Quotations

Most of the quotes come from my ever-growing collection of recreational math books. I am always on the lookout for math cartoons, jokes, puzzles, and quotations. These quotes have been used to stimulate student interest in math and can be tied into the lesson for the day, a current event, or a related subject of interest. Questions can be posed about the quotes, and short biographical essays about the authors can be made as assignments in the history of math. I like these quotes also because they remind me of great thoughts and keep my teaching interest keen.

Some quotations are selected from the Furman University Mathematics Quotation Server found at http://math.furman.edu/~mwoodard/mquot.html. This site contains a vast collection of mathematical quotations culled from many sources. You may conduct a keyword search through the quotation database, which is also organized alphabetically by author. You can download the entire collection for classroom use. This is an excellent source for student projects and daily or weekly classroom quotes that illustrate lessons or themes.

The quotations are listed alphabetically by author. If you have a favorite quote, please email me the quote and the source. I appreciate sharing great ideas; they’re a way to stimulate the thinking and feel great about mathematics and life.

Cordially,

Bill

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“There is no smallest among the small and no largest among the large; but always something still smaller and something still larger.”

– Anaxagoras
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“Give me a place to stand, and I will move the Earth.”

– Archimedes
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“In a book dealing with the achievements of the human mind, then, one should not write THE END for there is no end. One should write only . . .??

– Isaac Asimov
* * * * * * * * * * * *

“There is no such thing as a problem without a gift for you in its hands. You seek problems because you need their gifts.”

– Richard Bach, Illusions
* * * * * * * * * * * *

“Reading makes a full man.

Speaking makes a ready man.

Writing makes an exact man.”

– from Francis Bacon
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“All science requires mathematics.”

– Roger Bacon
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“Life is a school of probability.”

– Walter Bagehot
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“The greatest shortcoming of the human race is our inability to understand the exponential function.”

– Albert A. Bartlett, physicist
* * * * * * * * * * * *
“Man ever seeks perfection but inevitably it eludes him. He has sought ‘perfect numbers’ through the ages and has found only a very few – twenty-three up to 1964.”

– Albert H. Beiler, Recreations in the Theory of Numbers
* * * * * * * * * * * *
“The eye sees only what the mind is prepared to comprehend.”

– Henri L. Bergson
* * * * * * * * * * * *
“Out of nothing I have created a strange new universe.”

– János Bolyai
* * * * * * * * * * * *
“Structures are the weapons of the mathematician.”

– Bourbaki
* * * * * * * * * * * *
“Answers alone often fail to reveal the nature of a student’s thinking, the strategies used in the problem-solving process, or the level of understanding.”

– Larry Buschman
* * * * * * * * * * * *
“Answers alone often fail to reveal the nature of a student’s thinking, the strategies used in the problem-solving process, or the level of understanding.”

– Larry Buschman
* * * * * * * * * * * *
“When Newton saw an apple fall, he found a mode of proving that the earth turnd round in a most natural whirl, called gravitation.”

– Lord Byron
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“I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors.”

– James Caballero
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“A thing is obvious mathematically after you see it.”

– R. D. Carmichael
* * * * * * * * * * * *
“ . . . a theorem as ‘the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the sides’ is as dazzlingly beautiful now as it was in the day when Pythagoras discovered it.”

– Lewis Carroll
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“More significant mathematical work has been done in the latter half of this century than in all previous centuries combined.”

– John Casti, Five Golden Rules, 1996
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“Everything in nature adheres to the cone, the cylinder, and the cube.”

– Paul Cezanne
* * * * * * * * * * * *
“Mathematics works for today’s society like the fossil fuels worked for industrial society.”

– Graciela Chichilnisky, world economist
* * * * * * * * * * * *
“Teachers open the door. You enter by yourself.”

– Chinese Proverb
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”If you have knowledge, let others light their candles with it.”

– Winston Churchill
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“In today’s world, ‘innumeracy’ is an even greater danger than illiteracy, and is perhaps even
more common.”

– Arthur C. Clarke
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“Statistics is numbers that are part of a story.”

– George Cobb, statistician
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“The imagination in a mathematician who creates makes no less difference than in a poet who invents . . .”

– Jean Le Rond D'Alembert
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“Mathematics is the supreme arbiter. From its decisions there is no appeal.”

– Dantzig
* * * * * * * * * * * *
“Every new body of discovery is mathematical in form, because there is no other guidance we can have.”

– Charles Darwin
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“Mathematics seems to endow one with something like a new sense.”

– Charles Darwin
* * * * * * * * * * * *
“The belief that the underlying order of the world can be expressed in mathematical form lies at the very heart of science. So deep does this belief run that a branch of science is considered not to be properly understood until it can be cast in mathematics.”

– Paul Davies, The Mind of God
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“One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.”

– Philip J. Davis
* * * * * * * * * * * *
“For those, like me, who are not mathematicians, the computer can be a powerful friend to the imagination. Like mathematics, it doesn’t only stretch the imagination. It also disciplines and controls it.”

– Richard Dawkins, The Blind Watchmaker
* * * * * * * * * * * *
“Maybe people don’t realize that mathematics is not dead. There are a lot of unsolved problems in mathematics. And there are a lot of things about the world we don’t know, and it seems that maybe the only way we’ll ever know them is through the application of mathematics.”

– Nate Dean, data miner
* * * * * * * * * * * *
“Each problem that I solved became a rule which served afterwards to solve other problems.”

– René Descartes
* * * * * * * * * * * *
“With me everything turns into mathematics.”

– René Descartes
* * * * * * * * * * * *
“It is not enough to have a good mind. The main thing is to use it well.”

– René Descartes
* * * * * * * * * * * *
“Method consists entirely in properly ordering and arranging the things to which we should pay attention.”

– René Descartes
* * * * * * * * * * * *
“Human wisdom remains always one and the same although applied to the most diverse objects and it is no more changed by their diversity than the sunshine is changed by the variety of objects which it illuminates.”

– René Descartes
* * * * * * * * * * * *
“If I found any new truths in the sciences, I can say that they all follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortune of war was on my side.”

– René Descartes
* * * * * * * * * * * *
“Contemporary civilization rests so largely upon applied science that no one can really understand it who does not grasp something of the scientific methods and the results that underlie it.”

– John Dewey
* * * * * * * * * * * *
“The brain is a three-pound mass you can hold in your hand that can conceive of a universe a hundred-billion light-years across.”

– Marian Diamond, brain researcher
* * * * * * * * * * * *
“Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.”

– Paul Dirac
* * * * * * * * * * * *
“When you have eliminated the impossible, what ever remains,
however improbable, must be the truth.”

– Sir Arthur Conan Doyle, The Adventure of the Beryl Coronet
* * * * * * * * * * * *
“The fact is that our lives are largely spent in solving puzzles; for what is a puzzle but a perplexing question? And from our childhood upwards we are perpetually asking questions or trying to answer them.”

– Henry E. Dudeney, English puzzle maker
* * * * * * * * * * * *
“Puzzles, like virtue, are their own reward.”

– Henry E. Dudeney, English puzzle maker
* * * * * * * * * * * *
“And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art . . .”

– Albrecht Dürer
* * * * * * * * * * * *
“One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.”

– Freeman Dyson
* * * * * * * * * * * *
“The bottom line for mathematicians is that the architecture has to be right.”

– Freeman Dyson
* * * * * * * * * * * *
“Nobody is ever born to draw a picture in perspective, which is why it took so long to figure it out.”
– Sam Edgerton, artist and art instructor
* * * * * * * * * * * *
“Genius is one percent inspiration and ninety-nine percent perspiration.”
– Thomas Alva Edison
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“If you ask mathematicians what they do, you always get the same answer. They think.”
– M. Egrafov
* * * * * * * * * * * *
“I am One that transforms into Two,
I am Two that transforms into Four,
I am Four that transforms into Eight.
After this I am One again.”

– Egyptian creation myth
* * * * * * * * * * * *
“One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable...”

– Albert Einstein
* * * * * * * * * * * *
“Pure mathematics is, in its way, the poetry of logical ideas.”

– Albert Einstein
* * * * * * * * * * * *
“How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?”

– Albert Einstein
* * * * * * * * * * * *
“The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.”

– Albert Einstein
* * * * * * * * * * * *
“Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.”

– Albert Einstein
* * * * * * * * * * * *
“A mathematician is a machine for turning coffee into theorems.”

–Paul Erdös, Hungarian mathematician
* * * * * * * * * * * *
“It’s like asking why Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.

–Paul Erdös, Hungarian mathematician
* * * * * * * * * * * *
“Our biggest failure is our failure to see patterns.”

– Marilyn Ferguson
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“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature.”

– Richard Feynman
* * * * * * * * * * * *
“Many dormant minds have been aroused into activity through the mastery of a single problem.”

– Benjamin Franklin Finkel
* * * * * * * * * * * *
“Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.”

– Irving Fisher
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“Mathematics is the only universal language there is, Senator.”

– line spoken by Jodie Foster in the film Contact
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“Mathematical analysis is as extensive as nature itself.”

– Joseph Fourier
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“Research shows that a self-assessing activity fosters learning better than one in which a student merely receives a grade from the teacher.”

– Brad Fulton
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“The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics.”

– Galileo Galilei
* * * * * * * * * * * *
“The Universe . . . is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.”

– Galileo Galilei
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“The data with which the sciences start out are concrete, whereas the objectives they strive for are abstract.”

– Saadia Gaon (Sa’id ibn Yusuf)
* * * * * * * * * * * *
“Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals . . . The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.”

– Martin Gardner
* * * * * * * * * * * *
“Mathematics is the queen of the sciences and number theory is the queen of mathematics.”
–Karl Friedrich Gauss
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“If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.”

–Karl Friedrich Gauss
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“There is a geometry of art as there is a geometry of life, and, as the Greeks had guessed, they happen to be the same.”
– Matila Ghyka
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“Conversation enriches the understanding, but solitude is the school of genius.”

– Edward Gibbon
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“Mathematics is a language.”

– Josiah Willard Gibbs
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“I’m very well acquainted too with matters mathematical,
I understand equations, both the simple and quadratical,
About binomial theorem I’m teeming with a lot of news –
With many cheerful facts about the square of the hypotenuse.”

– W. S. Gilbert, The Pirates of Penzance
* * * * * * * * * * * *
“It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.”

– Johann Wolfgang von Goethe, German poet and philosopher
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“Mathematics is the hammer that shatters the ice of our unconscious.”

– Dr. Francis O. Googol
* * * * * * * * * * * *
"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."

-Godfrey Harold Hardy
* * * * * * * * * * * *
“The mathematician's patterns, like the painter's or the poet's must be beautiful;
. . . Beauty is the first test: there is no permanent place in this world for ugly mathematics.”

– Godfrey H. Hardy
* * * * * * * * * * * *
“[The works of Archimedes] are . . . so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.”

– Sir Thomas Heath
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“In most sciences, one generation tears down what another has built, and what one has established another undoes. In mathematics alone each generation adds a new story to the old structure.”

– Herman Henkel, from S. Gudder’s A Mathematical Journey
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“Arithmetic is usually taught as all scales and no music.”

– Persis Herold
* * * * * * * * * * * *
“Guess and check is not only a strategy, it is also an attitude.
. . . through your organization and your persistence, you will work toward a solution.”

– Ted Herr and Ken Johnson, from Crossing the River with Dogs
* * * * * * * * * * * *
“One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put in to them.”

– Heinrich Hertz
* * * * * * * * * * * *
“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”

– David Hilbert
* * * * * * * * * * * *

"A thorough training in the mental disciplines of mathematics precludes any tendency to be fuzzy, to be misled by red herrings . . . "

- Conrad Hilton, founder of the hotel chain

* * * * * * * * * * * *

“Descartes commanded the future from his study more than Napoleon from the throne.”

– Oliver Wendell Holmes
* * * * * * * * * * * *
“Mathematics is difficult for many human minds to grasp because of its hierarchical structure: one thing builds on another and depends on it.”

– M. Holt and D.T.E. Marjoram
* * * * * * * * * * * *
“Almost everyone has heard that ‘figures don’t lie, but liars can figure.’ We need statistics, but liars give them a bad name, so to be able to tell the liars from the statisticians is crucial.”
– Dr. Robert Hooke
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“Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. . . . In this convenient way, the person who knows geometry acquires intelligence.”

– Ibn Khaldun
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“From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.”

– Sir James Jeans
* * * * * * * * * * * *
“Nothing can stop the man with
the right mental attitude from
achieving his goal.”

“Nothing on earth can help the man with the wrong mental attitude.”

– Thomas Jefferson
* * * * * * * * * * * *
“It is clear that economics, if it is to be a science at all, must be a mathematical science.”

– William Stanley Jevons
* * * * * * * * * * * *
“The easiest way to refold a road map is differently.”
– Jones’s, Rule of the Road
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“The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.”

– Emmanual Kant
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“Mathematics is the science which uses easy words for hard ideas.”

– Edward Kasner and James Newman
* * * * * * * * * * * *
“A topologist is one who doesn't know the difference between a doughnut and a coffee cup.”

– John Kelley
* * * * * * * * * * * *
“As we move into the era of an information-based world, the value of mathematics as a former of our culture is going to become greater and greater.”
– Kevin Kelly, writer and publisher
* * * * * * * * * * * *
“The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it . . . revealed to us in the language of mathematics.”

– Johannes Kepler
* * * * * * * * * * * *
“Man is a puzzle-solving animal.”

– Ronald A. Knox
* * * * * * * * * * * *
“If you’re going to get good at golf, tennis, or algebra, it is a simple fact that it will take time and effort. Students who are on task the longest have the greatest chance for success.”

“School should not be a place where children come and watch adults work !”

– Ed Koscik
* * * * * * * * * * * *
“Many who have never had an opportunity of knowing much about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.”

– Sonya Kovalevsky
* * * * * * * * * * * *
“I’m absolutely convinced that mathematics is the most naturally human thing to be interested in, but it’s taught with a language that’s alien to many people.”

– Jaron Lanier, concert pianist and computer scientist
* * * * * * * * * * * *
“. . . the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value . . . appears so simple to us now that we ignore its true merits. But its very simplicity . . . puts our arithmetic in the first rank of useful inventions . . .”

– Pierre-Simon Laplace
* * * * * * * * * * * *
“A method of solution is perfect if we can foresee from the start, and even prove, that following that method we shall attain our aim.”

– Gottfried Wilhelm Leibniz
* * * * * * * * * * * *
“Music is a secret arithmetical exercise and the person who indulges in it does not realize that he is manipulating numbers.”

– Gottfried Wilhelm Leibniz
* * * * * * * * * * * *
“No human investigation can be called real science if it cannot be demonstrated mathematically.”

– Leonardo da Vinci
* * * * * * * * * * * *
“What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.”

– G. C. Lichtenberg
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“Points
Have no parts or joints.
How then can they combine
To form a line?

– J. A. Lindon
* * * * * * * * * * * *
“Perfect numbers certainly never did any good, but then they never did any particular harm.”

– J. E. Littlewood
* * * * * * * * * * * *
“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.”

– Nikolai Lobachevsky
* * * * * * * * * * * *
“. . .mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.”

– John Locke
* * * * * * * * * * * *
“Once I realized that math was just a tool, it suddenly opened a whole world for me. It allows me to be creative and expressive in whatever domain I want.”
– Pattie Maes, computer scientist
* * * * * * * * * * * *
“Population, when unchecked, increases in a geometrical ratio.”
– Thomas Malthus, An Essay on the Principle of Population
* * * * * * * * * * * *
“As we move forward into the next century, the fundamental literacy that’s required is the literacy of science – to understand that there are physical laws that can be expressed mathematically, and that there’s a way of making decisions for society based on some analysis, rather than a purely emotional approach.”
– John Marshall, America’s Cup racer
* * * * * * * * * * * *
“Man has within a single generation found himself sharing the world with a strange new species: the computer . . .”
– Marvin Minsky
* * * * * * * * * * * *
“The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.”

– Gösta Mittag-Leffler
* * * * * * * * * * * *
“Learners construct understanding for themselves.
To understand is to know relationships.
Knowing relationships depends on having prior knowledge.”

– Lawrence Lowery
* * * * * * * * * * * *
“The mathematical rules of the universe are visible to men in the form of beauty.”
– John Michell
* * * * * * * * * * * *
“The primary source of all mathematics is the integers.”
– Herman Minkowski
* * * * * * * * * * * *
“A mathematician confided
That a Möbius strip is one-sided,
And you’ll get quite a laugh
If you cut one in half,
For it stays in one piece when divided.”
– Anonymous description of Möbius strip
* * * * * * * * * * * *
“The advancement and perfection of mathematics are ultimately connected with the prosperity of the state.”
– Napoleon Bonaparte
* * * * * * * * * * * *
“The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy.”

– James R. Newman
* * * * * * * * * * * *
“Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises.”

– James R. Newman
* * * * * * * * * * * *
“No great discovery was ever made without a bold guess.”

–Isaac Newton
* * * * * * * * * * * *
“For every action there is an equal but opposite reaction.”

–Isaac Newton
* * * * * * * * * * * *
“If I have seen further than others, it is by standing upon the shoulders of giants.”

– Isaac Newton

* * * * * * * * * * * *
“The study of mathematics cannot be replaced by any other activity that will train and develop man's purely logical faculties to the same level of rationality.”

– C. O. Oakley
* * * * * * * * * * * *
“The odds of winning in a casino are very, very small. In general, with any game, the odds are stacked against you.
. . . any individual who plays for a reasonably long time is going to lose.”

– Ed Packel, mathematician
* * * * * * * * * * * *
“Probability theory helps you to put some kind of pattern on randomness. You can’t tell what’s going to happen from step to step, but you can predict what’s going to happen over the long haul.”

– Ed Packel, mathematician
* * * * * * * * * * * *
“The excitement that a gambler feels when making a bet is equal to the amount he might win times the probability of winning it.”

– Blaise Pascal
* * * * * * * * * * * *
“Chance favors only the prepared mind.”

– Louis Pasteur
* * * * * * * * * * * *
“Probability, like logic, is not just for mathematicians anymore. It permeates our lives.”
– John Allen Paulos, Innumeracy
* * * * * * * * * * * *
“Geometry is a skill of the eyes and the hands as well as of the mind.”

– Jean Pedersen
* * * * * * * * * * * *
“Mathematics is the science which draws necessary conclusions.”

– Benjamin Peirce

* * * * * * * * * * * *
“If a pendulum’s swinging quite free
Then it’s always a marvel to me
That each tick plus each tock
Of the grandfather clock
Is 2p root L over g.”
– p Limerick
* * * * * * * * * * * *
“The knowledge at which geometry aims is the knowledge of the eternal.”
– Plato
* * * * * * * * * * * *
“Arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number . . .”
– Plato
* * * * * * * * * * * *
“The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.”
– Henri Poincaré

* * * * * * * * * * * *
“Life is good for only two things, discovering mathematics and teaching mathematics.”
– Siméon Poisson
* * * * * * * * * * * *
“Mathematics is the abstract key which turns the lock of the physical universe.”
– John Polkinhorne
* * * * * * * * * * * *
“Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.”
– George Polyá
* * * * * * * * * * * *
“The real voyage of discovery consists not in seeking new lands but seeing with new eyes.”
– Marcel Proust
* * * * * * * * * * * *
“Mathematics is not playing with numbers and doing accounting. Mathematics is dealing with ideas in a creative and yet very precise way.”
– Przemyslaw Prusinkiewicz, computer scientist
* * * * * * * * * * * *
“Inspiration is needed in geometry, just as much as in poetry.”
– Aleksandr Pushkin
* * * * * * * * * * * *
“All is number.”
– Pythagoras
* * * * * * * * * * * *
“Defining the elements of a game in mathematical terms allows you to model the game and predict how changes will affect it.”
– Rudrapatna Ramnath, aerospace engineer
* * * * * * * * * * * *
“The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.”
– Ernest Renan
* * * * * * * * * * * *
“If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.”
– Alfréd Rényi
* * * * * * * * * * * *
“For thirty thousand years human beings have made patterns. It’s a fundamental way we have to organize and structure our experience.”
– Tony Robbin, artist
* * * * * * * * * * * *
“The infinitude of the primes,
Is the subject of plenty of rhymes,
But we can’t begin
To prove there’s a twin
An infinite number of times.”
– Peter Rosenthal, American mathematician and lawyer
* * * * * * * * * * * *
”The study of the infinite is much more than a dry, academic game. . . . Whether or not the goal is ever reached, an awareness of the process brings enlightenment.”
– Rudy Rucker, Infinity and the Mind
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“Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture . . . sublimely pure, and capable of a stern perfection such as only the greatest art can show.”
– Bertrand Russell
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“Teachers are more than any other the guardians of civilization.”
– Bertrand Russell
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“The wheel has come full circle.”
– William Shakespeare
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“One merit of mathematics few will deny: it says more in fewer words than any other science.”
– David Eugene Smith
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“It’s remarkable to discover how many connections mathematics makes, how many lightbulbs it suddenly turns on.”

– Sylvia Spengler, biologist
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“Nothing in nature is random . . . A thing appears random only through the incompleteness of our knowledge.”
– Spinoza
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“If you hang around with nice people you get nice friends, hang around with smart people and you get smart friends, hang around with yo-yo’s and you get yo-yo’s for friends. It’s simple mathematics.”

– Sylvester Stallone in Rocky
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“What humans do with the language of mathematics is to describe patterns. Mathematics is an exploratory science that seeks to understand every kind of pattern – patterns that occur in nature, patterns invented by the human mind, and even patterns created by other patterns.”

– Lynn Steen, On the Shoulders of Giants
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“We’re trying to make predictions of the future.”

– Grant Steer, actuary
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“People generally think of the numbers and less of what is to me the interesting part: using the numbers to make decisions about everything under the sun.”
– Hal Stern, mathematician
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“Mathematics is a sort of hidden tool for me. In the world of computer graphics, mathematics is behind everything I do.”

– Doug Trumbull, moviemaker
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“There are three kinds of lies:
lies, damned lies, and statistics.”

– Mark Twain
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“There is an astonishing imagination in the mathematics of nature; and Archimedes had at least as much imagination as Homer.”

– Voltaire
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“. . . children usually are taught what to think, not how to think. That‘s why so many adults live in a state of perpetual misunderstanding about the world.”

– Marilyn vos Savant
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“Even if you’re not going to make heavy use of math in your profession, you still need to know how to think logically.”

“Studying math accomplishes two goals:
? It prepares some kids to think like scientists, and
? It prepares all the rest of them to think, period.”

– Marilyn vos Savant
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“Mathematicians use intuition, conjecture, and guesswork all the time except when they are in the classroom.”

– Joseph Warren
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“Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.”

– H.G. Wells
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“Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.”

– Hermann Weyl
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“By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and, in effect, increases the mental power of the race.”
– Alfred North Whitehead
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“The science of pure mathematics . . . may claim to be the most original creation of the human spirit.”
– Alfred North Whitehead
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“The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil.”

– Norbert Wiener
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“Architecture is akin to music in that both should be based on symmetry of mathematics.”
– Frank Lloyd Wright
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“I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.”
– Malcolm X