Atheists From England

"There could be no democratic and independent Socialist Party in this country unless they aligned themselves with others against the insidious attempts of Communism to break the Socialist movement."

"Peace-or-war, not cost-of-living, was the most important issue at the election. He did not believe that peace with Stalin would be easy to achieve. Some delegates seemed to think it was all a matter of “getting together with Joe.” Had they forgotten their Marxism, and its interpretation of history. That was what they were dealing with, not Uncle Joe."

"Never let me hear anyone say again that a Socialist State cannot provide outlets for those with initiative. The rewards given to ability in the U.S.S.R. at all levels are far greater than those given to the employed in capitalist Britain. I have seen it and it works."

"There are times, perhaps once every thirty years, when there is a sea-change in politics. It then does not matter what you say or what you do. There is a shift in what the public wants and what it approves of. I suspect there is now such a sea-change and it is for Mrs. Thatcher."

"David Rose (ITN reporter): Industrial relations and picketing. What about the TUC putting its house in order? James Callaghan: The media's always trying to find what's wrong with something .. Let's try and make it work. Rose: What if the unions can't control their own militants? So there are no circumstances where you would legislate? Callaghan: I didn't say anything of that sort at all. I'm not going to take the interview any further. Look here. We've been having five minutes on industrial relations. You said you would do prices. I'm just not going to do this .. that programme is not to go. This interview with you is only doing industrial relations. I'm not doing the interview with you on that basis. I'm not going to do it. Don't argue with me. I'm not going to do it."

"Now that the House of Commons has declared itself, we shall take our case to the country."

"We can truly say that once the Leader of the Opposition had discovered what the Liberals and the SNP were going to do, she found the courage of their convictions. So, this evening, the Conservative Party, who want the Act repealed and oppose even devolution, will march through the Lobby with the SNP, who want independence for Scotland, and with the Liberals, who want to keep the Act. What a massive display of unsullied principle! The minority parties have walked into a trap. If they win, there will be a general election. I am told that the current joke going round the House is that it is the first time in recorded history that turkeys have been known to vote for an early Christmas."

"Jim said he was more depressed as a trade-unionist now about the future of this country than he had been for fifty years. He never believed it would come to this."

"Well, that's a judgment that you are making. I promise you that if you look at it from outside, and perhaps you're taking rather a parochial view at the moment, I don't think that other people in the world would share the view that there is mounting chaos."

"Seven women told The New York Times that Mr. Cohen had groped them or made other unwanted sexual advances over nearly two decades. Four insisted on anonymity, fearing professional repercussions. In each case, The [New York] Times reviewed documents or otherwise corroborated their accounts."

"In an unintentionally revealing moment, Brand describes attending a trade union march against austerity. He complains that the protesters are not like Islamic State terrorists but "flaccid" and placid. He has a case. For all its many faults, the British left does not imitate Isis. It does not commit genocide and practise sexual slavery. Its "revolution", when and if it comes, will consist of boring, gradual attempts to restrain an economic system that is running amok. Russell Brand will want no part of its tedious reforms and will go off in search of bigger thrills. The sooner he leaves the better."

"The reason why Blackpool has to pay out gets to the heart of the delusion behind New Labour's thinking. It's not the scale of the poverty that puts the casino operators off the town, but that Blackpool's poverty is not great enough. ... Blackpool, like most seaside towns, is too far from the big centres of population to provide enough poor, addicted, desperate or foolish gamblers to allow the casinos to operate seven days a week, 52 weeks a year."

"[Proposals for multiple Las Vegas-style "super casinos" in the UK were under discussion at the time] Yet, to date, it is far from clear if the casino will give money to Blackpool or Blackpool give money to the casino. ... It [Blackpool council] is promising to compulsorily purchase the land for the casino, which is currently occupied by the police station and law courts. In a sign of the times, the council will agree to demolish public buildings that once embodied law and order to clear the ground for a gambling den and then spend public money on new homes for the police and judges. It gets better. The council already has spent public money on designing the new casino and finding a developer to put it up."

"Former lefties can make a good living in the media by attacking their ex-comrades – I'd do it myself if the price was right."

"Informed that seven women had come forward with sexual misconduct complaints, Mr. Cohen exclaimed, "Oh, God." "I assume it's stuff I was doing when I was drunk," said Mr. Cohen, a recovering alcoholic."

"Mr. Cohen's reputation was widely known in the newsroom, according to 10 former colleagues, both male and female. One former colleague said she and other female journalists had used a different entrance to a pub to avoid being groped by him. Another woman said she had avoided the bar downstairs from the newsroom after Mr. Cohen grabbed her knee during work drinks."

"Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. ...There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts. The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. ...Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers."

"Hardy in his thirties held the view that the late years of a mathematician's life were spent most profitably in writing books; I remember a particular conversation about this, and though we never spoke of the matter again it remained an understanding."

"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.'"

"In 1933 Landau was dismissed from his [University of Göttingen] chair on the grounds of his race. An important colleague... Ludwig Bieberbach ...wrote the following lines in a treatise on Personality structure and mathematical creativity: "In this way... the ultimate reason behind the courageous rejection which the students at Göttingen University meted out to a great mathematician, Edmund Landau, was that his un-German style in research and teaching had become intolerable to German sensitivities. A people which has seen how alien desires for dominion are gnawing at its identity, how enemies of the people are working to impose their alien ways on it, must reject teachers of a type alien to it." The English mathematician Godfrey H. Hardy... responded to Bieberbach... "There are many of us, many English and many Germans, who said things during the (First) War which we scarcely meant and are sorry to remember now. Anxiety for one's own position, dread of falling behind the rising torrent of folly, determination at all costs not to be outdone, may be natural if not particularly heroic excuses. Prof. Bieberbach's reputation excludes such explanation for his utterances; and I find myself driven to the more uncharitable conclusion that he really believes them true.""

"Hardy was a great internationalist who worked with foreign mathematicians, visiting them, encouraging them to visit him and settling some, including Besicovitch, in England. There were some major probability figures in Hardy’s network: George Pólya (1887-1985) of Zürich, Norbert Wiener (1894-1964) of MIT and Harald Cramér (1893-1985) of Stockholm-appropriately Wiener and Cramér first met when visiting Hardy in 1920."

"It is never worth a first-class man's time to express a majority opinion. By definition, there are plenty of others to do that. (pg 46)"

"Bradman is a whole class above any batsman who has ever lived: if Archimedes, Newton and Gauss remain in the Hobbs class, I have to admit the possibility of a class above them, which I find difficult to imagine. They had better be moved from now on into the Bradman class. (pg 28)"

"No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

"I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people "Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.""

"No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years."

"We have still one more question to consider. We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not"

"Pure mathematics is on the whole distinctly more useful than applied. [...] For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics."

"317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way."

"...there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics."

"[T]here is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathematical position."

"The play is independent of the pages on which it is printed, and 'pure geometries' are independent of lecture rooms, [rough blackboard drawings] or of any other detail of the physical world. This is the point of view of a pure mathematician. Applied mathematicians, mathematical physicists... take a different view... preoccupied with the physical world itself, which also has its structure or pattern. ...We may be able to trace a ...resemblance between the two sets of relations, and then the pure geometry will become interesting to physicists; it will give us ...a map which 'fits the facts' ...The geometer offers ...a whole set of maps from which to choose."

"There is the science of pure geometry, in which there are many geometries, , , non-Euclidean geometry... [etc.]. Each... is a , a pattern of ideas... judged by the interest and beauty of... pattern. It is a map or picture, the... product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But... there is one thing... of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. ...[T]hey cannot be, since earthquakes and eclipses are not mathematical concepts."

"[M]athematical reality lies outside us ...our function is to discover or observe it, and ...the theorems ...we prove, and ...describe grandiloquently as our 'creations', are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards [...]"

"A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all."

"It is... natural to suppose that there is a great difference in utility between 'pure' and 'applied' mathematics. This is a delusion..."

"[S]cience works for evil as well as for good (...particularly ...in time of war); and... mathematicians may be justified in rejoicing that there is one science... their own, whose ...remoteness from ordinary human activities should keep it gentle and clean."

"[A] good deal of elementary mathematics... 'elementary' in the sense in which professional mathematicians use it... [e.g.,] knowledge of the differential and integral calculus—has considerable practical utility. These... are... rather dull... the parts which have least aesthetic value. The 'real' mathematics of the 'real' mathematicians... of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly 'useless' (...as true of 'applied' as of 'pure' mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of... 'utility'..."

"It is... astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility. ...We live either by or on other people's professional knowledge."

"I am interested in mathematics only as a creative art."

"A chess problem is genuine mathematics, but it is in some way 'trivial' mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful – important if you like, but the word is very ambiguous, and 'serious' expresses what I mean much better."

"Chess problems are the hymn-tunes of mathematics."

"', which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."

"The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."

"A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, [...] the importance of ideas in poetry is habitually exaggerated: '... Poetry is not the thing said but a way of saying it.' [In poetry,] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern."

"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."

"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean."

"Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself."

"If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full."

"… there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds."