"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.
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."
"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."
"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