Mathematics Quotes

Formal mathematics is nature's way of letting you know how sloppyyour mathematics is.

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.

Gary William Flake

In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.

James Henry Breasted

One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.

Herbert S. Gaskill

a fresh mind adds a better mathematic ability #Bweqy

Brendon

As a teacher, Tengo pounded into his students' heads how voraciously mathematics demanded logic. Here things that could not be proven had no meaning, but once you had succeeded in proving something, the world's riddles settled into the palm of your hand like a tender oyster.

Haruki Murakami

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack; it is not a mine, whose treasures may take long to reduce to possessions, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as the space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell, and is forever ready to burst forth into new forms of vegetable and animal existence.

James Joseph Sylvester

The physical method becomes a philosophy when it asserts there is no higher knowledge than the empirical knowledge of scientific phenomena. The mathematical method becomes a philosophy when it asserts that some higher knowledge is needed to explain scientific facts, and that higher knowledge is mathematics.

Fulton J. Sheen

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

Bertrand Russell

They shouldn't be allowed to teach math so early in the morning.

Kendare Blake

Mathematicians deal with large numbers sometimes, but never in their income.

Isaac Asimov

. . . the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it), thus generating snowballs and arbitrary and unpredictable planet-wide winner-take-all effects.

Nassim Nicholas Taleb

It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words—are we discovering Truth, or just wanking?

Neal Stephenson

Luck is the grand equalizer.

Nassim Nicholas Taleb

Is everyone with one face called a Milo?""Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things.""How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless.""I never thought of it that way," Milo admitted."Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.

Norton Juster

But that can never be," said Milo, jumping to his feet."Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where — but just because you can never reach it doesn't mean that it's not worth looking for.

Norton Juster

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

M.A. Nowak

And, most important of all," added the Mathemagician, "here is your own magic staff. Use it well and there is nothing it cannot do for you."He placed in Milo's breast pocket a small gleaming pencil which, except for the size, was much like his own.

Norton Juster

In his school, Bertrand Russell thought it was better if they had the sex, so they could give their undivided attention to mathematics, which was the main thing.

Paul Goodman

The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.

Paolo Aluffi

It is the definition of the word 'object' which destroys all religions.

Bill Gaede

A brick can be used to represent the zero probability of this book being any good.

Amy Sommers

Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture.

Lawrence Young

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.

Herbert S. Gaskill

People joke, in our field, about Pythagoras and his religious cult based on perfect geometry and other abstract mathematical forms, but if we are going to have religion at all then a religion of mathematics seems ideal, because if God exists then what is He but a mathematician?

Matt Haig

Schools were started to train human talents... The Guild... emphasizes almost pure mathematics. Bene Gesserit performs... politics. The original Bene Gesserit school was directed by those who saw the need of a thread of continuity in human affairs. They saw there count be no such continuity without separating human stock from animal stock - for breeding purposes.

Frank Herbert

It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

G H Hardy

I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.

Phillip A. Griffiths

Mathematics is a terrible calling. It’s as merciless as gravity. It swallows the soul. There’s a point near a black hole called the last stable orbit. Once you drop below that radius, no force in the universe can stop you falling all the way in. That’s what happened to your mother – she swam too close to theory, fell below the last stable orbit.

Alastair Reynolds

Mathematics should be studied if only for that it puts the mind in order.

Mikhail Lomonosov

PHI is one H of a lot cooler than PI!

Dan Brown

Who rebels with mathematics?

Khaled Hosseini

Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.

Haruki Murakami

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.

G H Hardy

Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.

C.S. Lewis

Topology is destiny,' he said, and put the drawers on. One leg at a time.

Neal Stephenson

Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears.

Haruki Murakami

Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.

Blaise Pascal

A term meant to convey a person's inability to make sense of the numbers that run their lives.

Douglas R. Hofstadter

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression,more exact,compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.

H.G.Wells

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.

Pierre-Simon Laplace

I hate math. It's hard, it's stupid, and it's nature's way of separating spinsters from women who end up breeding.

Douglas Coupland

Adaptability to change is itself a hallmark of successful education.

Peter Hilton

Anything you try to quantify can be divided into any number of "anythings," or become the thing - the unit - itself. And what is any number, itself, but just another unit of measurement? What is a 'six' but two 'threes', or three 'twos'...half a 'twelve', or just six 'ones' - which are what? (attrib: F.L. Vanderson)

Mort W. Lumsden

Patience is my virtue, but only in Math, Daddy,” - Ashley

Ryanne Salve

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.

Henry Hallett Dale

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

Paul Cohen

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.

William Elwood Byerly

Through the judicious employment of symbols, diagrams, and calculations, mathematics enables us to acquire significant facts about extremely significant things (universal laws, even), not by first forging out into the cosmos with teams of scientists, but rather from the comforts and confines of coffee tables in our living rooms! p. 72

G. Arnell Williams

The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.

Reuben Hersh

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

Terry Pratchett

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Andrew John Wiles

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

Andrew John Wiles

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.

Antoine Thomson d'Abbadie

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

Gian-Carlo Rota

And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music - is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.

Paul Lockhart

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

Clifford A. Truesdell

Although some of her passages seek to persuade the reader of the meaninglessness and marginalization of the mathematics, Hayles is content to use mathematics as a means for understanding Borges, perhaps in the same way a sponge riddled with holes is useful in sopping up fluid reality.

Bloch William Goldbloom

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

G H Hardy

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.

Joseph Fourier

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