Academics From France

"(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.""

"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."

"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.""

"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..."

"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."

"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)."

"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."

"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."

"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?"

"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!""

"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."

"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."

"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."

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

"‘[…] 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!’"

"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."

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

"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."

"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."

"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."

"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."

"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 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!"

"... 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."

"J'ai osé beaucoup, mais la prochaine fois, vous verrez, j'oserai plus encore..."

"The President of the Commission, M. Delors, said at a press conference the other day that he wanted the European Parliament to be the democratic body of the Community, he wanted the Commission to be the Executive and he wanted the Council of Ministers to be the Senate. No. No. No."

"We have preserved social security and the welfare state, but at the expense of employment. Neo-liberalism, which put the emphasis on the market, manifested itself in Europe by the policies led by Margaret Thatcher, who sometimes had good reasons to prise off the shackles which were condemning British society to decline. But [Thatcherite policies] fell into an excess of laissez faire."

"[The European Union must be a] federal union with a common currency, a tightly co-ordinated economic policy and a foreign policy capable of common diplomatic and military action. ... Britain is refusing to face reality. Does England have a future outside Europe? No. But it is difficult for a great nation to bid farewell to its golden age."

"Socialism had defeated her brand of ultra-liberal economics. ... [Margaret Thatcher believed that] the law of the market could be applied in the place of politics. She underestimated the dignity and grandeur of politics, which is an attempt to combine, an attempt to convince, an attempt to listen to others, to try to find a society which is not better but less bad than the one in which we live today."

"The spirit of the Right is dominated by scepticism towards the possibility of profound change in society and above all towards the idea that man can achieve progress over himself. On the Left, on the other hand, there exists a belief in human and social progress."

"What is perceived as a cost by some will turn out to be the competitive advantage of Europe by helping maintain a well-trained, secure workforce, open to change."

"I have a passion for reform, for the progress of man and society. I cannot stand the feeling of being useless."

"[Only federalism] allows democratic control and can punish abuses of power. Only federalism can guarantee respect for national character and regional variety. ... The springtime of Europe is still before us."

"According to [John Major], the issue now is to build a greater Europe around a single market and some areas of co-operation, notably in the environment. Everything else is flexible. I call that Europe à la carte. This is not my thesis. Mine is: the fathers of the Treaty of Rome wanted not just peace among us, but also that Europe should be able to continue existing in a world in which they sensed profound change in the wind, without being able to describe it. In consequence, if we want our nations to keep their universal capacity together, they must unite politically, without nostalgia for the old order."

"Europe will have 30 million unemployed by the end of the century if the continent's competitiveness and employment patterns are not rapidly changed. ... Europe's economic performance against America and Asia was declining and that the Community was faced with a choice between further decline and survival."

"What I see is European construction drifting towards a free-trade zone, that is to say an English-style Europe, which I reject. If we do nothing, this will lead in 15 years to a break-up. I reject a Europe that would be just a market, a free-trade zone without a soul, without a conscience, without political will, without a social dimension."

"[Greek voices] must not only be heard claiming their due but also contributing to the European Union."

"He thinks I am the man of the past but I am still here. He is the man of the past."

"Europe needs an army to fight the resource wars of the twenty-first century."

"We must define the political Europe that we want. We must plead for the federal approach."

"Cars are free to circulate but still there are speed limits, therefore I do not see why, at the international level, we should not study ways to limit monetary movements. Bankers cannot act at will. ... Why should we not draw up some rules of the game?"

"Politicians who attack the dream of a federal Europe are racist bigots intent on undermining the Continent's freedom and peace."

"The crux is the reform of the treaty which would lead to common action. There must be a will to defend the central interests of Europe. If there is no majority voting, then the same level of impotence will continue."

"Federalism is a guideline, not a pornographic word, you can speak it out loud...We have been focusing too much on a country that has said no, no, no!"

"If we are really on the way towards a political entity with a common foreign policy on basic issues, then I consider that France's nuclear force should be available to serve that policy."

"If we do not succeed with political union...then the historic decline of Europe which began with the First World War will resume."

"The Americans should stop insulting us, I'm not going to be an accomplice to the depopulation of the land. It's not up to the Americans to tell us how to organise our farm policy and the balance of our society. Their attitude is to treat the EC as if it had the plague and then encourage the rest of the world to join in."

"The social and human balance of our societies depend on the farming world."