All Quotes

"They who study mathematiks only to fix their minds, and render them the steadyer to apply to all other things, as there are many who profess to do, are as wise as those who think by rowing boats, to learn to swim."

"Mathematical development in England was at a low ebb in the early decades of the nineteenth century, with Cambridge stagnating in the shadow of Newton, who had produced his mathematics nearly a century and a half earlier. This dead hand of tradition, which stifled much initiative and originality, was in sharp contrast to the situation in France."

"Advanced mathematics opens doors to many fields of study. More importantly, it expands the way you think."

"Yeah, Silver and his math are jokes, because math has a liberal bias. After all, math is the reason Mitt Romney's tax plan doesn't add up."

"I was an atheist, finding no reason to postulate the existence of any truths outside of mathematics, physics and chemistry. But then I went to medical school, and encountered life and death issues at the bedsides of my patients. Challenged by one of those patients, who asked "What do you believe, doctor?", I began searching for answers."

"Magick, mysticism, and the mathematics are triplets."

"A man with all the algebra in the world is often only an ass when he knows nothing else. Perhaps in ten years society may derive advantage from the curves which these visionary algebraists will have laboriously squared. I congratulate posterity beforehand. But to tell you the truth I see nothing but a scientific extravagance in all these calculations. That which is neither useful nor agreeable is worthless. And as for useful things, they have all been discovered; and to those which are agreeable, I hope that good taste will not admit algebra among them."

"As to your Newton, I confess I do not understand his void and his gravity; I admit he has demonstrated the movement of the heavenly bodies with more exactitude than his forerunners; but you will admit it is an absurdity to maintain the existence of Nothing."

"Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!"

"Measuring is one of the more practical uses of mathematics, but the ability and desire to measure aren't always wrapped up with the need to know useful answers."

"Letting numbers take us where we can't go in person — whether that's to the top of a windmill or to the origin and borders of the universe — has been and still is one of humankind's favorite intellectual adventures."

"The Devil: Okay, boys...tonight's homework. Algebra. Xn + Yn = Zn. You're never gonna use that, are you? Imperialism and the First World War. What was done is done. No point thinking about it now. German, French, Spanish. Ja, ja, oui, oui, s, s. It's nonsense. Everyone speaks English anyway. And if they don't, they ought to. So, no homework tonight. But I want you to watch a lot of TV, don't neglect your video games...and I'll see you in the morning. Shall we say 10:00, 10:30? No point in getting up too early."

"Mathematics is really a liberal art if you look at it from a slightly different point of view."

"The mathematical genius can only carry on from the point which mathematical knowledge within his culture has already reached. Thus if Einstein had been born into a primitive tribe which was unable to count beyond three, life-long application to mathematics probably would not have carried him beyond the development of a decimal system based on fingers and toes."

"So far, all of reality seems to be described by exquisite, elegant mathematical equations. We can’t stop now – it’s got to be beautiful all the way down!"

"Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite."

"Halakhic man, well furnished with rules, judgments, and fundamental principles, draws near the world with an a priori relation. His approach begins with an ideal creation and concludes with a real one. To whom may he be compared? To a mathematician who fashions an ideal world and then uses it for the purpose of establishing a relationship between it and the real world. ... The essence of the Halakhah, which was received from God, consists in creating an ideal world and cognizing the relationship between that ideal world and our concrete environment."

"Mathematics is a versatile art; it can be applied to widely different purposes. Math has no morality; it does not care what it counts or what it proves."

"I had been to school most all the time and could spell and read and write just a little, and could say the multiplication table up to six times seven is thirty-five, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics anyway."

"School children and students who love God should never say: “For my part I like mathematics”; “I like French”; “I like Greek.” They should learn to like all these subjects, because all of them develop that faculty of attention which, directed toward God, is the very substance of prayer."

"The number 2 thought of by one man cannot be added to the number 2 thought of by another man so us to make up the number 4."

"The good Christian should beware of mathematicians, and all those who make empty prophesies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell."

"We always have urged people: Don't take LSD unless you are very well prepared, unless you are specifically prepared to go out of your mind. Don't take it unless you have someone that's very experienced with you to guide you through it. And don't take it unless you are ready to have your perspective on yourself and your life radically changed, because you're gonna be a different person, and you should be ready to face this possibility."

"People use the word "natural" … What is natural to me is these botanical species which interact directly with the nervous system. What I consider artificial is four years at Harvard, and the Bible, and Saint Patrick's cathedral, and the sunday school teachings."

"Art's certainly made a lot of money, and got on a lot of shows — he got himself into the Nixon White House riding on the death of his daughter. And I think that's ghoulish! That's ghoulish."

"I declare that The Beatles are mutants. Prototypes of evolutionary agents sent by God, endowed with a mysterious power to create a new human species, a young race of laughing freemen."

"To describe externals, you become a scientist. To describe experience, you become an artist. The old distinction between artists and scientists must vanish. Every time we teach a child correct usage of an external symbol, we must spend as much time teaching him how to fission and reassemble external grammar to communicate the internal. The training of artists and creative performers can be a straightforward, almost mechanical process. When you teach someone how to perform creatively (ie, associate dead symbols in new combinations), you expand his potential for experiencing more widely and richly."

"If you want to change the way people respond to you, change the way you respond to people."

"Turn on" meant go within to activate your neural and genetic equipment. Become sensitive to the many and various levels of consciousness and the specific triggers that engage them. Drugs were one way to accomplish this end. "Tune in" meant interact harmoniously with the world around you — externalize, materialize, express your new internal perspectives. Drop out suggested an elective, selective, graceful process of detachment from involuntary or unconscious commitments. "Drop Out" meant self-reliance, a discovery of one's singularity, a commitment to mobility, choice, and change. Unhappily my explanations of this sequence of personal development were often misinterpreted to mean "Get stoned and abandon all constructive activity."

"Women who seek to be equal with men lack ambition."

"We are dealing with the best-educated generation in history. They are a hundred times better educated than their grandparents, and ten times more sophisticated. There has never been such an open-minded group. The problem is that no one is giving them anything fresh. They've got a brain dressed up with nowhere to go."

"Think for yourself and question authority."

"That’s the left wing of the CIA debating the right wing of the CIA."

"I have always considered myself, when I learned what the word meant, I've always considered myself a Pagan."

"When I have needed solace and I have had to depend on my own resources, the mathematics has been there. I am grateful."

"[Mathematics is] the science that draws necessary conclusions."

"Though I don't really understand her I love my sister, her name's Miranda The boys from uptown they can't stand her The more she denies them the more they demand her But she just wants to lay in bed all night Reading Raymond Chandler"

"The only exception to his careful planning was plot; the best way to stop the reader guessing the end of a story, he decided, was not to know how it ended yourself."

"Over time you will get the wrong answer more times than you get the right answer. That’s not a problem! You’ve learnt what doesn’t work, just try again."

"Rather like the way the Hubble Space Telescope has made a significant contribution to astronomy in enabling astronomers to discover hidden structures and properties of our distant universe, dynamic geometry software has allowed new worlds to become viewable and tangible in mathematics and particularly in geometry."

"Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means."

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."

"In doing mathematics, I express something personal. It is a source of joy to know that, despite this personal aspect, the fruit of my work can be of interest to other mathematicians."

"It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances."

"Now comes the Einstein–Podolsky–Rosen entangled state. Now I see faces, people saying, "Oh..?" Don't worry! When you go to the concert, you don't need to be able to read the music, to enjoy the music. ...So here... [are] equations. It's a pleasure for my colleague physicists. If you can't read the equation, listen to me. I'm not going to sing, but... listen to the words... the words are... a way of describing the equations, and you don't need to know the mathematics..."

"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."

"Confused is of course the best state a mathematician can be in; the struggle out of that state is the primary drive for progress."

"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."

"Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers."

"We say that the string is 'random' if there is no other representation of the string which is shorter than itself. But we will say that it is 'non-random' if there does exist such an abbreviated representation. ...In general, the shorter the possible representation... the less random... On this view we recognize science to be the search for algorithmic compressions. ...It is simplest to think of mathematics as the catalogue of all possible patterns. ...When viewed in this way, it is inevitable that the world is described by mathematics. ...In many ways the search for a Theory of Everything is a manifestation of a faith that this compression goes all the way down to the bedrock of reality..."