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April 10, 2026
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"A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution."
"History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future."
"Good, he did not have enough imagination to become a mathematician."
"I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bath-house."
"Immer mit den einfachsten Beispielen anfangen."
"Keep computations to the lowest level of the multiplication table."
"Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view."
"But he (Galileo) was not an idiot,... Only an idiot could believe that scientific truth needs martyrdom — that may be necessary in religion, but scientific results prove themselves in time."
"One of the supreme achievements of purely intellectual human activity."
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?"
"If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology."
""Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs."
"Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country."
"One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it."
"The art of doing mathematics consists in finding that special case which contains all the germs of generality."
"Marx … was a very bad econometrician of his times, not realizing how much real wages in Western Europe had been raised by new techniques and equipment; and he was a bad theorist because his kind of model would almost certainly lead to shifts in schedules that would raise labor's wages tremendously."
"Never, after we have read The Eighteenth Brumaire, can the language, the conventions, the combinations, the pretensions, of parliamentary bodies, if we have had any illusions about them, seem the same to us again. They lose their consistency and color—evaporate before our eyes. The old sport of competition for office, the old game of political debate, look foolish and obsolete; for now we can see for the first time through the shadow-play to the conflict of appetites and needs which, partly unknown to the actors themselves, throw these thin silhouettes on the screen. These writings of Marx are electrical. Nowhere perhaps in the history of thought is the reader made to feel the excitement of a new intellectual discovery. Marx is here at his most vivid and his most vigorous—in the closeness and the exactitude of political observation; in the energy of the faculty that combines, articulating at the same time that it compresses; in the wit and the metaphorical phantasmagoria that transfigures the prosaic phenomena of politics, and in the pulse of the tragic invective—we have heard its echo in Bernard Shaw—which can turn the collapse of an incompetent parliament, divided between contradictory tendencies, into the downfall of a damned soul of Shakespeare."
"Similar though Marx and Thoreau may be in their accounts of the consequences of living in a society defined by money, their suggestions for how to respond to it are poles apart. Forget the Party. Forget the revolution. Forget the general strike. Forget the proletariat as an abstract class of human interest. Thoreau's revolution begins not with discovering comrades to be yoked together in solidarity but with the embrace of solitude. For Thoreau, Marx's first and fatal error was the creation of the aggregate identity of the proletariat. Error was substituted for error. The anonymity and futility of the worker were replaced by the anonymity and futility of the revolutionary. A revolution conducted by people who have only a group identity can only replace one monolith of power with another, one misery with another, perpetuating the cycle of domination and oppression. In solitude, the individual becomes most human, which is to say most spiritual."
"Marxism is undoubtedly a religion, in the lowest sense of the word. Like every inferior form of religious life, it has been continuously used, to borrow the apt phrase of Marx himself, as an opiate for the people."
"Liberty, happiness, autonomy, individuality, spirituality, self-guided development are ideals that Marx and Engels valued above everything else. If they are angry with the bourgeoisie, it is because the bourgeoisie seeks to deny the majority any opportunity to be free. Given Marx and Engels' adherence to Hegel's fantastic idea that no one is free as long as one person is in chains, their quarrel with the bourgeoisie is that they sacrifice everybody's freedom and individuality on capitalism's altar of accumulation."
"Even though communist parties have disappeared almost entirely from the political scene, the spirit of communism driving the manifesto is proving hard to silence."
"Marx completely lacked a scholar's conscience which is the hallmark of a genuine man of learning. In his works there is no trace of the humility of the true researcher who, aware of his own ignorance, approaches his material with an open mind in order to learn. For Marx what has to be proved is known before the research starts."
"Just heard Gen. White's proclamation that we "have Russia zeroed in from all directions." I am waiting now for Vannevar Bush and Ed Teller to announce that our new supersensitive radar picked up a rash of heart tremors from the direction of the USSR, immediately after White's remarkably insignificant statement, I could almost hear Karl Marx laughing in his tomb."
"I find it’s not necessary for me to read Marx because I already agree with him"
"He gave the impression not only of rare intellectual superiority but also of outstanding personality. If he had had as much heart as intellect and love as hate, I should have gone through fire for him. … In view of our aims, I regret that this man, with his fine intellect, is lacking in nobility of soul. I am convinced that the most dangerous personal ambition has eaten away all the good in him. He laughs at the fools who parrot his proletarian catechism, just as he laughs over the communists à la Willich and over the bourgeoisie. The only people he respects are the aristocrats, the genuine ones who are well aware of it. In order to drive them from government, he needs a source of strength, which he can find only in the proletariat. Accordingly, he has tailored his system to them. In spite of all his assurances to the contrary, and perhaps because of them, I took away with me the impression that the acquisition of personal power was the aim of all his endeavours."
"Marx never made a discovery in the scientific sense. He never had an illumination which turned his previous ideas upside down. He decided beforehand what he wanted to discover and then sure enough discovered it. In practice Marx and still more his friend Engels made many unavowed adjustments to their system, until by the end of their lives hardly any of it remained. At any rate it could be turned to almost any purpose from the most moderate to the most revolutionary."
"Marx called himself a scientist; but he lacked the solid groundwork of facts on which to operate a scientific method. His theories are dogma, true only because he said so; and any study of them is nearer to theology than to science. Mr. Landauer is particularly anxious to show that Marx, though personally assertive, was not a believer in dictatorship in the Stalinist sense; and this is true. Marxism could develop into German social democracy or into Bolshevism, with a certain amount of perversion in each case; neither was more than implicit in Marx's own writings."
"You cannot conquer an awakened people. You cannot Prussianize Belgium and France. You cannot eradicate the teachings of Marx and Engels from the minds of hundreds of thousands of German Socialists. Surely they would find some way of uniting in spirit and in deed with the comrades of other nations in case of such an invasion on the part of a government which they had always understood and denounced."
"Fundamentalist religion becomes, as Marx so aptly observed, an "opiate of the masses.""
"Summarizing his deficiencies, Karl Marx was neither progressive nor enlightened; he was a racist, anti-Semite, a German nationalist, a warmonger, autocratic, anti-freedom proponent, Machiavellian, pro-Black slavery, petty, homophobic, megalomaniac, a bully and slanderer, antichoice, and a reactionary against liberalism and industrial capitalism. In almost every sense, Marx fit the quintessential image of Hitler like a tight glove, both appearing almost indistinguishable. Like father and son, Marx and Hitler were two social justice warriors, determined to weaponize intolerance, racism, and nationalism for what they call the greater good. In so many ways, considering their almost identical political and social makeup, metaphorically speaking, Hitler could easily be regarded as the son of Marx."
"No wonder therefore that almost everyone rebelled against Hegel. No one did this more effectively than Marx. Marx claimed to have laid bare with finality the mystery of all history, including the present and the imminent future, but also the outline of the order which was bound to come and in which and through which men would be able or compelled for the first time to lead truly human lives. More precisely, for Marx human history, so far from having been completed, has not even begun; what we call history is only the pre-history of humanity. Questioning the settlement which Hegel had regarded as rational, he followed the vision of a world society which presupposes and establishes forever the complete victory of the town over the country, of the mobile over the deeply rooted, of the spirit of the Occident over the spirit of the Orient; the members of the world society which is no longer a political society are free and equal, and are so in the last analysis because all specialization, all division of labor, has given way to the full development of everyone."
"Marx saw the coming of communism (in his sense) as the result of a long series of struggles, transforming conditions and men. The kind of society he envisioned required, as Lenin observed, "a person not like the present man on the street." Marx saw this new sort of person emerging as a natural result of the sobering process of a social struggle lasting perhaps a half-century. The educational role of adversity and setbacks for the proletariat was a recurrent theme in the writings of Marx and Engles. Lenin, on the other hand, believed that the proletariat would never automatically the necessary class outlook and purposeful unity: "Class political consciousness can be brought to the working class only from without." Whatever the relative merits, in terms of realism, of the Marxist verses the Leninist conceptions of the working class, this crucial shift of assumptions necessitated a fundamental change, however covert, in the line of march towards communism, both before and after the seizure of power [by Lenin and the Bolsheviks]."
"Against anarchists Marx and Engles were in the position of defending the "authority of the majority over the minority." Marxian passages defending the use of state power against individuals in this connection were later avidly quoted by Lenin in defense of an autocratic power which Marx had not contemplated."
"It had to be admitted in the end that Marx had made mistakes on many points of importance."
"How can the labourer be at the mercy of the upper and middle classes when these are admittedly dependent on the labourer for their very subsistence? But let us pass by this contradiction, which underlies all the teaching of Marx, and proceed to consider the consequences of accepting his theory. Let us suppose that the labourer, by working for a day, produces a table worth a pound, ten shillings of which represents the value of the wood, wear and tear of tools, rent of workshop, lighting, &c., &c., and the remaining ten shillings the wear and tear of the man, or his labour. According to Marx, the capitalist who supplies the wood, tools, workshop, &c., does so on the condition that he shall, besides being reimbursed for them by receiving ten shillings out of the price of the table, receive also, out of the other ten shillings due solely to the labourer, as large a share as he can possibly screw out of him by the threat of putting the job up to auction among his starving competitors. Let us suppose that in this way he induces the labourer to content himself with three shillings out of the ten which he has earned, and pockets seven shillings as profit. (I may observe here that Marx, with all his ingenuity, could never explain why a labourer should make a present of more than half his earnings to an employer who was absolutely dependent on him for all his wealth.) Our imaginary capitalist then, selling the table for its value - one pound, makes a profit of seven shillings. But mark what must ensue. Some rival capitalist, trading in tables on the same principle, will content himself with six shillings profit for the sake of attracting custom. He will sell the table for nineteen shillings; that is, he will allow the purchaser one shilling out of his profit as a bribe to secure his custom. The first capitalist will thus be compelled to lower his price to nineteen shillings also, and presently the competition of brisk young traders, believing in small profits and quick returns, will bring the price of tables down to thirteen and sixpence, or even lower if the reduction in price can be used as a pretext for securing another sixpence out of the labourer's three shillings. Take the price at thirteen and sixpence. if the seven shillings be indeed robbed from the labourer, then the purchaser, getting a table worth a pound for thirteen and sixpence, gets six and sixpence of the plunder, and the capitalist only sixpence; that is, the buyer is thirteen times as great a thief as the seller. But who are the buyers?"
"We never talked about men or clothes or inconsequential things we got together. It was always Marx, Lenin and revolution - real girls' talk."
"Karl Marx, in envisioning the emancipation of the working class, determined that "money is the jealous god of Israel, in face of which no other god may exist." From antiquity to the modern era, Jews have proven tremendously useful as an external enemy, or as a scapegoat for society's ills."
"Never have I met a man [Karl Marx] of such offensive, insupportable arrogance. No opinion which differed essentially from his own was accorded the honor of even a half-way respectful consideration. Everyone who disagreed with him was treated with scarcely veiled contempt. He answered all arguments which displeased him with a biting scorn for the pitiable ignorance of those who advanced them, or with a libellous questioning of their motives. I still remember the cutting, scornful tone with which he uttered – I might almost say 'spat' – the word 'bourgeois'; and he denounced as 'bourgeois' – that is to say as an unmistakable example of the lowest moral and spiritual stagnation – everyone who dared to oppose his opinion."
"If Marx had not been more than a purveyor of phraseology, he would be dead by now."
"Marxism is a religion. To the believer it presents, first, a system of ultimate ends that embody the meaning of life and are absolute standards by which to judge events and actions; and, secondly, a guide to those ends which implies a plan of salvation and the indignation of the evil from which mankind, or a chosen section of mankind, is to be saved."
"Marx was fortunate to have been born eighty years before Walt Disney. Disney also promised a child's paradise and unlike Marx, delivered on his promise."
"Karl Marx deserves an honoured place among economic pioneers of steady state and balanced growth equilibrium. What is valid in this seminal contribution is in no sense contrary to mainstream economics of Marx’s predecessors, contemporaries or successors. Even we end with the view that Marx was not so much a mathematical economist as ‘merely’ a great economist, this recognition of his analytical abilities in no sense diminishes our appreciation of him as an original and creative shaper of the science of political economy."
"Marx has certainly had more customers than any other one aspiring economist. A billion people think his ideas are important; and for the historian of thought that fact makes them important."
"Marx wrote in Chapter 3 of the first volume of Capital: "The discovery of gold and silver in America, the extirpation, enslavement and entombment in mines of the aboriginal population, the beginning of the conquest and looting of the East Indies, the turning of Africa into a warren for the commercial hunting of black-skins, signalized the rosy dawn of the era of capitalist production. These idyllic proceedings are the chief momenta of primitive accumulation." Plunder, internal and external, was the most important means of primitive accumulation of capital, an accumulation which, after the Middle Ages, made possible a new historical stage in world economic evolution."
"Since Marx, studying the genesis of capitalism has been an obligatory step for activists and scholars convinced that the first task on humanity's agenda is the construction of an alternative to capitalist society."
"To our American bourgeois newspaper correspondents this all appears rampant disorder and blind mixture of events, defying and denying human intelligence. But to everyone who has read the Communist Manifesto, it is so sublimely ordered and intellectual a performance as to dispel all pessimism of propaganda forever, and raise intelligence and the dissemination of ideas to the highest place in their confidence. Without doubt it is the most momentous event in the history of peoples. And if such an event can be shown to be no accident or mystery, but the orderly maturing and accurate enactment of ideas full-born in a great mind sixty years ago, and cherished and disseminated in the meantime by all those who had strength to believe, then indeed there is hope that intelligence may play its part in every event. Never in all history before could one so joyfully and confidently enter upon the enterprise of publishing and propagating ideas. Dedicating our admiration to the fearless faith in scientific intelligence of Karl Marx, and our energy to hopes that are even beyond his, we issue THE LIBERATOR into a world whose possibilities of freedom and life for all, are now certainly immeasurable."
"Marx was an astronomer of history, not an astrologer."
"there is a link, it seems to me, between the internalization of the era of Karl Marx and the new globalisms we are seeking to build today. Of course, the global economy is far more complicated than Marx may have ever attempted to imagine. But at the same time his analyses, it seems to me, are equally resonant today. Capital begins with a look at commodity. The capitalist commodity has penetrated people's lives in ways that are unprecedented. The commodity has entered ... capitalism in general has entered structures of feeling, the intimate spaces of people's lives."
"Capitalism is still with us, and Marx developed the most compelling analysis of capitalism. I never saw Marx as a philosopher who informed us about what the revolution was going to be like or what would come after capitalism. He provided a way to understand the world we inhabit and the extent to which political economies insinuate themselves into all aspects of our lives. That was true fifty years ago when I first encountered Marx, but today, with the impact of global capitalism, it's even more true. I could never have imagined the degree to which capitalism would develop."
"Marxism does not have, and does not even pretend to have, any mechanism to explain the internal development of the social system it describes as "Asiatic." In these areas of traditionalist despotism, under which the larger part of the world's population lived for thousands of years, Marx quite explicitly and admittedly found no class conflict, in the absence of opposing groups categorized as economic classes. (Change only came, as he puts in, when Western culture bursts in on them: an unconscious illustration of Marx's Eurocentrism)."