The important thing is not to stop questioning.
-Albert Einstein 

Great spirits have always encountered violent opposition from mediocre minds.
 -Albert Einstein 

It's not that I'm so smart, it's just that I stay with problems longer
 -Albert Einstein

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

People like you and I, though mortal of course, like everyone else, do not grow old no matter how long we live. What I mean is that we never cease to stand like curious children before the great Mystery into which we were born. 
- Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice

It is, in fact, nothing short of a miracle that the modern methods of education have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wrack and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. To the contrary, I believe that it would be possible to rob even a healthy beast of prey of its voraciousness, if it were possible, with the aid of a whip, to force the beast to devour continuously, even when not hungry, especially if the food, handed out under such coercion, were to be selected accordingly.
- Albert Einstein

"I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world."
- Albert Einstein

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

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, quoted in A Mathematical Sampler: Topics for Liberal Arts, by W.P. Berlinghoff and K.E. Grant.

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. 
- Albert Einstein, quoted in The Magic of Mathematics, by Theoni Pappas.


"In the first place, God made idiots. That was for practice. Then he made school boards."  
- Mark Twain

I have never let my schooling interfere with my education.
- Mark Twain

"The tendency of democracies is, in all things, to mediocrity."  
-James Fenimore Cooper

"Today, if you are not confused, you are just not thinking clearly."  
-U. Peter

"I cannot say whether things will get better if we change; what I can say is they must change if they are to get better."  
-G. C. Lichtenberg

Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas.
- Alfred North Whitehead, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber

"A poor surgeon hurts one person at a time. A poor teacher hurts 130."
- Ernest Boyer

"Personally I am always ready to learn, although I do not always like being taught."
- Winston Churchill

"The pupil who is never required to do what he cannot do, never does what he can do."
- John Stuart Mill

"Wear the old coat and buy the new book."
- Austin Phelps

"Do you know the difference between education and experience? Education is when you read the fine print; Experience is what you get when you don't."
- Pete Seeger

"Teach the young people how to think, not what to think."
- Sidney Sugarman

"It is better to ask some of the questions than to know all the answers."
- James Thurber

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

"I didn't do very well in math - I could never seem to persuade the teacher that I hadn't meant my answers literally."
- Calvin Trillin

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.
- H. G. Wells, quoted in Flaws and Fallacies in Statistics, by Campbell.

No trace of slavery ought to mix with the studies of the freeborn man. . . . No study, pursued under compulsion, remains rooted in the memory.
- Plato (c. 427–347 B.C.), Greek philosopher. Socrates, The Republic, bk. 7, sct. 536

Thou hast most traitorously corrupted the youth of the realm in erecting a grammar school.
- William Shakespeare (1564–1616), English dramatist, poet. Jack Cade, in King Henry VI, pt. 2, act 4, sc. 7

Our entire school system is based on the notion of passive students that must be "taught" if they are to learn. . . . Our country spends tens of billions of dollars each year not just giving students a second-rate education, but at the same time actively preventing them from getting an education on their own. And I'm angry at how school produces submissive students with battered egos. Most students have no idea of the true joys of learning, and of how much they can actually achieve on their own.
- Adam Robinson, co-founder of The Princeton Review

I think my deepest criticism of the educational system at that period [junior high and high school], and that also applies to other periods, is that it's all based upon a distrust of the student. Don't trust him to follow his own leads; guide him; tell him what to do; tell him what he should think; tell him what he should learn. Consequently at the very age when he should be developing adult characteristics of choice and decision making, when he should be trusted on some of those things, trusted to make mistakes and to learn from those mistakes, he is, instead, regimented and shoved into a curriculum, whether it fits him or not.
- Carl Rogers (1902 - ) U.S. psychologist, in R. Evans Carl Rogers: The Man and His Ideas, (1975), p. 39

Our schools have become vast factories for the manufacture of robots. We no longer send our young to them primarily to be taught and given the tools of thought, no longer primarily to be informed and acquire knowledge; but to be "socialized" -- which in the current semantic means to be regimented and made to conform.
- Robert Lindner, psychoanalyst in Must You Conform? (1956)

Academies that are founded at public expense are instituted not so much to cultivate men's natural abilities as to restrain them.
- Baruch Spinoza (1632 - 1677)

When I was in school, I cheated on my metaphysics exam. I looked into the soul of the boy sitting next to me.
- Woody Allen

Reading maketh a full man...and writing an exact man.
- Francis Bacon

What we become depends on what we read after all of the professors have finished with us. The greatest university of all is a collection of books.
- Thomas Carlyle

"I suppose it is because nearly all children go to school nowadays, and have things arranged for them, that they seem so forlornly unable to produce their own ideas." - Agatha Christie

There are only two places in the world where time takes precedence over the job to be done. School and prison.
- William Glasser

Education is a private matter between the person and the world of knowledge and experience, and has little to do with school or college.
- Lillian Smith

You can lead a boy to college, but you cannot make him think.
- Elbert Hubbard (1856-1915) American author, editor and printer

A mind once stretched by a new idea never regains its original dimension.
- Oliver Wendell Holmes (1809-1894)

The school system, custodian of print culture, has no place for the rugged individual. It is, indeed, the homogenizing hopper into which we toss our integral tots for processing.
- Marshall McLuhan (1911-1980)

My schooling not only failed to teach me what it professed to be teaching, but prevented me from being educated to an extent which infuriates me when I think of all I might have learned at home by myself.
- George Bernard Shaw

The best education consists in immunizing people against systematic attempts at education.
- Paul Karl Feyerabend (1924-1994) Farewell to Reason, 1987

Education rears disciples, imitators, and routinists, not pioneers of new ideas and creative geniuses. The schools are not nurseries of progress and improvement, but conservatories of tradition and unvarying modes of thought.
- Ludwig von Mises

The founding fathers in their wisdom decided that children were an unnatural strain on their parents. So they provided jails called school, equipped with tortures called education.
- John Updike

The most extraordinary thing about a really good teacher is that he or she transcends accepted educational methods.
- Margaret Mead

Children need models rather than critics.
- Joseph Joubert

"Self-education is, I firmly believe, the only kind of education there is."
- Isaac Asimov

It will be said that the joy of mental adventure must be rare, that there are few who can appreciate it, and that ordinary education can take no account of so aristocratic a good. I do not believe this. The joy of mental adventure is far commoner in the young than in grown men and women. ...It is rare in later life because everything is done to kill it during education.
- Bertrand Russell, (1872-1970) English philosopher, mathematician, and writer

When the mind is ready, a teacher appears.
- Zen Proverb

Public schools are the nurseries of all vice and immorality.
- Henry Fielding (1707-1754) English novelist, dramatist

He was so learned that he could name a horse in nine languages; so ignorant that he bought a cow to ride on.
- Benjamin Franklin (1706-1790) American statesman, author, scientist, inventor and philosopher

"We spend the first twelve months of our children's lives teaching them to walk and talk, and the next twelve years telling them to sit down and shut up."
- Phyllis Diller

Everything I did in my life that was worthwhile I caught hell for.
- Earl Warren, quoted in The Fourth, and By Far the Most Recent, 637 Best Things Anybody Ever Said, by Robert Byrne

"Why don't they pass a constitutional amendment prohibiting anybody from learning anything? If it works as well as prohibition did, in five years Americans would be the smartest race of people on Earth."
- Will Rogers

"My problems all started with my early education. I went to a school for mentally disturbed teachers."
- Woody Allen

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, from "My IQ," on the album Puddle Dive.

 A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.
- Paul Halmos

Easy reading is damned hard writing.
- Nathaniel Hawthorne, quoted in A Primer of Mathematical Writing by Steven G. Krantz.

When I was young, all of my radical friends were in reform school. Today, all of my radical friends are in school reform.
- Dan Kennedy, from "A Tale of Two CD's," American Mathematical Monthly, Aug.- Sept., 1994.

If you could lead through testing, the U.S. would lead the world in all education categories. When are people going to understand you don't fatten your lambs by weighing them?
- Jonathan Kozol

As I inched sluggishly along the treadmill of the Maycomb County school system, I could not help receiving the impression that I was being cheated out of something. Out of what I knew not, yet I did not believe that twelve years of unrelieved boredom was exactly what the state had in mind for me.
- Harper Lee, from To Kill a Mockingbird.

If we succeed in giving the love of learning, the learning itself is sure to follow. 
- John Lubbock

Thought that accepts reality as given is no thought at all.
- Herbert Marcuse

Taking an interest in what students are thinking and doing is often a much more powerful form of encouragement than praise. 
- Robert Martin, quoted in The Teachers' Quotation Book, edited by Wanda Lincoln and Murray Suid.

We encourage children to read for enjoyment, yet we never encourage them to "math" for enjoyment. We teach kids that math is done fast, done only one way and if you don't get the answer right, there's something wrong with you. You would never teach reading this way.
- Rachel McAnallen, from "Math? No Problem," The Hartford Courant, October, 1998.

It seems quite unrealistic to judge a curriculum by its general outline, or to judge a course by its syllabus. We can "cover" very impressive material, if we are willing to turn the student into a spectator. But if you cast the student in a passive role, then saying that he has "studied" your course may mean no more than saying of a cat that he has looked at a king. Mathematics is something that one does. 
- Edwin E. Moise, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz

When we try to pick anything by itself we find it hitched to everything else in the universe. 
- John Muir, quoted in The Magic of Mathematics, by Theoni Pappas.

Unless we want mathematics to continue to be viewed as something distinct and separate from the mainstream of culture and consisting of a bag of clever tricks or skills, we must change the way we relate to the general public and the way we teach mathematics. 
- Harald M. Ness, Jr., in "Mathematics: an integral part of our culture", from Essays in Humanistic Mathematics.

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

My twenty years in my own classroom tells me that children"s significant discoveries are never in the lesson plan. Almost no education outsiders, and a minority of insiders, understand this very basic fact about the way the schools work.
- Susan Ohanian, from Garbage Pizzas, Patchwork Quilts and Math Magic.
 
Children need to do what "real" mathematicians do - explore and invent for the rest of their lives.
- Susan Ohanian, from Garbage Pizzas, Patchwork Quilts and Math Magic.

Mathematics is a process of contstructing knowledge, not acquiring it.
- Susan Ohanian, from Garbage Pizzas, Patchwork Quilts, and Math Magic.

Teaching children how to make choices is risky business, and we are increasingly becoming a society that prefers a pre-packaged curriculum to the vagaries of individual judgment, a society whose leaders confuse a facile declaration of educational standards with a genuine commitment to educational excellence.
- Susan Ohanian, quoted in "Pushing a Dead Literacy Can Kill Kids Love of Reading."

There are too many people who get degrees and think that they're educated. In order to be a truly knowledgeable person one has got to be engaged in serious, systematic, lifelong learning.
- Benjamin Payton, quoted in My Soul Looks Back, 'Less I Forget, by Dorothy Winbush Riley

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
- George Polya, quoted in "Thinking the Unthinkable: The Story of Complex Numbers (with a Moral)," by Israel Kleiner, Mathematics Teacher, Oct. 1988

Indeed, only a few are mathematically gifted in the sense that they are endowed with the talent to discover new mathematical facts. But by the same token, only a few are musically gifted in that they are able to compose music. Nevertheless there are many who can understand and perhaps reproduce music, or who at least enjoy it. We believe that the number of people who can understand simple mathematical ideas is not relatively smaller than the number of those who are commonly called musical, and that their interest will be stimulated if only we can eliminate the aversion toward mathematics that so many have acquired from childhood experiences. 
- Hans Rademacher, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz 449
 
- The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life. 
Ernest Renan, quoted in The Oxford Book of Quoations, 3d edition

I must study politics and war that my sons may have liberty to study mathematics and philosophy. My sons ought to study mathematics and philosophy, geography, natural history, naval architecture, navigation, commerce, and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain.
- John Adams, quoted in Bartlett's Familiar Quotations

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

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

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music... In the same way, the symbolism of mathematics is merely its coded form, not its substance. 
- Ian Stewart, from From Here to Infinity.

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories. 
- P.J. Davis, quoted in "The Role of Paradoxes in the Evolution of Mathematics", by I. Kleiner and N. Movshovitz-Hadar, American Mathematical Monthly, vol. 101, no. 10, December 1994.

Given the brief -- and generally misleading -- exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle. But if you believe, as I do, that one of the main reasons why our country"s schoolchildren consistently perform poorly in international comparisons of mathematical ability is the attitude toward mathematics they pick up from society, then it"s a battle we should engage in.
- Keith Devlin, from "What"s Going On During Mathematics Awareness Month", April 1999 column on MAA Online.

Sure, some [teachers] could give the standard limit definitions, but they [the students] clearly did not understand the definitions - and it would be a remarkable student who did, since it took mathematicians a couple of thousand years to sort out the notion of a limit, and I think most of us who call ourselves professional mathematicians really only understand it when we start to teach the stuff, either in graduate school or beyond.
Keith Devlin, from "The Calculus Ultrafilter," Focus, Dec. 1994.

The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying. 
- Jean Dieudonne, from Mathematics - The Music of Reason

It demeans mathematics to justify it to appeals to work, to getting and spending... Can you recall why you fell in love with mathematics? It was not, I think, because of its usefulness in controlling inventories.
- Underwood Dudley, from "Is Mathematics Necessary?", Mathematics Education Dialogues, March 1998. 709

It is time to stop claiming that mathematics is necessary for jobs. It is time to stop asserting that students must master algebra to be able to solve problems that arise every day, at home or at work. It is time to stop telling students that the main reason they should learn mathematics is applications. We should not tell our students lies. They will find us out, sooner or later.
- Underwood Dudley, from "Is Mathematics Necessary?", Mathematics Education Dialogues, March 1998

Every human activity, good or bad, except mathematics, must come to an end.
- Paul Erdos, quoted in "To Prove and Conjecture: Paul Erdos and His Mathematics", by Bela Bollobas, American Mathematical Monthly, vol. 105, no. 3, March 1998.

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

If present trends continue, our country may soon find itself far behind many other nations in both science and technology--nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks.
- Martin Gardner, quoted in More Mathematical People by D.J. Albers, G.L. Alexanderson, and C. Reid.

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 general - the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.
- M. Gardner, quoted in the American Mathematical Monthly, Dec. 1994.

A mathematicians ultimate concern is that his or her inventions be logical, not realistic. 
- Michael Guillen, from Bridges to Infinity.

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, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz

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, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.

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 into them.
- Heinrich Hertz,

Particularly perverse and absurd is the multiple-choice format. I have been doing mathematics now as a professional for nearly 40 years and have never met a situation (outside of finite group theory!) in which I was faced with a mathematical problem and knew that the answer was one of five possibliites. Moreover if faced, artifically, by such a situation, may approach would, and should, be quite different from that in which I simply had to solve the problem. 
- Peter J. Hilton, from "Avoiding Math Avoidance," in Mathematics Tomorrow, by Lynn Arthur Steen. 

Tests tyrannize us -- they tyrannize teachers and children. They loom so large that they distort the teaching curriculum and the teacher"s natural style; they occur so frequently, and with such dire consequences, that they appear to the child (and, perhaps, to the teacher) to be the very reason for learning mathematics. 
- Peter J. Hilton, from "Avoiding Math Avoidance," in Mathematics Tomorrow, by Lynn Arthur Steen.

Just as any sensitive human being can be brought to appreciate beauty in art, music or literature, so that person can be educated to recognize the beauty in a piece of mathematics. The rarity of that recognition is not due to the "fact" that most people are not mathematically gifted but to the crassly utilitarian manner of teaching mathematics and of deciding syllabi and curricula, in which tedious, routine calculations, learned as a skill, are emphasized at the expense of genuinely mathematical ideas, and in which students spend almost all their time answering someone else's questions rather than asking their own.
- Peter Hilton, from "Review: The Pleasures of Counting", American Mathematical Monthly, vol. 105, no. 5, May 1998.

We have to reinvent the wheel every once in a while, not because we need a lot of wheels; but because we need a lot of inventors.
- Bruce Joyce, quoted in Discovering Geometry, by M. Serra

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.
- G. W. Leibniz, quoted in "The Twins" by Oliver Sacks

Bridges would be safer if only people who knew the proper definition of a real number were allowed to design them.
- Norman David Mermin, from "Topological Theory of Defects," in Review of Modern Physics, July 1979.

The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word.
- W. F. Osgood, quoted in Bulletin American Mathematical Society

Bees…by virtue of a certain geometrical forethough…know that the hexagon is greater than the square and the triangle, and will hold more honey for the same expenditure of material.
- Pappas, quoted in Agnesi to Zeno, by Sanderson Smith

The anceints devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point. Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? 
- John Perry, quoted in Memorabilia Mathematica, by Robert E. Moritz. 457

I love mathematics...principally because it is beautiful; because man has breathed his spirit of play into it, and because it has given him his greatest game - the encompassing of the infinite.
- Rozso Peter, quoted in Out of the Mouths of Mathematicians, by R. Schmalz. 290

To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
- Ivars Peterson, from The Mathematical Tourist.

When school children study analytic geometry, they should be made aware that his seemingly trivial and esoteric subject exists to us only because of the heroic efforts of a succession of brilliant minds, culminating in the work of Descartes. Its depth, originality, and profundity are lost on students. It has been carefully polished and refined so exquisitely, presented so elegantly and simply, that students myopically receive it as a trifle.
- J. D. Philips, from "Mathematics as an Aesthetic Discipline," in The Humanistic Mathematics Network Journal, No. 12, Oct. 1995

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
- Henri Poincare, quoted in Contemporary Abstract Algebra, by J. Gallian

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, quoted in More Joy of Mathematics, by Theoni Pappas. 

Life is good for only two things: discovering mathematics and teaching mathematics.
- Simeon Poisson

Mathematics is the abstract key which turns the lock of the physical universe. 
- John Polkinghorne, quoted in Mathematics: The Science of Patterns by Keith Devlin.

[Hilbert] once had a student in mathematics who stopped coming to his lectures, and [he] was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: "I never thought he had enough imagination to be a mathematician."
- George Polya, quoted in Mathematics Magazine, vol. 60, no. 5.

You must know that Hardy had a running feud with God. In Hardy's view God had nothing more important to do than frustrate Hardy. This led to a sort of insurance policy for Hardy one time when he was trying to get back to Cambridge after a visit to [Herald] Bohr in Denmark. The weather was bad and there was only a small boat available. Hardy thought there was a real possibility the boat would sink. So he sent a postcard to Bohr saying, "I proved the Riemann Hypothesis. G.H. Hardy." That way if the boat sank, everyone would think that Hardy had proved the Riemann Hypothesis. God could not allow so much glory for Hardy so he could not allow the boat to sink.
- George Polya, quoted in Out of the Mouths of Mathematicians, by R. Schmalz

The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance. 
- E. Purcell and D. Varberg, from Calculus with Analytic Geometry

We [as children] had a lot of time to develop games. We had few toys. There was no movie house in town. We listened to things on the radio. That was our only contact with the outside world. But our games were very elaborate and purely in the imagination. I think actually that that is something that contributes to making a mathematician - having some time to think and being in the habit of imagining all sorts of complicated things. 
- Mary Ellen Rudin, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz.

Mathematics is a linguistic activity; its ultimate area is preciseness of communication.
- William L. Schaff

Giving students a lot of worksheets to fill out is indicative of low expectations. It suggests that you don"t think they"re capable of deep thinking about mathematics.
- Midge Siegfried, quoted in "Positive numbers: math equity programs unlock the gate to algebra and beyond," by David Ruenzel, Teaching Tolerance, Spring 1998

[Mathematicians] feel free to to use any word we like for any concept, as long as we define the word clearly, but most people learn most words from context and from experience. No wonder, then, that mathematics is viewed as a foreign language by many students -- not only is the vocabulary unfamiliar, but even the process by which one learns the vocabulary is different!
- Stephanie F. Singer, quoted in The Language of Mathematics.

The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few - primarily those who are independently motivated and who will learn under any conditions.
- Lynn A. Steen, from "Does Everybody Need to Study Algebra?"

What one learns about mathematics in primary school corresponds to the alphabet. What one learns in high school corresponds to sentences in a primer. What one learns in elementary college courses corresponds to simple little stories. Scholars alone are aware of the mathematics that corresponds to literature.
- Carl Stoermer, quoted in Mathematics: People, Problems and Results, by D.M. Campbell and J.C. Higgins.

What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections.
- Lynn Arthur Steen, From On the Shoulder of Giants.


And of course . . .

I hate quotations.
- Ralph Waldo Emerson