Prisoners

"Wonderful, I like cars, too, I like all the great things you can buy in a department store. But when you have to buy them in order to stay unaware, comatose, then the price you pay is too high."

"This is the Auschwitz generation, and there's no arguing with them!"

"The people in our country and in America and in all West European countries, they have to gorge and guzzle so that they don't even start to think about the fact that we have something to do with Vietnam or what it might be about, OK?"

"Don’t blather that it is too hard. The action to liberate Baader wasn’t crocheting doilies either."

"I am also overcome by fury and helplessness when I read these letters... What twisted thinking! What helplessness! What desperation and brutality against themselves, against me and others."

"I just can't believe that there won't come a day when people won't be fed-up with being overfed. That they won't get fed-up with the self-deception that all this fantastic food is the whole point of life."

"These letters have come to be important to me because they help throw a little sand in the inevitability of the great story-telling machine in which everything is propelled towards death, murder, suicide."

"On a double-log plot, my grandmother fits on a straight line."

"In the... ensuing year, he sent three more papers to mathematical journals and a new memoir to the Academie. The permanent secretary, Fourier, took it home with him, but died before having examined it, and... [it] was not retrieved... Thus his second memoir was lost like the former."

"He considered himself a victim of a... social organization which... sacrifices genius to mediocrity, and... he cursed the hated regime of oppression which... precipitated his father's death and against which the storm was gathering."

"His French biographer very clearly explains his attitude:There was in him a hardly disguised contempt for whosoever did not bow spontaneously and immediately before his superiority, a rebellion against a judgment which his conscience challenged beforehand and a sort of unhealthy pleasure in leading it further astray and in turning it entirely against himself. Indeed, it is frequently observed that those people who believe that they have most to complain of persecution could hardly do without it and, if need be, will provoke it. To pass oneself off for a fool is another way and not the least savory, of making fools of others."

"Evariste was in the possession of his general principles by the beginning of 1830... at the age of eighteen, and that he... knew their importance. ...[H]e did not trouble himself to write his memoirs with sufficient clearness and to give the explanations... necessary because his thoughts were... novel. ...Instead ...Galois enveloped his thought in ...secrecy by his efforts to attain ...conciseness, that coquetry of mathematicians."

"On July 2... 1829, his father had been driven to commit suicide... This terrible blow, following many smaller miseries, left a very deep mark... His hatred of injustice became the more violent... his father's death incensed him, and developed his tendency to see injustice and baseness everywhere."

"was... the highest mathematical school in France and... also a daughter of the Revolution who had remained faithful... The young Polytechnicians were the natural leaders of every political rebellion; liberalism was for them a matter of traditional duty. ...[T]hus twice sacred to Galois, and his failure to be accepted was a double misfortune."

"[H]e was probably pressed by his friend, [Auguste] Chevalier, to join the Saint-Simonists, but he declined, and preferred to join... the "Societe des amis du peuple"."

"In 1829 he entered the Ecole Normale... then passing through the most languid period of its existence. ...[T]here too, the main student body inclined toward liberalism, though their convictions were very weak and passive as compared with the... Polytechnique... Evariste suffered doubly, for his political desires were checked and his mathematical ability remained unrecognized."

"He had read... books of geometry as easily as a novel... No sooner had he begun to study algebra than he read Lagrange's original memoirs. This extraordinary facility had been at first a revelation... but... it became more difficult for him to curb his own domineering thought and to sacrifice it to the routine of class work. ...By 1827 it had reached a critical point. This might be called the second crisis of his childhood: his scientific initiation. His change of mood was observed by the family. Juvenile gaiety was suddenly replaced by concentration; his manners became stranger every day. A mad desire to march forward along the solitary path... possessed him."

"In his last year at the college, 1828-1829... [his] teacher of mathematics... wrote of him: "This student has a marked superiority over all his school-mates. ...He works only at the highest parts of mathematics." ...[O]ther teachers were less indulgent. For physics and chemistry, the note often repeated was: "Very absent-minded, no work whatever.""

"It is likely that... [in] a few centuries... [he] will appear... surrounded by the same halo of wonder as... Euclid, Archimedes, Descartes and Newton."

"[A]t the age of sixteen he believed that he had found a method of solving general equations of the fifth degree. ...[B]efore succeeding in proving the impossibility of such resolution, Abel had made the same mistake."

"[D]iscoverers of fundamental principles are not generally awarded much recompense. They often die misunderstood and unrewarded. But... the fame... of Galois ...is based upon the unlimited future. He well knew the pregnancy of his thoughts, yet they were even more far-reaching than he could possibly dream of."

"Galois was already trying to... enter the ... as early as 1828 — but failed. This failure was very bitter to him... he considered it as unfair... [but] his extra knowledge could not compensate for his deficiencies... The next year he published his first paper, and sent his first communication to the Academie des Sciences... lost through Cauchy's negligence. This embittered Galois even more. A second failure to enter Polytechnique seemed to... climax... his misfortune..."

"It was... another man who reentered the Ecole Normale in the autumn of 1830. ...The revolution had opened to him a fresh source of disillusion..."

"His complete works fill only sixty-one small pages; but a French geometer, publishing a large volume some forty years after Galois' death, declared... it... simply a commentary on... [Galois'] discoveries. Since then, many more consequences have been deduced... and Galois'... ideas have influenced the whole of mathematical philosophy."

"Since my mathematical youth, I have been under the spell of the classical theory of Galois. This charm has forced me to return to it again and again."

"It is... not true... that he proved and used the simplicity of s. He did not need to: he was much cleverer than that; his treatment of solubility of equations is... simpler and more elegant than... textbook tradition."

"Langlands and Grothendieck are both (at least) Giants by any measure, and both were consciously successors of Galois."

"He was still a mere boy, yet within these short years he had accomplished enough to prove indubitably that he was one of the greatest mathematicians of all times."

"Galois's introduction of imaginary roots of congruences has not only led to an important extension of the theory of numbers, but has given rise to wide generalizations of theorems which had been obtained in subjects like linear congruence groups by applying the ordinary theory of numbers."

"An excessive desire for conciseness was the cause of this fault which one must try to avoid when writing on the mysterious abstractions of pure Algebra. Clarity is indeed an absolute necessity. ... Galois too often neglected this precept."

"[T]he soul of Galois will burn on throughout the ages and be a perpetual flame of inspiration."

"It is perhaps less well known that [Galois] had also, without any possible doubt, discovered the essentials of the theory of abelian integrals, as Riemann would develop it 25 years later. By what route did he arrive at these conclusions? The fragments of calculations in Analysis found among his papers do not seem to permit much of an answer to that question, but there is room to imagine that he must have been very close to the idea of the Riemann surface associated with an algebraic function, and that such an idea must also be fundamental in his investigations into what he calls the "théorie de l'ambiguïté"."

"It angered Galois sufficiently that he wrote directly below it:"

"Nous avons transcrit textuellement la démonstration que nous avons donnée de ce lemme dans un mémoire présenté en 1830. Nous y joignons 154 IV The First Memoir comme document historique le note suivante qu’a cru ^devoir^ y apposer M. Poisson. On jugera. Note de l’auteur [We have faithfully transcribed the proof of this lemma that we have given in a memoir presented in 1830. We append as a historical document the following note which Mr Poisson believed he should add. Posterity will judge. Note by the author]"

"La démonstration de ce lemme n’est pas suffisante; mais il est vrai d’après le No . 100 du mémoire de Lagrange, Berlin, 1771. [The proof of this lemma is insufficient; but it is true according to No . 100 of the memoir by Lagrange, Berlin, 1771.]"

"[In the first case, the problem is solving equations, including solving an algebraic equation with an unknown variable. In the second case, the problem is integrating differential equations. Galois was the first to recognize with absolute clarity how extraordinarily important the concepts of substitution group and invariant of a discontinuous group are for dealing with problems of the first kind.] Im ersten Falle hat man das Problem der Auflösung der Gleichungen, unter Anderm der Auflösung einer algebraischen Gleichung mit einer Unbekanuten. Im zweiten Falle hat man das Problem der Integration von Differentialgleichungen. Galois war der erste, der vollkommen klar erkannte, wie ausserordentlich wichtig die Begriffe Substiutionengruppe und Invariante einer discontinuirlichen Gruppe für die Behandlung von Problemen jener ersten Art sind."

"[We will not dwell further on the theory of transformation groups of a linear equation. We believe we have sufficiently demonstrated... the value of this theory, which is simply the natural extension to a question of analysis of the fruitful ideas introduced into algebra by Galois] Nous n'insisterons pas davantage sur la théorie des groupes de transformations d'une équation linéaire. Nous pensons avoir suffisamment montré... l'intérèt de cette théorie, qui n'est que l'extension bien naturelle à une question d'Analyse des idées si fécondes introduites en Algèbre par Galois."

"No existence could be more tragic... and the only one at all comparable... is.. that of... Niels Henrik Abel, who died of consumption at twenty-six in 1829... just when Galois was ready to take the torch from his hand and to run... further. Abel had the inestimable privilege of living six years longer... full years at the time that genius was ripe... of divine inspiration. What would not Galois have given us, if he had been granted six more such years at the climax of his life."

"[U]nder a more liberal guise, the same oppression, the same favoritism, the same corruption soon took place under Louis-Philippe as under Charles X."

"Poisson, reading Galois' First Memoir, found the proof of Lemma III insufficient, and wrote in pencil the following comment."

"Ne pleure pas, Alfred ! J'ai besoin de tout mon courage pour mourir à vingt ans !"

"Dès le commencement de ce siècle, l'algorithme avait atteint un degré de complication tel que tout progrès était devenu impossible par ce moyen, sans l'élégance que les géomètres modernes ont su imprimer à leurs recherches et au moyen de laquelle l'esprit saisit promptement et d'un seul coup un grand nombre d'opérations. Il est évident que l'élégance si vantée et à si juste titre n'a pas d'autre but. Du fait bien constaté que les efforts des géomètres les plus avancés ont pour objet l'élégance on peut donc conclure avec certitude qu'il devient de plus en plus nécessaire d'embrasser plusieurs opérations à la fois, parce que l'esprit n'a plus le temps de s'arrêter aux détails. ... Sauter à pieds joints sur les calculs, grouper les opérations, les classer suivant leurs difficultés et non suivant leurs formes; telle est, suivant moi, la mission des géomètres futurs; telle est la voie où je suis entré dans cet ouvrage."

"... un auteur ne nuit jamais tant à ses lecteurs que quand il dissimule une difficulté."

"Preserve my memory, since fate has not given me life enough for the country to know my name."

"[This] science is the work of the human mind, which is destined rather to study than to know, to seek the truth rather than to find it."

"How to console oneself for having exhausted in one month the greatest source of happiness which is in man — of having exhausted it without happiness, without hope, being certain that one has drained it for life? Oh! come and preach peace after that! Come and ask men who suffer to take pity upon what is! Pity, never! Hatred, that is all. He who does not feel it deeply, this hatred of the present, cannot really have in him the love of the future. ...I like to doubt your cruel prophecy when you say that I shall not work any more. But I admit that it is not without likelihood. To be a savant, I should need to be that alone. My heart has revolted against my head. I do not add as you. do: It is a pity."

"Mais je n’ai pas le temps et mes idées ne sont pas encore bien développées sur ce terrain qui est immense. [But I don't have the time and my ideas are not yet well developed on this immense terrain.]"

"The publication in the "Gazette des Ecoles" of a letter of Galois... which... scornfully criticised the director's tergiversations was... the last of many offenses. On Dec. 9, he was invited to leave the school, and his expulsion was ratified by the Royal Council on Jan. 3, 1831."

"Il parait après cela qu'il n'y a aucun fruit à tirer de la solution que nous proposons. [It seems there is no fruit to be drawn from the solution we offer.]"

"To support himself Galois announced that he would give a private course of higher algebra... [A] new copy of his second lost memoir... communicated... to the Academie... was returned to him by Poisson, four months later, as being incomprehensible. Galois was partly responsible... for he had taken no pains to explain himself clearly. This was the last straw. ...[H]e plunged himself entirely into the political turmoil. ...He is said to have exclaimed: "If a corpse were needed to stir the people up, I would give mine.""