jews-from-germany

"Out of the interaction of form and content in mathematics grows an acquaintance with methods which enable the student to produce independently within certain though moderate limits, and to extend his knowledge through his own reflection. The deepening of the consciousness of the intellectual powers connected with this kind of activity, and the gradual awakening of the feeling of intellectual self-reliance may well be considered as the most beautiful and highest result of mathematical training."

"It may be asserted without exaggeration that the domain of mathematical knowledge is the only one of which our otherwise omniscient journalism has not yet possessed itself."

"Just as the musician is able to form an acoustic image of a composition which he has never heard played by merely looking at its score, so the equation of a curve, which he has never seen, furnishes the mathematician with a complete picture of its course. Yea, even more: as the score frequently reveals to the musician niceties which would escape his ear because of the complication and rapid change of the auditory impressions, so the insight which the mathematician gains from the equation of a curve is much deeper than that which is brought about by a mere inspection of the curve."

"I have come to the conclusion that the exertion, without which a knowledge of mathematics cannot be acquired, is not materially increased by logical rigor in the method of instruction."

"The true mathematician is always a good deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly connected with it, mathematicians have intellectually created an ideal world, which they attempt to develop into the most perfect of all worlds, and which is being explored in every direction. None has the faintest conception of this world, except he who knows it."

"The domain, over which the language of analysis extends its sway, is, indeed, relatively limited, but within this domain it so infinitely excels ordinary language that its attempt to follow the former must be given up after a few steps. The mathematician, who knows how to think in this marvelously condensed language, is as different from the mechanical computer as heaven from earth."

"If in Germany the goddess Justitia had not the unfortunate habit of depositing the ministerial portfolios only in the cradles of her own progeny, who knows how many a German mathematician might not also have made an excellent minister."

"The analysis which is based upon the conception of function discloses to the astronomer and physicist not merely the formulae for the computation of whatever desired distances, times, velocities, physical constants; it moreover gives him insight into the laws of the processes of motion, teaches him to predict future occurrences from past experiences and supplies him with means to a scientific knowledge of nature, i.e. it enables him to trace back whole groups of various, sometimes extremely heterogeneous, phenomena to a minimum of simple fundamental laws."

"Mathematical knowledge, therefore, appears to us of value not only in so far as it serves as means to other ends, but for its own sake as well, and we behold, both in its systematic external and internal development, the most complete and purest logical mind-activity, the embodiment of the highest intellect-esthetics."

"It is true that mathematics, owing to the fact that its whole content is built up by means of purely logical deduction from a small number of universally comprehended principles, has not unfittingly been designated as the science of the self-evident [Selbstverständlichen]. Experience however, shows that for the majority of the cultured, even of scientists, mathematics remains the science of the incomprehensible [Unverständlichen]."

"I was amazed at how this outstanding connoisseur of Indian knowledge in the field of exact sciences showed himself to be so captive to Cantor’s authority."

"Aims, methods, and persistency, are common to the medical profession of all countries. On its flag is inscribed what should be the life rule of all nations: Fraternity and solidarity."

"Without darkness there would be no concept of light For light to be self aware it must have its opposite—darkness."

"Even aperson deprived of his own ideas and individuality, at the very moment he gains power, acquires substance and content The function of power is to transform the inner being of the holder of power. Power credit and fame create individuality and a face for a person deprived of these qualities by nature."

"The desire for power is the most reliable of emotions."

"Women are most adorable when they are afraid; that's why they frighten so easily."

"A queer fellow, impulsive and one-sided. A great walker and talker - he liked that kind of walk to which frequent stops at a beer-garden or a cafe belong. Either with friends, and then accompanying his discussions with violent gesticulations, completely irrespective of his surroundings; or alone, and then murmuring to himself and pondering over mathematical problems; or if in an idler mood, carrying out long numerical calculations by heart. There always remained something of the eternal "Bursche" of the 1848 type about him – an air of dressing gown, beer and tobacco, relieved however by a keen sense of humor and a strong dash of wit. When he had to listen to others, in classrooms or at meetings, he was always half asleep."

"His strength rested on the invention and calculative execution of formal processes. There exist papers of his where twenty pages of formulas are not interrupted by a single text word; it is told that in all his papers he himself wrote the formulas only, the text being added by his friends."

"The Spaniards waiting there gathered around us, watching our reunion and smiling with the indomitable hearts of passionate people not yet hardened by war, detention camps, or the horror of thousands of deaths. (chapter 6 p127)"

"I felt anxious, the way you do when a dream seems too real and at the same time something intangible, imperceptible, tells you that whatever makes you feel happy or sad can never be reality. (chapter 7 p156)"

"It had all been in vain. The prayers in churches and in mosques-all in vain. The invocations, the appeals to long-forgotten, long-ignored gods-in vain. And their final resistance with knives and teeth-in vain. Cowardice had also been in vain. Hiding, waiting-everything in vain. In vain, too, the promises, the hopes, the unexpected generosity of strangers. Whether their fathers had started plowing only yesterday or their forefathers two thousand years ago-it was all in vain. Men who looked death in the eye as they did life, coldly without blinking, and wore lions' claws made of iron on their belts, their courage was in vain; and in vain did the lion keep his vigil before the palace in the capital city. The conquerors rode astride his back and tore at his mane, yelling and hooting. Everything that had existed before had become incomprehensible. The totality of life and living, because it was suddenly all in vain. The simple yesterday and the day before yesterday that were clear to everyone, and the two thousand years that some men could look back on, the incredible, hazy yet real life, one's own existence from time immemorial-the one as much in vain as the other. If there is not going to be any future, then the past will all have been in vain. (beginning of "The Guide")"

"Seghers is one of those rare twentieth-century German writers who had a need and a use for the short-story form throughout the entire span of her career. The genre enabled her to react relatively quickly to shifting situations. The stories in this collection span a period of just over thirty years-covering the Weimar Republic after the onset of inflation, the Great Depression, the Nazis' seizure of power, Seghers's escape to France, the Spanish Civil War, World War II, and her emigration to Mexico, and extending on into the postwar period, the Cold War, the emergence of two German states, and the Twentieth Congress of the Communist Party of the Soviet Union in 1956, which exposed the crimes of Stalinism. There is no other writer working in the German language over that long span of time whose stories and novellas have such stylistic diversity and such a wide range of approaches and aims. Seghers wanted to describe the world in order to change it. In this sense, each specific time finds its embodiment in one of her stories."

""With me it's something else," he said. "I'm Jewish. For me the magnanimity of the German people was never even a consideration." (Chapter 4 p98)"

"They're saying that the Montreal went down between Dakar and Martinique. That she ran into a mine. The shipping company isn't releasing any information. It may just be a rumor. But when you compare it to the fate of other ships and their cargoes of refugees which were hounded over all the oceans and never allowed to dock, which were left to burn on the high seas rather than being permitted to drop anchor merely because their passengers' documents had expired a couple of days before, then what happened to the Montreal seems like a natural death for a ship in wartime. That is, if it isn't all just a rumor. And provided the ship, in the meantime, hasn't been captured or ordered back to Dakar. In that case the passengers would now be sweltering in a camp at the edge of the Sahara. Or maybe they're already happily on the other side of the ocean. Probably you find all of this pretty unimportant? You're bored?-I am too. May I invite you to join me at my table? Unfortunately I don't have enough money for a regular supper. But how about a glass of rosé and a slice of pizza? Come, sit with me. Would you like to watch them bake the pizza on the open fire? Then sit next to me. Or would you prefer the view of the Old Harbor? Then you'd better sit across from me. You can see the sun go down behind Fort St. Nicolas. That certainly won't be boring. (beginning of chapter 1)"

"[He] got up out of bed and stuck his head out of his little window as far as he could. It was utterly quiet. But for the first time this quiet failed to give him a sense of peace-the world wasn't quiet, it was speechless. Involuntarily he pulled his hands out of the moonlight which, like no other light, has the faculty of clinging to every surface and penetrating every crevice. (chapter I p60)"

"The whole town was a tortuous net in which he was already caught. He would have to slip through the meshes. (chapter III p173)"

"And yet although all this transit whispering made me feel quite miserable, it was amazing to think that even though thousands, no, hundreds of thousands, had died in the flames of the air raids and the furious attacks of the Blitzkrieg, there were many more who were born quite without being noticed by the consuls. They hadn't asked for letters of transit, hadn't applied for visas; they were not under the jurisdiction of this place. And what if some of these poor souls, still bleeding physically and spiritually, had fled to this house, what harm could it do to a giant nation if a few of these saved souls, worthy, half-worthy, or unworthy, were to join them in their country-how could it possibly harm such a big country? (chapter 8 p178)"

"Der Beweis des Hilbertschen Satzes und anderer Sätze ist sehr abstrakt, aber an sich ganz einfach und darum logisch zwingend. Eben darum leitet diese Arbeit von Hilbert eine neue Epoche der algebraischen Geometrie ein. Ebenso einfach ist dann auch die Anwendung auf die Invariantentheorie, die ich hier noch weniger zergliedern kann. Die ganze Frage der Endlichkeit der Invarianten, welche Gordan seinerzeit nur mit umfangreichen Rechnungen für binäre Formen hatte erledigen können (vgl. oben S. 308), wird hier mit einem Schlage für Formen mit beliebig vielen Veränderlichen gelöst. Ihrer Eigenart entsprechend wurde diese Arbeit zunächst mit sehr verschiedener Stimmung aufgenommen. Mich hat sie damals bestimmt, Hilbert bei nächster Gelegenheit nach Göttingen zu ziehen. Gordan war anfangs ablehnend: „Das ist nicht Mathematik, das ist Theologie.“ Später sagte er dann wohl: „Ich habe mich überzeugt, daß auch die Theologie ihre Vorzüge hat.“ In der Tat hat er den Beweis des Hilbertschen Grundtheorems selbst später sehr vereinfacht (Münchener Naturforscherversammlung 1899)."

"A miracle that he was even speaking, and then to say what he had said. Usually you hear only about the things that excited people, never about what silenced them. (from "Tales of Artemis")"

"If there remained in him only the strength for one tiny movement in the direction of freedom, no matter how senseless and useless the movement, he would still want to make it. (chapter III p173)"

"In seiner eigenen Wissenschaft war es weniger ein Vertiefen in fremde Arbeiten -- denn solche las er sehr wenig -, als ein Überblick über die inneren Zusammenhänge und ein instinktives Gefühl für die Wege und Ziele der mathematischen Bestrebungen, was ihn schon aus kleinen Andeutungen Wertvolles von Minderem scheiden lieb. Aber den auf die Grundlagen gehenden Begriffsentwicklungen ist Gordan nie gerecht geworden: auch in seinen Vorlesungen hat er alle Grunddefinitionen begrifflicher Art, selbst die der Grenze, vollständig gemieden. Sein Vorlesungsprogramm hat sich nur auf die Vorlesungen allgemeiner Art, gelegentlich auch auf binäre Formentheorie, erstreckt; die Übungen waren mit Vorliebe der Algebra entnommen. Über Jacobisches, so über Funktionaldeterminanten, trug er gern vor, nie über Funktionentheoretisches, höhere Geometrie oder Mechanik; auch ließ er keine Seminarvorträge halten. Die Vorlesungen wirkten wesentlich durch die Lebhaftigkeit der Ausdrucksweise und durch eine zum Selbststudium anregende Kraft, eher als durch Systematik und Strenge."

"Gordan, eine in sich geschlossene Individualität, war kräftig und einheitlich im Leben und in der Arbeit. Kein Neuerer in der Wissenschaft: er griff nur an, was seiner Art gemäß war; aber was er angriff, führte er nnermüdlich durch bis zu Ende. Aus dem Stoffe selbst heraus neue kombinatorische Methoden zu schaffen und seine Instrumente kräftig zu handhaben, das war sein mächtiges Können: er war Algorithmiker."

"Das ist keine Mathematik; das ist Theologie."

"What normally is spread over the span of a lifetime, over a number of years, an exertion of all of one's powers to the breaking point, the relaxing and yielding and painful straining again-all this took place in his mind in the space of an hour-while minutes changed. (Chapter V, p262)"

"It happened the first week of April, I think. (beginning of "The Lord's Prayer")"

"Ich habe mich davon überzeugt, daß die Theologie auch nützlich sein kann."

"The proof of this theorem of Hilbert's and of others is very abstract, but in itself quite simple and hence logically compelling. And for just this reason this work of Hilbert's ushered in a new epoch of algebraic geometry. But application to invariant theory is just as simple, but I can analyze it here even less. The whole question of the finiteness of the invariants, which Gordan had been able to solve for binary forms only by means of comprehensive calculations (see p. 290), is here solved, with one stroke, for forms with arbitrarily many variables. Because of its uniqueness, this work was first received with very diverse reactions. I had then resolved to draw Hilbert to Goettingen at the earliest opportunity. Gordan at first declined, saying, "It is not mathematics, it is theology" But later he said: "I have convinced myself that even theology has its merits". In fact, Gordan himself later on much simplified Hilbert's basic theorem (Muenchener Naturforscherversammlung 1899)."

"38 Jahre von 1874 an hat Gordan in Erlangen verbracht. Sie sind für ihn gleichmäßig verlaufen: täglich Vorlesungen, Arbeit, und die unentbehrlichen Spaziergänge entweder mit Mitarbeitern … in drastisch lebhaften Zwiegesprächen, unbekümmert um alle Umgebung, oder allein in tiefem Nachdenken und seine Gedanken im Kopfe so fertig verarbeitend, dass er seine Rechnungen zuhause fast ohne Striche [Streichungen] ausführen konnte."

"One morning in September 1940, when the largest swastika flag in all of the countries occupied by Germany was flying over the Place de la Concorde in Paris, and the lines outside the shops were as long as the streets themselves, a certain Luise Meunier, the wife of a lathe operator and mother of three children, heard that one could buy eggs at a shop in the 14th arrondissement. (beginning of "Shelter")"

"If now a far-reaching theory has grown . . . I attribute this result primarily to Professor Gordan. I am not here referring to his trenchant and profound labours, which shall be fully reported upon hereafter. In this place I must report what cannot be expressed in quotations or references, namely, that Professor Gordan has spurred me on when I flagged in my labours, and that he has helped me . . . over many difficulties which I should never have overcome alone."

"Hilberts Doktor-Vater Ferdinand Lindemann nannte diesen Existenzbeweis „unheimlich“ und Paul Gordan meinte (zitiert nach Otto Blumenthal ‚ Lebensgeschichte‘ in Hilberts ‚Gesammelten Abhandlungen‘, Band 3 (Berlin 1935), S. 388–429, dort S. 394): „Das ist keine Mathematik; das ist Theologie.“ Etwas später milderte Gordan seinen Ausspruch etwas ab und meinte: „Ich habe mich davon überzeugt, daß die Theologie auch nützlich sein kann“. Aber es gab auch viele Mathematiker, die sich nicht überzeugen ließen. Oskar Becker (1889–1964) beispielsweise reagierte sehr heftig und bezeichnete den Hilbert’schen Beweis des Basis-Satzes als „Schleichweg einer Schein-Konstruktion“ (O. Becker in: ‚Mathematische Existenz‘, 1927, op. cit., S. 471)."

"He stopped before a shopwindow, and we recognized his face. On the left side of his forehead, just below the hairline, he had an incredible scar. He stood there, with this hole in his temple, in the middle of the colorful Parisian winter-evening throngs, like one risen from the dead, like the captain of a ship of the dead. Such people wear their own legend like a heraldic crest wherever they go. And whenever we see such people, their external appearance reminds us of this legend. (from "Meeting Again")"

"Gordan - anfänglich diesen begrifflichen Deduktionen gegenüber mehr ablehnend: „das ist keine Mathematik, das ist Theologie!" - ist dann zweimal (53), (69) dem diesem Beweise zugrunde liegenden Hilbertschen Endlichkeitssatze nähergetreten, indem er die gegebenen Formen F nach verschiedenen Kriterien in eine Reihe anordnete, die das Bilden eines endlichen Moduls aus ihnen deutlich machte; das erstemal in komplizierterer Weise speziell für die Invariantenformen, das zweitemal allgemein und einfach."

"The fascination emanating as usual from the historical material itself prevailed over any desire of practical or moral application and, needless to say, preceded any afterthought."

"The antithesis served the Anonymous, it is true, to observe very strictly the inherent difference between the God and the king; but it served him also to blur that line of distinction and to show where the difference between "God by nature" and "god by grace" ended; that is, in the case of potestas, of power. Essence and substance of power are claimed to be equal in both God and king, no matter whether that power be owned by nature or only acquired by grace."

"That the phrase actually originated in the Hispana is obvious for a simple reason: only in that collection do we find a textual corruption of the acts of the Council of Chalcedon at which one of the bishops modestly said that God imperatorem erexit ad zelum [i.e. fidei]. In other words, a scribe copying the canons of Chalcedon misread the text and changed ad zelum into ad celum; and this erroneous reading must have reached, perhaps through the channels of Pseudo-Isidorus, the Norman Anonymous for whom even that great forgery in favor of the hierarchy could turn into grist brought to his royalist mill. This reading is merely an error, though an error remarkable by itself, since it shows how easily any extravagant exaltation of the imperial power could flow from the pen of a scribe in those centuries."

"It appears relevant to the general subject of this study, and also otherwise worth our while, to inspect more closely the varieties of royal duplications which Shakespeare has unfolded in the three bewildering central scenes of Richard II. The duplications, all one, and all simultaneously active, in Richard — "Thus play I in one person many people" (V. v.31) — are those potentially present in the King, the Fool, and the God. They dissolve, perforce, in the Mirror. Those three prototypes of "twin-birth" intersect and overlap and interfere with each other continuously."

"In late antique art, we often find the halo bestowed on such figures as might impersonate a supra-individual idea or general notion. This special mark of distinction indicated that the figure was meant to represent in every respect a continuum, something permanent and sempiternal beyond the contingencies of time and corruption."

"In other words, whenever we capitalize a notion and, in the English language, even change the gender from neuter to feminine, we actually are "haloing" the word or the notion and are indicating its sempiternity as an idea or power."

"Over against his lost outward kingship he sets an inner kingship, makes his true kingship to retire to inner man, to soul and mind and "regal thoughts": You may my glories and my state depose, But not my briefs, still am I king of those. (IV.i.192ff)"