Quotes

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"I turn away with fear and horror from this lamentable plague of functions which do not have derivatives." Hermite, in a letter to Stieltjes

"Mathematics is a game played according to certain simple rules with meaningless marks on paper." David Hilbert

As long as algebra is taught in school, there will be prayer in school. (Cokie Roberts)

Algebraic symbols are used when you do not know what you are talking about. (Philippe Shnoebelen)

A man whose mind has gone astray should study mathematics. (Francis Bacon)

A person who can, within a year, solve x2 - 92y2 = 1 is a mathematician. (Brahmagupta)

A mathematician is a blind man in a dark room looking for a black cat which isn't there. (Charles R Darwin)

We will prove this by the method of prolonged staring. (Joel Franklin)

I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favor to men of skill; but time and chance happeneth to them all.
-- Ecclesiastes

When I was a boy of 14, my father was so ignorant I could hardly stand to have the old man around. But when I got to 21, I was astonished at how much the old man had learned in 7 years.
-- Mark Twain

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.
-- Harish Chandra (Mathematician)
Quoted in R Langlands, Biographical Memoirs of Fellows of the Royal Society 31 (1985) 197 - 225.

If you want to get something done, find a busy man.

Confidence is not about being always right, but always knowing what to do when things go wrong.

The three most important things in programming: notation, notation, notation.
(with apologies to all real estate agents)

Palindromic advice from a priest to William Tell.
Pray tell, William Dear, is that child your target? You, as father, cry, but despair will not do. Do not, Will, despair but cry "Father!" as you target your child. That is, dear William Tell, pray!
-- Submitted to NPR's word-unit palindrome contest by Denis Hirschfeldt
(by way of http://www.math.uchicago.edu/~chruska/recursive/palindrome.html)

A bit beyond perception's reach
I sometimes believe I see
that life is two locked boxes
each containing the other's key.
-Piet Hein, poet and scientist (1905-1996)

We're going to turn this team around 360 degrees.
- Jason Kidd

"The only teaching that a professor can give, in my opinion, is that of thinking in front of his students. " Lebegue (quoted in math-learn)

"An educated mind is useless without a focused will, and dangerous without a loving heart."  W.J. Deijmann

"That which any one has been long learning unwillingly, he unlearns with proportional eagerness and haste."
(William Hazlitt, English writer)

"Any fool can know. The point is to understand."  Albert Einstein

"Fortune favors the prepared mind."  Louis Pasteur

"Idealism increases in direct proportion to one's distance from the problem."  John Galsworthy, Nobel Laureate in Literature

"Always tell the truth, that way you won't have to remember what you said."  Mark Twain

"Getting a good education for your child is not a spectator sport."  Charlie Hoff

"Those who love peace must learn to organize as well as those who love war." Martin Luther King, Jr., civil rights leader

"Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations."  Morris Kline, mathematician

"Today is the tomorrow we worried about yesterday."  Anonymous

"Sandwich every bit of criticism between two thick layers of praise."  Mary Kay Ash, founder of Mary Kay cosmetics

"If there is anything more dangerous to the life of the mind than having no independent commitment to ideas, it is having an excess of commitment to some special and constricting idea."  Richard Hofstadter, American historian

"The real leader has no need to lead -- he is content to point the way."  Henry Miller, American novelist

" At age 50, every man has the face he deserves. " George Orwell

" Advertising is the rattling of a stick inside a swill bucket. " George Orwell again

"What would you dream for if you knew you couldn't fail?"  (Schuller)

"Understanding binary is as easy as 1, 10, 11."

"Opportunity is missed by most people because it is dressed in overalls and looks like work." Thomas Edison

"Let early education be a sort of amusement. You will then be better able to find out the natural bent."
Plato Quoted in Des MacHale, Wisdom (London, 2002).

"The ultimate inspiration is the deadline."  (Nolan Bushnell, computer pioneer)

"Life without geometry is pointless."  (Unknown)

"The beginning is the most important part of the work."  Plato, Greek philosopher

"When my kids become wild and unruly, I use a nice, safe playpen. When they're finished, I climb out." (Erma Bombeck, humorist, columnist)

"Never doubt that a small group of thoughtful citizens can change the world. Indeed, it is the only thing that ever has." M. Mead

"It is the mark of an educated mind to be able to entertain a thought without accepting it." Aristotle

"We learn more by looking for the answer to a question and not finding it than we do from learning the answer itself."  ~Lloyd Alexander

"Get over the idea that only children should spend their time in study.  Be a student so long as you still have something to learn, and this will mean all your life."  ~Henry L. Doherty

"What does education often do?  It makes a straight-cut ditch of a free, meandering brook."  ~Henry David Thoreau

"The great difficulty in education is to get experience out of ideas."  ~George Santayana

"I read Shakespeare and the Bible, and I can shoot dice.  That's what I call a liberal education." ~Tallulah Bankhead

"You don't understand anything until you learn it more than one way."  ~Marvin Minsky

"Education... has produced a vast population able to read but unable to distinguish what is worth reading."  ~G.M. Trevelyan

"Only the curious will learn and only the resolute overcome the obstacles to learning. The quest quotient has always excited me more than the intelligence quotient."     Eugene S. Wilson

"Much learning does not teach understanding."   Heraclitus (540 BC - 480 BC), On the Universe

"Whenever you are asked if you can do a job, tell 'em, 'Certainly I can!' Then get busy and find out how to do it."      Theodore Roosevelt (1858 - 1919)

"Learning is not compulsory... neither is survival."    W. Edwards Deming (1900 - 1993)

"The most useful piece of learning for the uses of life is to unlearn what is untrue."  ~Antisthenes

"You have learned something.  That always feels at first as if you had lost something."  ~H.G. Wells

"The ink of the scholar is more sacred than the blood of the martyr."  ~Mohammed

"The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn."  ~Alvin Toffler

"If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties." -- Francis Bacon

"A man should keep his little brain attic stocked with all the furniture that he is likely to use, and the rest he can put away in the lumber-room of his library, where he can get it if he wants it." -- Sir Arthur Conan Doyle

"Knowledge is like money: to be of value it must circulate, and in circulating it can increase in quantity and, hopefully, in value." -- Louis L'Amour

"The only fence against the world is a thorough knowledge of it." -- John Locke

"We have not the reverent feeling for the rainbow that a savage has, because we know how it is made. We have lost as much as we gained by prying into that matter." -- Mark Twain

"The problems of the world cannot possibly be solved by skeptics or cynics whose horizons are limited by the obvious realities. We need men who can dream of things that never were." -- John F. Kennedy

"My imagination makes me human and makes me a fool; it gives me all the world and exiles me from it." -- Ursula K. Le Guin

"Imagination grows by exercise and contrary to common belief is more powerful in the mature than in the young." -- W. Somerset Maugham

"If you pay peanuts, you get monkeys." -- James Goldsmith

"October. This is one of the peculiarly dangerous months to speculate in stocks in. The others are July, January, September, April, November, May, March, June, December, August, and February." -- Mark Twain

"Making money is art and working is art and good business is the best art." -- Andy Warhol

"Perpetual devotion to what a man calls his business is only to be sustained by perpetual neglect of many other things." -- Robert Louis Stevenson

"Money is better than poverty, if only for financial reasons." -- Woody Allen

Never ask of money spent
Where the spender thinks it went.
Nobody was ever meant
To remember or invent
What he did with every cent.
----  Robert Frost

"Money is only useful when you get rid of it. It is like the odd card in "Old Maid"; the player who is finally left with it has lost."  -- Evelyn Waugh

"It is better to have a permanent income than to be fascinating." -- Oscar Wilde

"Most people die of a sort of creeping common sense, and discover when it is too late that the only things one never regrets are one's mistakes."  -- Oscar Wilde

"What is reading but silent conversation?" -- Walter Savage Landor

"Some books are to be tasted, others to be swallowed, and some few to be chewed and digested." -- Francis Bacon

"I have never known any distress that an hour's reading did not relieve." --Montesquieu

"A truly great book should be read in youth, again in maturity and once more in old age, as a fine building should be seen by morning light, at noon and by moonlight." -- Robertson Davies

I suggest that the only books that influence us are those for which we are ready, and which have gone a little farther down our particular path than we have yet got ourselves." -- E. M. Forster

"Books are the bees which carry the quickening pollen from one to another mind." -- James Russell Lowell

"Man has such a predilection for systems and abstract deductions that he is ready to distort the truth intentionally, he is ready to deny the evidence of his senses only to justify his logic." -- Fyodor Mikhailovich Dostoyevsky

"The want of logic annoys. Too much logic bores. Life eludes logic, and everything that logic alone constructs remains artificial and forced." -- André Gide

"A mind all logic is like a knife all blade. It makes the hand bleed that uses it." -- Rabindranath Tagore

"The fact that logic cannot satisfy us awakens an almost insatiable hunger for the irrational." -- A. N. Wilson

"However, no two people see the external world in exactly the same way. To every separate person a thing is what he thinks it is--in other words, not a thing, but a think." -- Penelope Fitzgerald

"Everything has beauty, but not everyone sees it." -- Confucius

"I was allowed to ring the bell for five minutes until everyone was in assembly. It was the beginning of power." -- Jeffrey Archer

"I was asked to memorise what I did not understand; and, my memory being so good, it refused to be insulted in that manner." -- Aleister Crowley

"Minerva House...was "a finishing establishment for young ladies," where some twenty girls of the ages from thirteen to nineteen inclusive, acquired a smattering of everything and a knowledge of nothing." -- Charles Dickens

"I think the family is the place where the most ridiculous and least respectable things in the world go on." -- Ugo Betti

"I don't pretend to understand the Universe--it's a great deal bigger than I am." -- Thomas Carlyle

"Nothing puzzles me more than the time and space; and yet nothing troubles me less." -- Charles Lamb

"Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose." -- J. B. S. Haldane

"We are all failures--at least, all the best of us are." -- J. M. Barrie

"Ever tried. Ever failed. No matter. Try Again. Fail again. Fail better." -- Samuel Beckett

"Flops are a part of life's menu and I've never been a girl to miss out on any of the courses." -- Rosalind Russell

"I do not believe in a fate that falls on men however they act; but I do believe in a fate that falls on them unless they act." -- G. K. Chesterton


For in much wisdom is much grief: and he that increaseth knowledge increaseth sorrow.
* Bible -- Ecclesiastes 1:18



"Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." -- Bertrand Russell

"Beauty in mathematics is seeing the truth without effort."   -- George Polya

"There is a difference between not knowing and not knowing yet." -- Shelia Tobias

"There is no Royal Road to Geometry." – Euclid

"Teaching is the royal road to learning."  -- Jassamyn West

"Mathematics is no more computation than typing is literature." -- John Allen Paulos

"What is laid down, ordered, factual, is never enough to embrace the whole truth: life always spills over the rim of every cup." Boris Pasternak, 1890-1960

"There is an astonishing imagination even in the science of mathematics...We repeat, there is far more imagination in the head of Archimedes than in that of Homer."  -- Francios Voltaire

"The purpose of computing is insight, not numbers!"  -- R. W. Hamming

"A great memory does not make a mind, any more than a dictionary is a piece of literature." --John Henry Newman

“Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand."  -- Native American saying

"The creator of the universe works in mysterious ways. But he uses a base ten counting system and likes round numbers." -- Scott Adams

"Five out of four people have trouble with fractions."-- Steven Wright

“The lottery is a tax on people who are bad at math."

"How is it that little children are so intelligent and men so stupid? It must be education that does it."  -- Alexandre Dumas

"Arithmetic is being able to count up to twenty without taking off your shoes." -- Mickey Mouse

"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

"There ain't no rules around here! We're trying to accomplish something!" - Thomas Edison

"It is impossible to be a mathematician without being a poet in soul  -- Sophia Kovalevskaya

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

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder

"Logic is invincible, because in order to combat logic it is necessary to use logic."  -- Pierre Boatroux

"Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."   -- Albert Einstein

"There are 10 types of people in the world -- Those who understand binary, and those who don't." "Binary People" t-shirt slogan

"Education is what survives when what has been learned has been forgotten."    -- B. F. Skinner

"Imagination is more important than knowledge." -- Albert Einstein

"I do not teach, I relate." -- Montaigne 

"The notion of infinity is our greatest friend; it is also the greatest enemy of our peace of mind." -- James Pierpont

"We make a living by what we get, but we make a life by what we give." -- Winston Churchill

"St. Augustine had good insight on the division of labor between God and his children when he wrote that we should work as if everything depended on our efforts and pray as if everything depended on the Almighty."

"Black holes are where God divided by zero." -- Steven Wright

"Math class is tough." -- Barbie Doll (1992)

"After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier.  I realized that this was as far as I could go, and to do this day I have never successfully gone beyond it in any but the most superficial way."  -- Isaac Asimov

"I must study politics and war that my sons may have liberty to study mathematics and philosophy." -- John Adams

"The Good Lord made all the integers; the rest is man's doing."  -- Leopold Kronecker

"Science without religion is lame; religion without science is blind."   -- Albert Einstein

"I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; in short, in matters vegetable, animal, and  mineral, I am the very model of the modern Major General."  -- W.S. Gilbert in the Pirates of Penzance

"Perhaps the greatest paradox of all is that there are paradoxes in mathematics." -- Kasner and Newman

"All great theorems were discovered after midnight."   -- Adrian Mathesis

"In mathematics, you don't understand things. You just get used to them."   -- Johann von Neumann

"A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction." – Tolstoy

"There are no solved problems; there are only problems that are more or less solved”  -- Henri Poincare

"A mathematician is a machine for turning coffee into theorems."     Paul Erdös.
 
"When I was a child, the Earth was said to be two billion years old. Now scientists say it's four and a half billion. So that makes me two and a half billion."     Paul Erdös.
 
"I will know I really am in trouble when I forget the name Alzheimer's."
   Paul Erdös, who wasn't very good at remembering names.

"A mind is a fire to be kindled, not a vessel to be filled."  -- Plutarch

"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."  --  Henri Poincare

"A teacher affects eternity; he can never tell where his influence stops." -- Henry Brooks Adams

"A topologist is a man who doesn't know the difference between a coffee cup and a doughnut."
   Kelley

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."
   Albert Einstein.
 
"Mathematics -- this may surprise or shock some -- is never deductive in creation."  -- Paul Halmos

"Mathematicians create by acts of insights and intuition.  Logic then sanctions the conquests of intuition."  -- Morris Kline

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more."  -- Albert Einstein

"Mighty is geometry; joined with art, resistless."  -- Euripides

"Where there is matter, there is geometry."  -- Johannes Kepler

"Truth is much too complicated to allow anything but approximations."-- John von Neumann

"Statistics are no substitute for judgment."  -- Henry Clay

"When I get a little money, I buy books and if any is left, I buy food and clothes."  -- Erasmus

"Any teacher that can be replaced by a computer should be replaced by a computer.”


George Polya Quotes:
"Geometry is the science of correct reasoning on incorrect figures." - George Polya

"If there is a problem you can't solve, then there is an easier problem you can't solve: find it." - George Polya

My method to overcome a difficulty is to go round it. - George Polya

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching. - George Polya

A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. - George Polya

A mathematics teacher is a midwife to ideas. - George Polya

"A GREAT discovery solves a great problem but there is a grain of discovery in any problem." - George Polya

"The first rule of discovery is to have brains and good luck.  The second rule of discovery is to sit tight and wait till you get a bright idea."  - George Polya

"There are many questions which fools can ask that wise men cannot answer." - George Polya

"I am too good for philosophy and not good enough for physics. Mathematics is in between." - George Polya

G. K. Chesterton Quotes:

"You can't have the family farm without the family." G.K. Chesterton

"The simplification of anything is always sensational." G. K. Chesterton

"Men do not differ much about what things they will call evils; they differ enormously about what evils they will call excusable." G.K. Chesterton

"There are some desires that are not desirable." G.K. Chesterton

"All science, even the divine science, is a sublime detective story. Only it is not set to detect why a man is dead; but the darker secret of why he is alive." G.K.Chesteron

"Art, like morality, consists of drawing the line somewhere." G. K. Chesterton

"There are two kinds of paradoxes. They are not so much the good and the bad, nor even the true and the false. Rather they are the fruitful and the barren; the paradoxes which produce life and the paradoxes that merely announce death. Nearly all modern paradoxes merely announce death." G.K. Chesterton

"A queer and almost mad notion seems to have got into the modern head that, if you mix up everybody and everything more or less anyhow, the mixture may be called unity, and the unity may be called peace. It is supposed that, if you break down all doors and walls so that there is no domesticity, there will then be nothing but friendship. Surely somebody must have noticed by this time that the men living in a hotel quarrel at least as often as the men living in a street." G. K. Chesteron

"A great curse has fallen upon modern life with the discovery of the vastness of the word Education." G.K. Chesterton

"He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever." -– Confucius

"Histories make men wise; poets witty; the mathematics, subtile; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend." -- Francis Bacon

"Beauty is the first test: there is no permanent place in the world for ugly mathematics." -- Godfrey Harold Hardy, A Mathematician's Apology (1940)

"Physicists defer only to mathematicians, and mathematicians defer only to God."

"I do not believe in the gifted. If [the students] have ganas[Spanish for desire], I can make them do it." -– Jaime Escalante

"When I was four years old they tried to test my IQ. They showed me a picture of three oranges and a pear. They asked me, "which one is different and does not belong?" They taught me different was wrong." -- Ani DiFranco

"Numbers constitute the only universal language." --Nathanael West

"The essence of mathematics is in its freedom." -- Georg Cantor

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

"Inspiration is the impact of a fact on a well-prepared mind." -- Louis Pasteur

"Men who say it cannot be done should not interrupt those who are doing it." Chinese Proverb

"For every complex problem, there is a solution that is simple, neat, and wrong." H. L. Mencken"

“The probability that we may fail in the struggle ought not to deter us from the support of a cause we believe to be just."Abraham Lincoln

"The deep study of nature is the most fruitful source of mathematical discoveries." -- Jean-Baptist-Joseph Fourier

"But don't panic. Base 8 is just like Base 10 really. If you're missing two fingers." -- Tom Lehrer

"Experience is the hardest kind of teacher. It gives you the test first, and the lesson afterward." Vernon Law

"When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity." -- Albert Einstein

"Not everything that counts can be counted. Not everything that can be counted counts. -- Albert Einstein

"What's one and one and one and one and one and one and one and one and one and one?" "I don't know," said Alice. "I lost count." "She can't do addition," said the Red Queen." -- Lewis Carroll

"Infinity converts the possible into the inevitable." -- Norman Cousins

“Education is learning more than is being taught. It's the chemistry of curiosity exposed to information. In that sense all of life is potentially school. And even I can pass that." -- Bob Guiccione, Jr.

"The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics…" -- Galilei Galileo

"I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn." -- Archimedes

"Everything tries to be round." -- Black Elk

"A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?" -- Martin Gardner

"One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers." -- Martin Gardner

"The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method, ..." -- Paul Halmos

"A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." -- Paul Halmos

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

"The real danger is not that computers will begin to think like men, but that men will begin to think like computers." -- Sydney J. Harris

"We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility." -- Mary Beth Ruskai

"You get what you settle for." -- Louise Sawyer, from the movie Thelma and Louise

"Think! Think and wonder. Wonder and think. How much water can 55 elephants drink?" -- Dr. Seuss

"One can invent mathematics without knowing much of its history. One can use mathematics without knowing much, if any, of its history. But one cannot have a mature appreciation of mathematics without a substantial knowledge of its history." -- Abe Shenitzer

"The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." -- Albert Einstein

"God not only plays dice. He also sometimes throws the dice where they cannot be seen. " -- Stephen Hawking

"One should always generalize." -- Carl Jacobi

"If you would make a man happy, do not add to his possessions but subtract from the sum of his desires." -- Seneca

"We think in generalities, but we live in details." -- Alfred North Whitehead

"To state a theorem and then to show examples of it is literally to teach backwards.”-- E. Kim Nebeuts

"Mathematics is not a deductive science – that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." -- Paul Halmos

"Mathematics is the Queen of the Sciences and number theory the queen of mathematics." - Carl Friedrich Gauss

"We've all heard that a million monkeys banging on a million typewriters will eventually reproduce the entire works of Shakespeare. Now, thanks to the internet, we know this is not true." -- Professor Robert Silensky

"If I have seen farther than other men, it is because I have stood on the shoulders of giants." -- Isaac Newton

"The greater part of our happiness or misery depends on our dispositions, and not on our circumstances." -- Martha Washington

"The world is not given to you by your parents. It is loaned to you by your children." -- Kenyan proverb

"In a completely rational society, the best of us would be teachers and the rest of us would have to settle for something less, because passing civilization along from one generation to the next ought to be the highest honor and the highest responsibility anyone could have." -- Lee Iacocca

"Small deeds done are better than great deeds planned." -- Peter Marshall.

"The most important questions in life are, for the most part, really only problems of probability." -- Pierre Simon de La Place

"The more you know, the less sure you are." – Voltaire

"Well done is better than well said." -- Ben Franklin

"Perfect numbers like perfect men are very rare." -- Descartes

"Cogito, Ergo Sum. I think, therefore I am." -- Descartes

"The reading of all good books is like a conversation with the finest people of past centuries." – Descartes

"I hear and I forget. I see and I remember. I do and I understand." -- Chinese Proverb.

"Natural numbers are better for your health."

"Life is too short for long division."

"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime."

“Give a man a fish and you feed him for a day. Teach a man to fish and you will realize why some people think golf is exciting."

"There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world."-- Nicolai Lobachevsky

"Logic is the anatomy of thought." -- John Locke

"I tell them if they will occupy themselves with the study of mathematics, they will find in it the best remedy against the lusts of the flesh." -- Thomas Mann

"The mathematical rules of the universe are visible to men in the form of beauty." -- John Michel

"The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." -- William James

"The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver." -- I.N. Herstein

"The infinite! No other question has ever moved so profoundly the spirit of man." -- David Hilbert

"One person's constant is another person's variable." -- Susan Gerhart

"Mathematics is the gate and key to the sciences." -- Roger Bacon

"Pure mathematics is, in its way, the poetry of logical ideas." - Albert Einstein

"Numbers are the highest degree of knowledge. It is knowledge itself." – Plato

"God ever geometrizes." – Plato

“Let no one ignorant of geometry enter here." -- inscription above Plato's Academy

"Circles to square and cubes to double would give a man excessive trouble." -- Matthew Prior

"The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit. -- Alfred North Whitehead

"He who can properly define and divide is to be considered a god." – Plato

"Medicine makes people ill, mathematics makes them sad, and theology makes them sinful." -- Martin Luther

"Obvious is the most dangerous word in mathematics." -- E.T. Bell

"Each problem that I solved became a rule which served afterwards to solve other problems." -- Rene Descartes

"There are three kinds of lies: lies, damned lies, and statistics." -- Benjamin Disraeli

"Who has not been amazed to learn that the function y = e^x, like a phoenix rising from its own ashes, is its own derivative?" -- Francois le Lionnais

"One's work may be finished some day, but one's education never." -- Alexandre Dumas

"Geometry is the foundation of all painting." -- Albrecht Durer

"I am not a teacher, I am an awakener." -- Robert Frost

"It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts." -- Paul Halmos

"I write rhymes with addition and algebra, mental geometry." -- Ice-T

“Science is what we understand well enough to explain to a computer. Art is everything else we do." -- Donald Knuth

"Statistics are human beings with the tears wiped away." -- Paul Brodeur

"Education is what survives when what has been learned has been forgotten." -- B. F. Skinner

"Nature's great book is written in mathematics." -- Galileo

"From the very beginning of his education, the child should experience the joy of discovery." -- Alfred North Whitehead

"Mathematical knowledge adds vigor to the mind, frees it from prejudice, credulity, and superstition." -- John Arbuthnot

"The mathematical sciences particularly exhibit order, symmetry, and limitations; and these are the greatest forms of the beautiful." -- Aristotle

"A diagram is worth a thousand words." -- Dr. Carl E. Linderholm

"God wrote the universe in the language of mathematics." – Galileo

"Some people study all their life, and at their death have learned everything but to think." - Demergue

"A problem well stated is half-solved." - John Dewey

"The best way to have a good idea is to have lots of ideas." -- Linus Pauling

"Questions are creative acts of intelligence." - Frank Kingdon

"From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." -- James Hopwood Jeans

"It is truth very certain that, when it is not in one's power to determine what is true, we ought to follow what is more probable." -- Rene Descartes

"But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer." -- Tom Lehrer

"The mathematician's patterns, like the painter's or 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 is the science which uses easy words for hard ideas." -- Edward Kasner and James R. Newman

"The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human inquiry can be a science unless it pursues its path through mathematical exposition and demonstration." -- Leonardo Da Vinci

"Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics."-- Leonardo da Vinci

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." -- Bertrand Russell

"I have hardly ever known a mathematician who was capable of reasoning." -- Plato

"Q.E.D. (Quod Erat Demonstrandum: Which was to be proven.)"—Euclid

"Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio." -- Thomas Robert Malthus

"The theory of probabilities is at bottom nothing but common sense reduced to calculus." -- Pierre de La Place

"Failure is the opportunity to begin again, more intelligently." -- Henry Ford

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

"God does not play dice with the cosmos." Albert Einstein to Niels Bohr

"Ah, women. They make the highs higher and the lows more frequent." Friedrich Nietzsche

"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." -- Gosta Mittag-Leffler

"[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited;" -- Galileo Galilei

"Bees … by virtue of a certain geometrical forethought … know that the hexagon is greater than the square and the triangle, and will hold more honey for the same expenditure of material." -- Pappas

"Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself." -- Claude Bragdon

"Learning without thought is labor lost; thought without learning is perilous." -- Confucius

"One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories."-- P.J. Davis

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" -- Sir Arthur Conan Doyle

"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." -- Albert Einstein

"I have no particular talent. I am only inquisitive." -- Albert Einstein

"In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematics methods by means of deduction." -- Albert Einstein

"It will be another million years, at least, before we understand the primes." - Paul Erdos

"Science and art sometimes can touch one another, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the borderline between the two respective domains."-- M.C. Escher

"Father [M.C. Escher] had difficulty comprehending that the working of his mind was akin to that of a mathematician. He greatly enjoyed the interest in his work by mathematicians and scientists, ..." -- George Escher

"For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear." -- Leonhard Euler

"Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects, such as economics, physics, navigation, finance, biology and even the arts." -- H. F. Feh
"The journey for an education starts with a childhood question."-- David L. Finn

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." -- Joseph Fourier

"The deep study of nature is the most fruitful source of mathematical discoveries." -- Jean-Baptist-Joseph Fourier

"What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?" -- Benjamin Franklin

"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

“Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure." -- David Hilbert

"The infinite in mathematics is always unruly unless it is properly treated." -- Edward Kasner and James Newman

"Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time." -- Sophus Lie

"If you hold yourself up to your children, hold yourself up as an object lesson and not as an example." -- George Bernard Shaw

"Mathematics, in the common lay view, is a static discipline based on formulas...But outside the public view, mathematics continues to grow at a rapid rate...the guide to this growth is not calculation and formulas, but an open ended search for pattern." -- Lynn A. Steen

"What humans do with the language of mathematics is to describe patterns..." -- Lynn A. Steen
"Symmetry, as wide or as narrow as you define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection." -- Hermann Weyl

"A mathematician's reputation rests on the number of bad proofs he has given." -- A. S. Besicovitch

"Poetry is as exact a science as geometry." -- Gustave Flaubert

“There still remain three studies suitable for free man. Arithmetic is one of them." -- Plato

"God grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference." -- Reinhold Niebuhr

"Millions saw the apple fall, but Newton asked why." – Bernard Baruch

"The symbolism of algebra is its glory. But it also is its curse." -- William Betz

"I have always wished that my computer would be as easy to use as my telephone. My wish has come true ... I no longer know how to use my telephone." -- Bjarne Stroustrup

"The most powerful single idea in mathematics is the notion of a variable." -– K. Dewdney

"Home computers are being called upon to perform many new functions, including the consumption of homework formerly eaten by the dog." -- Doug Larson

"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. –- Albert Einstein

"A word to the wise ain't necessary -- it's the stupid ones that need our advice." -- Bill Cosby

"Hardware -- the parts of a computer that can be kicked." -- Jeff Pesis

"Do the math: Count your blessings."