenty-nine years ago, in Chile, on the 11th of September 1973, General Pinochet overthrew the democratically elected government of Salvador Allende in a CIA-backed coup. “Chile should not be allowed to go Marxist just because its people are irresponsible,” said Henry Kissinger, Nobel Peace Laureate, then the U.S. Secretary of State... Guatemala, Costa Rica, Ecuador, Brazil, Peru, the Dominican Republic, Bolivia, Nicaragua, Honduras, Panama, El Salvador, Mexico and Colombia – they’ve all been the playground for covert – and overt – operations by the CIA. Hundreds of thousands of Latin Americans have been killed, tortured or have simply disappeared under the despotic regimes that were propped up in their countries..."

"The armed forces have acted today solely from the patriotic inspiration of saving the country from the tremendous chaos into which it was being plunged by the Marxist government of Salvador Allende.… The Junta will maintain judicial power and consultantship of the Public Accounts Control. The Chambers will remain in recess until further orders. That is all."

"His greatest virtue was following through but fate could grant him only that rare and tragic greatness of dying in armed defence of an anachronistic booby of bourgeois law, defending a Supreme Court of Justice that had repudiated him but would legitimise his murderers, defending a miserable Congress that had declared him illegitimate but which was to bend complacently before the will of the usurpers, defending the freedom of opposition parties that had sold their souls to fascism, defending the whole moth-eaten paraphernalia of a shitty system that he had proposed abolishing but without a shot being fired. The drama took place in Chile, to the greater woe of the Chileans, but it will pass into history as something that has happened to us all, children of this age, and it will remain in our lives for ever."

"The Popular Unity government represented the first attempt anywhere to build a genuinely democratic transition to socialism — a socialism that, owing to its origins, might be guided not by authoritarian bureaucracy, but by democratic self-rule."

"In Chile, a CIA-supported coup helped put Gen. Augusto Pinochet in power from 1973 to 1990."

"I knew what none of them could possibly know, that the corporatocracy, its band of EHMs [economic hitmen), and the jackals waiting in the background would never allow the little guys to gain control. I only had to draw upon the examples of Arbenz and Mossadegh — and more recently, upon the 1973 CIA overthrow of Chile's democratically elected president, Salvador Allende."