University Of Cambridge Faculty

"If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: 'If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician'. In practice he is apt to say: 'try this; if it works that will justify it'. But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence."

"I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now."

"I read in the proof-sheets of Hardy on Ramanujan: 'As someone said, each of the positive integers was one of his personal friends.' My reaction was, 'I wonder who said that; I wish I had.' In the next proof-sheets I read (what now stands): 'It was Littlewood who said...' (What had happened was that Hardy had received the remark in silence and with a poker face, and I wrote it off as a dud....)"

"Landau kept a printed form for dealing with proofs of Fermat's last theorem. 'On page blank, lines blank to blank, you will find there is a mistake.'"

"'The surprising thing about this paper is that a man who could write it--would.'"

"(A. S. Besicovitch) A mathematician's reputation rests on the number of bad proofs he has given. (Pioneer work is clumsy.)"

"A good mathematical joke is better, and better mathematics, than a dozen mediocre papers."

"The Greeks first spoke a language which modern mathematicians can understand; as Littlewood said to me once, they are not clever schoolboys or "scholarship candidates", but "Fellows of another college"."

"It was Mr. Littlewood (I believe) who remarked that "every positive integer was one of his personal friends.""

"In 1908 Herman quoted to my father an extract from the main report on my first Fellowship thesis. 'He is to be a great mathematician, and his work is singularly mature.' (Herman, on the evidence of my Minor Scholarship and perhaps a first term's work, broke it to my father that he couldn't expect much of me. I'm not sure when this was reversed, and my father knew the ropes enough not to build too much on a Senior Wranglership. I remember, to my surprise, as being a prodigy of 14 in South Africa, his implying that I might expect at Cambridge to be nearly as good as himself, or possibly a shade better. The Fellowship report was something of a surprise; he said 'I feel like a hen that has hatched an eagle.')"

"To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.'"

"There is much to be said for being a mathematician. To begin with, he has to be completely honest in his work, not from any superior morality, but because he simply cannot get away with a fake. ... A mathematician's normal day contains hours of close concentration, and leaves him jaded in the evening. ... This is why we tend to relax either on mild nonfiction like biographies, or - to be crude, and to the derision of arts people - on trash. There is, of course, good trash and bad trash. ... Minor depressions will occur, and most of a mathematician's life is spent in frustration, punctuated with rare inspirations. A beginner can't expect quick results; if they are quick they are pretty sure to be poor. ... When one has finished a substantial paper there is commonly a mood in which it seems that there is really nothing in it. Do not worry, later on you will be thinking 'At least I could do something good then.' At the end of a particularly long and exacting work there can be a strange melancholy. This, however, is romantic, and mildly pleasant, like some other melancholies."

"I had been struggling for two months to prove a result I was pretty sure was true. When I was walking up a Swiss mountain, fully occupied by the effort, a very odd device emerged - so odd that, though it worked, I could not grasp the resulting proof as a whole. But not only so; I had a sense that my subconscious was saying, 'Are you never going to do it, confound you; try this.'"

"'Always verify references.' This is so absurd in mathematics that I used to say provocatively: 'never...' When I began writing I innocently adopted the French habit of M. (Monsieur) in front of any surname. I thus created a ghost mathematician M. Landau (to whom some 'non-verified' references were made)."

"G. H. Hardy said he thought on paper ('with my pen'). He wrote everything out (in his invariably admirable handwriting), scrapping and copying whenever a page got into a mess. When I am thinking about a difficult problem everything goes onto a single page - all over the place with odd equations, diagrams, rings. However appalling the mess, I feel that to scrap this page would somehow break threads in the unconscious."

"[For an unproved Lemma] I had what looked like a promising idea for this, but it was fallacious. In the middle of a three week holiday - mathematics completely below the horizon - the idea came again out of the blue when I was in bed. I forgot it had been rejected as fallacious, and this forgetting did the trick; because this time I noticed that it did prove something, and, by what was nearly, or quite, automatic writing, a proof got written down which deduced the Lemma from the something. ... I did experience automatic writing again. ... my pencil wrote down the formula [omitted] for no reason at all, and almost unattended by consciousness. On the face of it the formula has no apparent connexion with the problem, but it turns out to be an essential key to the proof. ... as if my subconsciousness knew the thing all the time, and finally got impatient."

"It is possible for a mathematician to be 'too strong' for a given occasion. He forces through, where another might be driven to a different, and possibly more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)"

"The Astronomer's fallacy. It is very hard to make a random selection of stars. If, for example, you see a star (with the naked eye) it is probably bright (as stars go). A lecturer was once making the point that middle class families were smaller than lower class ones. As a test he asked everyone to write down the number of children in his family. The average was larger than the lower class average. The obvious point he overlooked were that zero families were unrepresented in the audience. But further, families of n have a probability of being represented proportional to n; with all this, the result is to be expected."

"Besicovitch and Harry Williams asked me what God was doing before the Creation. I said: 'Millions of words must have been written on this; but he was doing Pure Mathematics and thought it would be a pleasant change to do some Applied.'"

"Improbabilities are apt to be overestimated. It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 10⁶ : 1. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely. ... There must exist a collection of well-authenticated coincidences, and I regret that I am not better acquainted with them. ... I sometimes ask the question: what is the most remarkable coincidence you have experienced, and is it, for the most remarkable one, remarkable? (With a lifetime to choose from, 10⁶ : 1 is a mere trifle.) ... Eddington once told me that information about a new (newly visible, not necessarily unknown) comet was received by an Observatory in misprinted form; they looked at the place indicated (no doubt sweeping a square degree or so), and saw a new comet. ..."

"There is a story about German students who were told by their Professor of Philosophy that they, the students, had a real existence, and who went wild with joy on being given this information. Ethnomethodology also teaches us that our daily lived world and experience are real, and we can and do rejoice in this."

"Primitive man has lived twice: once in and for himself, and the second time for us, in our reconstruction."

"I am deeply sensitive to the spell of nationalism. I can play about thirty Bohemian folk songs ... on my mouth-organ. My oldest friend, who is Czech and a patriot, cannot bear to hear me play them because he says I do it in such a schmalzy way, 'crying into the mouth organ'. I do not think I could have written the book on nationalism which I did write, were I not capable of crying, with the help of a little alcohol, over folk songs, which happen to be my favourite form of music."

"It is this which explains nationalism: the principle — so strange and eccentric in the age of agrarian cultural diversity and the 'ethnic' division of labour — that homogeneity of culture is the political bond, that mastery of (and, one should add, acceptability in) a given high culture ... is the precondition of political, economic and social citizenship."

"Knowledge which ... transcends the bounds, the prejudices and prejudgements of any one society and culture is not an illusion but, on the contrary, a glorious and luminous reality. Just how it was achieved remains subject to debate."

"[I am a humble adherent of]...Enlightenment Rationalist Fundamentalism."

"It is nationalism which engenders nations, and not the other way round."

"When knowledge is the slave of social considerations, it defines a special class; when it serves its own ends only, it no longer does so. There is of course a profound logic in this paradox: genuine knowledge is egalitarian in that it allows no privileged source, testers, messengers of Truth. It tolerates no privileged and circumscribed data. The autonomy of knowledge is a leveller."

"Wittgenstein's appeal lies in the fact that he provides a strange kind of vindication of romanticism, of conceptual Gemeinschaft, of custom-based concepts rather than statute-seeking Reform, and that he does so through a very general theory of meaning, rather than from the premisses habitually used for this purpose. Because there is no unique formal notation valid for all speech, each and every culture is vindicated. One never knew that could be done — and so quickly too! It is that above all which endows his philosophy with such a capacity to attract and to repel. His mystique of consensual custom denies that anything can sit in judgment of our concepts, that some may be more rational and others less so. So all of them are in order and have nothing to fear from philosophy, as indeed he insists. This is a fairly mild form of irrationalism, invoking no fierce dark Gods, merely a consensual community. It is the Soft Porn of Irrationalism."

"Dr J. O. Wisdom once observed to me that he knew people who thought there was no philosophy after Hegel, and others who thought there was none before Wittgenstein; and he saw no reason for excluding the possibility that both were right."

"Just as every girl should have a husband, preferably her own, so every culture must have its state, preferably its own."

"The way forward does not lie in amateur and comically timeless linguistic sociology which takes ‘forms of life’ for granted (and this is what philosophy has been recently), but in the systematic study of forms of life which does not take them for granted at all. It hardly matters whether such an inquiry is called philosophy or sociology."

"(J. L. Austin's) admirers claim that his supreme preoccupation was truth. His work, with its sad conjunction of extraordinary cunning in presentation with very thin content, leaves rather the impression of a man who had little sense of real problems but who liked winning arguments and dominating people in the course of them, and who was well equipped to gratify his taste. He was the supreme dialectical poker player, unsurpassed at making people believe that their bluff had been called when in fact they weren’t bluffing, and at stone-walling any attempt to call his own. It would be hypocritical not to say all this. Hypocrisy might not matter, but it would also be unfair to those students who are still conned into supposing that this kind of philosophizing has much in common with serious intellecual endeavour."

"Gellner was a polymath, whose training had been in philosophy, and the peculiarity of his contribution to anthropology lies in this fact : he theorized at a deep philosophical level with remarkable acuity what was involved in the practice of the discipline. The arguments he made are highly distinctive because they suggest that mainstream anthropological self-understanding is not correct. He is a powerful, indeed almost scandalous figure. Differently put, he was not and is not an accepted insider within anthropology."

"The state is the dominant political form in the world today, and nationalism remains a powerful political force. This book will help you understand where it came from and why it endures."

"Whereas Weber was so bewitched by the spell of nationalism that he was never able to theorize it, Gellner has theorized nationalism without detecting the spell."

"America was born modern; it did not have to achieve modernity, nor did it have modernity thrust upon it."

"I do not recommend any legislative action against hermeneutics. I am a liberal person opposed to all unnecessary state limitation of individual liberties. Hermeneutics between consenting adults should not, in my view, be the object of any statutory restrictions. I know, only too well, what it would entail. Hermeneutic speakeasies would spring up all over the place, smuggled Thick Descriptions would be brought in by the lorry-load from Canada by the Mafia, blood and thick meaning would clot in the gutter as rival gangs of semiotic bootleggers slugged it out in a series of bloody shoot-outs and ambushes. Addicts would be subject to blackmail. Consumption of deep meanings and its attendant psychic consequences would in no way diminsh, but the criminal world would benefit, and the whole fabric of civil society would be put under severe strain. Never!"

"This is indeed one of the most important general traits of a modern society: cultural homogeneity, the capacity for context-free communication, the standardization of expression and comprehension."

"Civil Society is a cluster of institutions and associations strong enough to prevent tyranny, but which are, none the less, entered and left freely, rather than imposed by birth or sustained by awesome ritual. You can join the Labour Party without slaughtering a sheep ..."

"This is Disenchantment: the Faustian purchase of cognitive, technological and administrative power, by the surrender of our previous meaningful, humanly suffused, humanly responsive, if often also menacing or capricious world."

"Obstruction of mobility, where it occurs, is one of the most serious and intractable problems of industrial society."

"Capital, like capitalism, seems an overrated category."

"Tribalism never prospers, for when it does, everyone will respect it as a true nationalism, and no-one will dare call it tribalism."

"In brief, nationalism is a theory of political legitimacy, which requires the ethnic boundaries should not be cut across political ones, and, in particular, that ethnic boundaries within a given state — a contingency already formally excluded by the principle in its general formulation — should not separate the power holders from the rest."

"In practice, those who espouse this universal cultural tolerance are indeed inevitably selective; what they mean is nice, cosy, traditional cultures, not as they exist, but as they are pictured in the romantic imagination. And above all, they are interested in selective preservation within their own society. Not surprisingly, they dislike scientism, positivism, rationalism in their own society, and rather ignore the fact that these traits also constitute a culture, and one which, from the viewpoint of their initial and rather abstract starting point, has at least as good a claim as the cosiest of closed societies."

"What are the motives of those who wish to endorse all cultures? A part of their motive is, no doubt, a kind of universal benevolence — let a hundred flowers bloom, let all cultures enjoy their own life and their own values. This kind of liberalism on behalf of cultural wholes faces the same difficulty as liberalism on behalf of individuals (but it does not even attempt to face it) — is it to be freedom for the pikes or the minnows? Many traditional cultures are exclusive and intolerant, and oppress subcultures within their own territory. Who exactly is to be granted this protected status?"

"People are even more reluctant to admit that man explains nothing, than they were to admit that God explains nothing."

"Looking at the contemporary world, two things are obvious: democracy is doing rather badly, and democracy is doing very well. New states are born free, yet everywhere they are in chains. Democracy is doing very badly in that democratic institutions have fallen by the wayside in very many of the newly independent 'transitional' societies, and they are precarious elsewhere. Democracy, on the other hand, is doing extremely well in so far as it is almost (though not quite) universally accepted as a valid norm."

"The model that can be drawn up, of a plural society in which the multiplicity of forces and institutions prevent any one of their number dominating the rest, and which function on the basis of a broad and non-doctrinaire consensus — this picture does not warm the blood like wine. To appreciate and savour its appeal, one needs a rather sophisticated taste, perhaps."