Political Activists

"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."

"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."

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

"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."

"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."

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

"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."

"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."

"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."

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

"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"."

"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."

"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."

"[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."

"[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."

"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]"

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

"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.]"

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

"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.]"

"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.]"

"[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."

"You start out in 1954 by saying, "Nigger, nigger, nigger." By 1968 you can't say "nigger"—that hurts you. Backfires. So you say stuff like forced busing, states' rights and all that stuff. You're getting so abstract now [that] you're talking about cutting taxes, and all these things you're talking about are totally economic things and a byproduct of them is [that] blacks get hurt worse than whites. And subconsciously maybe that is part of it. I'm not saying that. But I'm saying that if it is getting that abstract, and that coded, that we are doing away with the racial problem one way or the other. You follow me—because obviously sitting around saying, "We want to cut this," is much more abstract than even the busing thing, and a hell of a lot more abstract than "Nigger, nigger.""

"[T]here is a big part of me that is anti-intellectual."

"The '80s were about acquiring—acquiring wealth, power, prestige. I know. I acquired more wealth, power, and prestige than most. But you can acquire all you want and still feel empty. What power wouldn't I trade for a little more time with my family? What price wouldn't I pay for an evening with friends? It took a deadly illness to put me eye to eye with that truth, but it is a truth that the country, caught up in its ruthless ambitions and moral decay, can learn on my dime. I don't know who will lead us through the '90s, but they must be made to speak to this spiritual vacuum at the heart of American society, this tumor of the soul."

"Without the help of the people our exertions would be as nothing."

"Why should Ireland be treated as a geographical fragment of England, as he had heard an ex-Chancellor of the Exchequer call it some time ago. Ireland was not a geographical fragment, but a nation."

"The law gave those landlords extensive power at the present time, and unless they went in for a revolution he confessed he did not see how they were going to bring about a radical reform of the system of land tenure in this country."

"You can never have civil liberty so long as strangers and Englishmen make your laws and so long as the occupiers of the soil own not an inch of it."

"[Y]ou have an expenditure of five or six millions of pounds sterling—nearly all of it paid by the English taxpayers, and all for the purpose of screwing rack-rents out of the Irish tenants. I am very sure that that sort of thing will not be allowed to go on. Would not it be a very wise thing for the Irish landlords to recognize the situation in time, to see that if they do not be reasonable they will be chucked overboard altogether?"

"Fellow citizens:The hour to try your souls and to redeem your pledges has arrived."

"Stand together in face of the brutal, cowardly enemies of your race!"

"Bring English tyranny to its knees."

"Pay no rent under any pretext!"

"The government, with its bayonets, will learn in a single Winter how powerless are armed forces against the will of a united determined, and self-reliant nation."

"Do what is beyond your strength even should you fail sometimes."

"No man has the right to fix the boundary to the march of a nation."

"No man has the right to say to his country "Thus far shalt thou go and no further"."

"While we leave those things to time, circumstances and the future, we must each one of us resolve in our own hearts that we shall at all times do everything which within us lies to obtain Ireland the fullest measure of her rights."

"I would not have taken off my coat and gone to work had I not known that we were laying the foundations by this movement for the recovery of our legislative independence."

"Richard Barry O'Brien: Every Irish Nationalist would go for separation if he thought he could get it; we are all Home Rulers because we do not believe separation is possible. Charles Stewart Parnell: I have never gone for separation. I never said I would. The physical force men understand my position very well. I made it clear to them that I would be satisfied with a Parliament, and that I believed in our constitutional movement; but I also said that if our constitutional movement failed, I could not then stand in the way of any man who wished to go further and to try other means. That was the position I always took up. I have never changed, and I still believe in our constitutional movement. I believe that with our own Parliament, if England does not meddle, we can build up our country."

"Parnell's death is as unexpected as most of his proceedings. I don't think you and I ever quite agreed in our estimate of him. I still regard him—measured by his opportunities and his achievements—as one of the half-dozen great men of action of this century. Napoleon stands by himself; he has in our time—in many respects in all time—neither equal nor second. But the only others of this age that I would rank higher than Parnell are Abraham Lincoln, Bismarck, and (perhaps) Cavour. Of course you understand that I am not speaking of the goodness (in any of the cases) of the result, but of the width and depth of the changes brought about by personal initiative. Like Bismarck, and Napoleon himself, Parnell lived too long, and the later part of his life was an anti-climax. I think myself that his mental and moral equilibrium was at all times very delicately poised, and once lost, he never regained it."

"Parnell was not eloquent, much less an orator. Possessed of singularly handsome features, he was slovenly in dress and untidy in appearance. He used to speak with one of his hands buried deeply in a front pocket of his trousers. He had no great command of language. But as he hissed out his sentences of concentrated passion and scorn, scattering his notes as he proceeded upon the seat behind him, he gave an impression of almost dæmonic self-control and illimitable strength. When he spoke for his party, in the tremendous moments of the crisis, Mr. Gladstone would move to the end of the front bench, and with his hand held behind his ear, listen to the freezing but impressive display with rapt attention. Either in the House or outside of it, Parnell appeared an isolated figure; "remote, unfriended, melancholy, slow," he came in and out without exchanging a word with anyone: the utmost concession that he appeared to make to companionship was when he would be met tramping the lobbies in earnest conversation with one of the few associates whom he deigned to consult."

"He had statesmanlike qualities; and I found him a wonderfully good man to do business with, until I discovered him to be a consummate liar."

"Accident made him a parliamentarian, but he was a cold-blooded tactician, amenable to liberal considerations but utterly immune from liberal sympathies. The romantic notion of the “brotherhood of man” disgusted Parnell."

"[T]he one man in politics for whom I was ever able to feel a genuine respect."

"Home Rule apart, he was himself a Tory."

"Mr. Parnell has proved to the world the kind of leader the Irish nation is on the point of losing. He is a man of iron determination, inflexible will, matchless courage and audacity and of peerless skill as a leader, but a man who will not allow even the demands of conscience and honour to stand in the way of his purposes, 'who neither fears God nor respects man'. ... Who can withhold his meed of admiration from the old fallen commander and who can help feeling compassion at the ruin of such grandeur!"

"Mr Butt was a lawyer, and believing that he could persuade Parliament of the justness of his cause, he attempted to effect a revolution by argument. ... Parnell appreciated the situation more correctly, but he was hampered by the crimes that clung round the Land League, and by the opposition of the landlords, naturally exasperated by attacks on their property."