All Quotes

"Good, he did not have enough imagination to become a mathematician."

"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."

"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."

"It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning."

"To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts."

"If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems."

"This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus."

"Hilbert was on the verge of retirement. He was the dignified chairman of the mathematical society's meetings, though he no longer came up with those caustic quips that people would repeat afterwards, imitating as best they could his Baltic accent. It is a pity these were not recorded before it was too late. The samples cited in English translation, in Constance Reid's biography of Hilbert, give only the palest idea of his biting wit."

"Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly."

"The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!"

"An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us."

"In mathematics, as in any scientific research, we find two tendencies... [T]he tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects... a live rapport with them... which stresses the concrete meaning of their relations. ...[I]ntuitive understanding plays a major role in geometry. ...[S]uch concrete intuition is of great value not only for the research worker, but... for anyone who wishes to study and appreciate the results of research in geometry."

"[O]ur purpose is to give a presentation of geometry... in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems... beyond this, it is possible... to depict the geometric outline of the methods of investigation and proof, without... entering into the details... In this manner, geometry being as many-faceted as it is and being related to the most diverse branches of mathematics, we may even obtain a summarizing survey of mathematics as a whole, and a valid idea of the variety of problems and the wealth of ideas it contains. Thus a presentation of geometry in large brushstrokes... and based on the approach through visual intuition, should contribute to a more just appreciation of mathematics by a wider range of people than just the specialists."

"[M]athematics is not a popular subject... The reason for this is to be found in the common superstition that [it] is but a continuation... of the fine art of arithmetic, of juggling with numbers. [We] combat that superstition, by offering, instead of formulas, figures that may be looked at and that may easily be supplemented by models which the reader may construct. This book... bring[s] about a greater enjoyment of mathematics, by making it easier... to penetrate the essence of mathematics without... a laborious course of studies."

"The various branches of geometry are all interrelated closely and quite often unexpectedly. This shows up in many places in the book. Even so... it was necessary to make each chapter...self-contained... We hope that... we have rendered each chapter taken by itself... understandable and interesting. We want to take the reader on a leisurely walk... in the big garden that is geometry, so that each may pick for himself a bouquet to his liking."

"Physics is too difficult for physicists!"

"More decisive than any other influence for the young Hilbert at Königsberg was his friendship with Adolf Hurwitz and Minkowski. He got his thorough mathematical training less from lectures, teachers or books, than from conversation."

"David Hilbert—the undisputed, foremost living mathematician in the world and lifelong close friend and collaborator of the by then deceased Minkowski—had already presented to the Göttingen Academy his own version of the same equations a few days earlier [than Einstein]. Although Minkowski and Hilbert accomplished their most important achievements in pure mathematical fields, their respective contributions to relativity should in no sense be seen as merely occasional excursions into the field of theoretical physics. Minkowski and Hilbert were motivated by much more than a desire to apply their exceptional mathematical abilities opportunistically... On the contrary, Minkowski's and Hilbert's contributions to relativity are best understood as an organic part of their overall scientific careers."

"A more thorough study of Euclid's axioms and postulates proved them to be inadequate for the deduction of Euclid's geometry. ...Hilbert and others succeeded in filling the gap by stating explicitly a complete system of postulates for Euclidean and non-Euclidean geometries alike. Among the postulates missing in Euclid's list was the celebrated postulate of Archimedes, according to which, by placing an indefinite number of equal lengths end to end along a line, we should eventually pass any point arbitrarily selected on the line. Hilbert, by denying this postulate, just as Lobatchewski and Riemann had denied Euclid's parallel postulate, succeeded in constructing a new geometry known as non-Archimedean. It was perfectly consistent but much stranger than the classical non-Euclidean varieties. Likewise, it was proved possible to posit a system of postulates which would yield Euclidean or non-Euclidean geometries of any number of dimensions; hence, so far as rational requirements of the mind were concerned, there was no reason to limit geometry to three dimensions."

"Hilbert's problems have the characteristics of any good founding document. Each one is a short essay on its subject, not overly specific, and yet Hilbert makes his intent remarkably clear. He leaves room for change and adjustment. Hilbert's goal was to foster the pursuit of mathematics."

"If you can walk down the street in women's clothes, you can do anything."

"In my first year I was taught about the slide rule. They said, "The slide rule is important. Without it you can do nothing. The slide rule is the modern weapon of efficiency. With the slide rule you can get from here to the stars. Buy it, use it – your slide rule!" Within one year it was, "Burn the slide rule. The calculator can add up with none of this fucking sliding the shit around and working out where that bit in the middle goes. Smash it over your head.""

"Religion and philosophy, philosophy and religion – they're two words which are both … different. In spelling."

"Agatha Christie? We go back years, me and Ag. She's a … she's just a … she's dead, isn't she?"

"She said, "Spell 'ant' ", and I wrote out the entire alphabet. She said, "That doesn't spell 'ant' ", and I said, "It's in there somewhere! There's the A, there's the N, there's the T – the rest are silent!""

"And we're going, "Oh, Captain Clever! Whoa-ho-ho! Rattle it, and if it doesn't go off, it can't be a bomb!""

"And in the back, behind there, not giving a damn … and all the bright colours and stuff just drops off when you get to this section. White wrap-up, big red letters; LARD! Eat this shit and die! LARD! Kills you stone dead! Does blood move through your arteries? Block it up with LARD! Nutritional advice? No! Proteins? What the hell are they? Carbohydrates? Never heard of them, Guv! Fat? You bet your bum! We've got some some of that, yes sirree Bob! Oh, we're full of that, mate … [later on] Remember that campaign for butter, "Welcome back to butter"? "Welcome back to LARD!" We never went nowhere! Just been sitting at the back, quietly waiting … like Jack Nicholson …"

"I am a lesbian trapped in a man's body."

"We throw sticks at dogs, that's the level we have dogs at. You'd never dream of throwing one for a cat. We throw sticks for dogs, and dogs go, "Oh, he's dropped his stick! I better go and get that. [mimes chasing after the stick] Saw you dropped your stick there, thought I'd bring it back. And you – hang on! [mimes giving the stick back and follows it with eyes as it's thrown again] Did you see me just bring that back? And then you … you dropped it again? This is very weird. I don't know what's going on here. [mimes bringing the stick back again] Now, hang on to it this time, I don't want to piss about all the time. You think I enjoy this? There you … don't fucking throw it!" That's why the third time, when they come back, they won't give it to you. They go, [through clenched teeth] "No … I won't let you take it!""

"Cats have a scam going – you buy the food, they eat the food, they fuck off; that's the deal."

"You have no control over your cat! You can't say to your cat, "Cat, heel! Stay! Wait! Lie down! Roll over!" 'Cause the cat's just gonna be sitting there going, "Interesting words … have you finished?" While you're shouting all this to your cat, your dog's next to you, going … [mimes obeying all commands] "What the hell are you doing? I'm talking to the cat!" "Oh, I'm sorry!""

"And cats leap up walls! Six foot walls, they just go … *fwang* [mimes cat jumping] Lands perfectly, and turn … turn … and back flip and forward flip, and dismount! They always land perfectly, they never do that sort of wobbly-gymnast … [mimes wobbling] You never see cats on a wall having a problem, do you? You never see a cat going, [mimes tentative walk] "Fucking 'ell! I'm not sure about this …" and a cat on the ground, going, "Easy, Ginger! I'll walk you down!""

"[About homophobes] As long as they're homophobic behind closed doors, and don't hurt anyone, I'm fine with it."

"My name is Mrs. Smith, I've made apples out of bread and dripping, a bit of green paint, and corrugated iron." "No, these are horrible apples, Mrs. Smith. Go away, Mrs. Smith! Go away until your daughter has a baby." "Shag, daughter, shag! It's a marketing idea, shag for babies! [mimes running back] My daughter's had a baby, I'm Granny Smith now!" "Come in, Granny Smith! You wonderful idea, you! Come in with your shiny apples."

"Pears can just fuck off too. 'Cause they're gorgeous little beasts, but they're ripe for half an hour, and you're never there. They're like a rock or they're mush. In the supermarket, people banging in nails. "I'll just put these shelves up, mate, then you can have the pear." … So you think, "I'll take them home and they'll ripen up." But you put them in the bowl at home, and they sit there, going, "No! No! Don't ripen yet, don't ripen yet. Wait til he goes out the room! Ripen! Now now now!""

"What? … The Carthaginians are attacking? God, I knew they'd do that. What? … They are attacking over the Alps? Damn, I knew they'd do that. What? … They're coming on elephants? … Where'd they get the elephants? There aren't any elephants in Europe. This I got to see … are you sure? … It's not just a typo mistake? Perhaps the Carthaginians are attacking over the Alps and they are in their element? Kind of upbeat, you know. They're coming on fucking elephants, huh."

"If you've never seen an elephant ski, then you've never been on acid."

"Day One: Rang bell, cat fucked off. (Oh dear.) Day Two: Rang bell, cat went and answered door. Day Three: Rang bell, cat said he had eaten earlier. (Cheeky bugger.) Day Four: Went to ring bell, but cat had stolen batteries. Final Day – Day Five: Went and rang bell with new batteries, but cat put his paw on bell so it only made a thunk noise. Then cat rang his own bell. I ate food."

"Off to Azerbaijan!"

"I always wonder if I'd grown up in Germany in the 1930s, would I have joined the Hitler Youth? Would I have signed up for this thing? Would I have tried on one of those uniforms? I hope that I would have said: 'No, this is rubbish. This person is lying.' And some Germans did, but you don't hear much about those stories."

"Beekeepers, yes … they've gotta want to be – "I want to be a beekeeper! I wanna keep bees! Don't wanna let them get away; I wanna keep them! They have too much freedom … I want bees on elastic, so when they get pollen, they come back here! My father was a beekeeper before me, his father was a beekeeper before him; I wanna walk in their footsteps." And their footsteps were like this: [running wildly from imaginary bees] "I'm covered in bees!""

"I like my coffee like I like my women... in a plastic cup."

"I like my women like I like my coffee... covered in beeees!"

"[God, who was James Mason, to Noah] "Noah, stop what you're doing and build me an ark!" [Noah, who was Sean Connery] "I'm working on a speed boat at the moment. Much more exciting. It'll really kick ass, give great photographs for the people in Bible.""

"So then God created the world, and on the first day he created light and air and fish and jam and soup and potatoes and haircuts and arguments and small things and rabbits and people with noses and jam – more jam, perhaps – and soot and flies and tobogganing and showers and toasters and grandmothers and, uh … Belgium. And the second day he created fire and water and eggnog and radiators and lights and Burma and things that go "urh" and … and Colonel Gaddafi and Arthur Negus. On the third day he probably got lists and said, "I can't remember what I've invented now. I've just been ad-libbing so far.""

"Give us cash! I steal from the rich and give to the poor! I'm trying to be a myth; give us cash!" "No, I'm not gonna give you cash." "Go on, I steal from the rich. Are you rich?" "No, I'm … comfortable." "That's no good, I can't steal from the fairly well off and give to the moderately impoverished! That's not gonna swing, is it?"

"I don't have techno-fear, I have techno-joy! I love technology! I love to get a new machine. Every time I get a new machine, I think, "This is the one! I won't have to work again; I've got this thing!" And if you have techno-joy, you get the instructions, you unwrap it, and you throw the instructions out the window! [mimes doing so] Forget them! Fuck 'em! [mimes turning on a computer] On. [mimes typing] I must know how this works, I've used machines before!"

"We stole countries with the cunning use of flags. Just sail around the world and stick a flag in. "I claim India for Britain!" They're going, "You can't claim us, we live here! Five hundred million of us!" "Do you have a flag…? "What? We don't need a bloody flag. This is our country, you bastards!" "No flag, no country, you can't have one! Those are the rules ... that I just made up! And I'm backing it up with this gun that was lent from the National Rifle Association.""

"Someone's killed 100,000 people. We're almost going, "Well done! You killed 100,000 people? You must get up very early in the morning! I can't even get down the gym. Your diary must look odd: 'Get up in the morning, death, death, death, death, death, death, death – lunch – death, death, death – afternoon tea – death, death, death – quick shower …' ""

"They went to the Moon and they brought back rock. Trouble is, we've got rock. That was the one thing we didn't need, wasn't it? "Rock, Neil? I don't know whether you looked at the planet before you took off, but it's made of fucking rock!" "But it's Moon rock …" "Oh, fucking hell, this is Earth rock, Neil, come on! Have you heard, on the stock market, rock's gone up three points? No, it hasn't, has it? 'Cause it's fucking rock! We wanted diamonds, sherbet or a squirrel with a gun!""