Black holes are where God divided by zero. – Steven Wright
He uses statistics as a drunken man uses lamp posts – for support rather than illumination. – Andrew Lang
Logic is the art of going wrong with confidence. – Morris Kline
There are three kinds of lies: lies, damned lies, and statistics. – Benjamin Disraeli
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world. – Alfred North Whitehead
Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man can answer. – Charles Caleb Colton
Geometry is the right foundation of all painting. – Albrecht Dürer
1 "Mathematics is the Queen of the Sciences." - Carl Friedrich Gauss 2 "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 3 "One machine can do the work of fifty men. No machine can do the work of one extraordinary man." 4 "If I have seen farther than other men, it is because I have stood on the shoulders of giants." -- Isaac Newton 5 "When I get a little money, I buy books and if any is left, I buy food and clothes." -- Erasmus 6 "The length of your education is less important than its breadth, and the length of your life is less important than its depth." -- Marilyn vos Savant 7 "A mind is a fire to be kindled, not a vessel to be filled." -- Plutarch 8 "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 9 "What happens to you in life is not as important as your attitude toward it." 10 "The secret of success is to have more good days than bad days." 11 "Small deeds done are better than great deeds planned." -- Peter Marshall. 12 "The more you know, the less sure you are." -- Voltaire 13 "Well done is better than well said." -- Ben Franklin 14 "Perfect numbers like perfect men are very rare." -- Descartes 15 "Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency." -- Descartes 16 "We make a living by what we get, but we make a life by what we give." -- Winston Churchill 17 "Teaching high school, in addition to knowing one's subject matter thoroughly and being able to convey it to others, requires the grit of a long-distance runner, the stamina of a boxer going 15 rounds, the temperament of a juggler and the street smarts of a three-card monte dealer." -- Professor Larry Cuban 18 "If a doctor, lawyer, or dentist had 25 people in his office at one time, all of whom had different needs, and some of whom didn't want to be there and were causing trouble, and the doctor, lawyer, or dentist, without assistance, had to treat them all with professional excellence for nine months, then he might have some conception of the classroom teacher's job." -- Colman McCarthy in The Washington Post 19 "How you teach is more important than what you teach." 20 "Life is too short for long division." 21 "I hear and I forget. I see and I remember. I do and I understand." -- Chinese Proverb. 22 "Any teacher that can be replaced by a computer should be replaced by a computer." 23 "Old math teachers never die, they just tend to infinity." 24 "Old teachers never die; they just lose their class." 25 "Natural numbers are better for your health." 26 "Decimals have a point." 27 "Calculus has its limits." 28 "Geometry is just plane fun." 29 "Polar coordinates aren't just arctic fashions." 30 "The only time a question should be asked is when all other possibilities of finding the answer for yourself have been eliminated." -- Ben Franklin. 31 "Old math teachers never die; they just pass into another sphere." 32 "An educational system isn't worth a great deal if it teaches young people how to make a living and doesn't teach them how to live." -- Charles Snitow. 33 "Life is a ladder: Every step we take is either up or down." -- Brewster 34 "Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime." 35 "Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics." 36 "There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world." -- Nicolai Lobachevsky 37 "Logic is the anatomy of thought." -- John Locke; 38 "The mathematical rules of the universe are visible to men in the form of beauty." -- John Michel 39 "It is easier to square a circle than to get round a mathematician." -- de Morgan 40 "The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." -- William James; 57 "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 59 "All the effects of nature are only mathematical results of a small number of immutable laws." - La Place 60 "Music is the pleasure the human mind experiences from counting without being aware that it is counting." -- Leibniz 61 "The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder 63 "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 64 "The infinite! No other question has ever moved so profoundly the spirit of man." -- David Hilbert 66 "One person's constant is another person's variable." -- Susan Gerhart 67 "People who don't count won't count." -- Anatole France 69 "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." -- Albert Einstein 70 "Mathematics is the gate and key to the sciences." -- Roger Bacon 71 "Logic is invincible, because in order to combat logic it is necessary to use logic." -- Pierre Boatroux; 72 "Algebra is generous; she often gives more than is asked of her." -- D'Alembert 73 "A mathematician is a blind man in a dark room looking for a black cat which isn't there." -- Charles Darwin (quoted by Jaime Escalante in the film, STAND and DELIVER) 74 "Pure mathematics is, in its way, the poetry of logical ideas." -- Albert Einstein 75 "Imagination is more important than knowledge." -- Albert Einstein 78 "The notion of infinity is our greatest friend; it is also the greatest enemy of our peace of mind." -- James Pierpont 80 "Geometry existed before creation." -- Plato 82 "Let no one ignorant of geometry enter here." -- inscription above Plato's Academy 83 "Circles to square and cubes to double would give a man excessive trouble." -- Matthew Prior 84 "Wherever there is number, there is beauty." -- Proclus 86 "There is geometry in the humming of the string." -- Pythagoras 91 "Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world." -- Alfred North Whitehead 94 "The best teacher is not the one who knows most, but the one who is most capable of reducing knowledge to that simple compound of the obvious and wonderful ..." -- H.L. Mencken 97 "It is clear that the chief end of mathematical study must be to make the students think." -- John Wesley Young 100 "Mathematics is not a spectator sport!" 102 "The Good Lord made all the integers; the rest is man's doing." -- Leopold Kronecker 108 "Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different." -- Johann Wolfgang von Goethe 112 "I was x years old in the year x^2." -- Augustus De Morgan (when asked about his age) 113 "Each problem that I solved became a rule which served afterwards to solve other problems." -- Rene Descartes 114 "It is not enough to have a good mind. The main thing is to use it well." -- Descartes 115 "There are three kinds of lies: lies, damned lies, and statistics." -- Benjamin Disraeli 118 "The mathematician has reached the highest rung on the ladder of human thought." -- Havelock Ellis 123 "Perhaps the greatest paradox of all is that there are paradoxes in mathematics." -- Kasner and Newman 124 "No human investigation can be called real science if it cannot be demonstrated mathematically." -- Leonardo da Vinci 125 "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 128 "Life is good for only two things: discovering mathematics and teaching mathematics." -- Simeon Poisson 129 "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 130 "I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it." -- Malcolm X 131 "Mathematics is no more computation than typing is literature." -- John Allen Paulos 133 "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 134 "Beauty in mathematics is seeing the truth without effort." -- George Polya 135 "Teaching is the royal road to learning." -- Jassamyn West 136 "We only think when confronted with a problem." -- John Dewey 137 "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 138 "One's work may be finished some day, but one's education never." -- Alexandre Dumas 139 "Geometry is the foundation of all painting." -- Albrecht Durer 140 "The arithmetic of life does not always have a logical answer." -- Inshirah Abdur-Rauf 141 "A teacher affects eternity; he can never tell where his influence stops." -- Henry Brooks Adams 142 "I am not a teacher, I am an awakener." -- Robert Frost 143 "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 144 "Mathematics should be fun." -- Peter J. Hilton 145 "I write rhymes with addition and algebra, mental geometry." -- Ice-T 146 "There is a famous formula, perhaps the most compact and famous of all formulas -- developed by Euler from a discovery of de Moivre: e^(i pi) + 1 = 0... It appeals equally to the mystic, the scientist, the philosopher, the mathematician." -- Edward Kasner and James Newman 147 "God exists since mathematics is consistent and the devil exists since we cannot prove the consistency." -- Morris Kline 148 "Science is what we understand well enough to explain to a computer. Art is everything else we do." -- Donald Knuth 149 "Be ashamed to die until you have won some victory for humanity." -- Horace Mann 150 "Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand." -- Native American saying 151 "Statistics are human beings with the tears wiped away." -- Paul Brodeur 152 "Education is what survives when what has been learned has been forgotten." -- B. F. Skinner 153 "Calculus is the most powerful weapon of thought yet devised by the wit of man." -- W. B. Smith 154 "Nature's great book is written in mathematics." -- Galileo 155 "Numbers constitute the only universal language." --Nathanael West 156 "To err is human, but to really foul things up requires a computer." 157 "The essence of mathematics is in its freedom." -- Georg Cantor 158 "Mathematics, in one view, is the science of infinity." -- P. Davis and R. Hersh 159 "From the very beginning of his education, the child should experience the joy of discovery." -- Alfred North Whitehead 160 "Mathematics -- this may surprise or shock some -- is never deductive in creation." -- Paul Halmos 161 "Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition." -- Morris Kline 162 "I have discovered a truly marvelous proof of this , which however the margin is not large enough to contain." -- Pierre de Fermat, referring to the result known as Fermat's Last Theorem 163 "How can it be that mathematics, a product of human thought independent of experience, is so admirably adapted to the objects of reality?" -- Albert Einstein 164 "Our greatest natural resource is the minds of our children." -- Walt Disney 165 "The moving power of mathematical invention is not reasoning but imagination." -- Augustus de Morgan 166 "Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more." -- Albert Einstein 167 "Every human activity, good or bad, except mathematics, must come to an end." -- Paul Erdos 168 "We are all concerned about the future of American education. But as I tell my students, you do not enter the future -- you create the future. The future is created through hard work." -- Jaime Escalante 169 "I never got a pass mark in math ... Just imagine -- mathematicians now use my prints to illustrate their books." -- M.C. Escher 170 "Mighty is geometry; joined with art, resistless." -- Euripides 171 "Getting the degree meant more to me than an NCAA title, being named All-American or winning an Olympic gold medal." -- Patrick Ewing 172 "The calculus is one of the greatest edifices constructed by mankind." -- Cambridge Conference on School Mathematics 173 "Statistics are no substitute for judgment." -- Henry Clay 174 "Alcohol and Calculus Don't Mix; Never Drink and Derive." 175 "You don't have to teach people to be human. You need to teach them how to stop being inhuman." -- Eldridge Cleaver 176 "By the end of the first month of the 1995 session, each senator will have made more money than any person who works 40 hours a week at minimum wage for the entire year." -- Bill Clinton 177 "The title which I most covet is that of teacher. The writing of a research paper and the teaching of freshman calculus, and everything in between, falls under this rubric. Happy is the person who comes to understand something and then gets to explain it." -- Marshall Cohen 178 "All mathematicians share ... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics." -- Martin Gardner 179 "Mathematical knowledge adds vigor to the mind, frees it from prejudice, credulity, and superstition." -- John Arbuthnot 180 "The mathematical sciences particularly exhibit order, symmetry, and limitations; and these are the greatest forms of the beautiful." -- Aristotle 181 "My philosophy of learning, like my blood type, is be positive. Keeping student attitudes positive is vital to their success in learning. – David Pleacher" 182 "Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind." -- Hermann Weyl 183 "A diagram is worth a thousand words." -- Dr. Carl E. Linderholm 184 "Where the pessimist sees a half-closed interval, the optimist sees a half-open interval." 185 "Discovery lessons, students writing to learn mathematics, the teaching of so-called general problem solving concepts, field trips, math lab lessons, alternate assessments, collaborative partner tests, student presentations, and open-ended problems should all be used sparingly. I use some of them, but they have limited value. Pencil-and-paper analytic solutions are the heart of mathematics education." --Michael Stueben in Twenty Years Before the Blackboard 186 "There are 10 types of people in the world -- Those who understand binary, and those who don't." 187 "Character is what you are when no one is watching." 188 "Morality, like art, consists in drawing a line somewhere." 189 "The heart of education is education of the heart." 190 "Education is worth little if it teaches only how to make a living rather than how to make a life." - Mary Hatwood Futrell 191 "I have never let my schooling interfere with my education." - Mark Twain 192 "Life is 10% what happens to us and 90% how we respond to it." -- Charles Swindoll 193 "If you find a path with no obstacles, it probably doesn't lead anywhere." -- Frank A. Clark 194 "Arithmetic is being able to count up to twenty without taking off your shoes." -- Mickey Mouse 195 "Although I am absolutely without training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists." -- M.C. Escher 196 "The only angle from which to approach a problem is the TRY-Angle" 197 "Education is what you get from reading the small print. Experience is what you get from not reading it!" 198 "Newton's First Law: Somedays it's better to stay in bed." 199 "Education's purpose is to replace an empty mind with an open one." -- Malcolm S. Forbes 200 "The shortest distance between two points is under construction." -- Bill Sanderson 201 "He who laughs, lasts." -- Mary Pettibone Poole 202 "Positive attitudes bring positive results. Negative attitudes bring negative results." 203 "Geometry is the science of correct reasoning on incorrect figures." - George Polya 204 "If there is a problem you can't solve, then there is an easier problem you can't solve: find it." - George Polya 205 "A GREAT discovery solves a great problem but there is a grain of discovery in any problem." - George Polya 206 "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 207 "There are many questions which fools can ask that wise men cannot answer." - George Polya 208 "I am too good for philosophy and not good enough for physics. Mathematics is in between." - George Polya 209 "God wrote the universe in the language of mathematics." - Galileo 210 "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is." 211 "Inspiration is the impact of a fact on a well-prepared mind." - Louis Pasteur 212 "New facts often trigger new ideas" - Osborn 213 "What is now proved was once only imagined" - Proverb 214 "Men who say it cannot be done should not interrupt those who are doing it." 215 "If you go fishing you may not catch any fish. If you don’t go fishing, you’ll never catch any fish." - Alex F. Osborn 216 "Some people study all their life, and at their death have learned everything but to think." - Demergue 217 "The past must be a springboard, not a sofa." - Harold MacMillan 218 "A problem well stated is half-solved." - John Dewey 219 "The best way to have a good idea is to have lots of ideas." - Linus Pauling 220 "Daring ideas are like chessmen moved forward; they may be beaten but they may start a winning game." - Goethe 221 "Questions are creative acts of intelligence." - Frank Kingdon 222 "A learned man is an idler who kills time by study." - George Bernard Shaw 223 "Nothing was ever achieved without enthusiasm." - Emerson 224 "Our minds are finite, and even in these circumstances of finitude we are surrounded by possibilities that are infinite; and the purpose of human life is to grasp as much as we can out of that infinitude. " -- Alfred North Whitehead 225 "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." -- James Hopwood Jeans 226 "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 227 "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 228 "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 229 "But don't panic. Base 8 is just like Base 10 really. If you're missing two fingers." -- Tom Lehrer 230 "Sufficient unto the day is the rigor thereof. -- Eliakim H. Moore 231 "Mathematics is a body of knowledge, but it contains no truths. -- Morris Kline 232 "Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders, designs, and harmonies. -- William L. Schaaf 233 "Mathematics -- the subtle fine art." -- Jamie Byrnie Shaw" 234 "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 235 "Mathematics is the science which uses easy words for hard ideas." -- Edward Kasner and James R. Newman 236 "Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life." -- Cassius Jackson Keyser 237 "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 238 "Experience is the hardest kind of teacher. It gives you the test first, and the lesson afterward." 239 "Not everything that counts can be counted. Not everything that can be counted counts. -- Albert Einstein 240 "I had been to school ... and could say the multiplication table up to 6 x 7 = 35, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics anyway." -- Huckleberry Finn (by Mark Twain) 241 "The creator of the universe works in mysterious ways. But he uses a base ten counting system and likes round numbers." -- Scott Adams 242 "42.7% of all statistics are made up on the spot." -- Steven Wright 243 "Five out of four people have trouble with fractions." -- Steven Wright 244 "Two and two the mathematician continues to make four, in spite of the whine of the amateur for three, or the cry of the critic for five." -- James McNeill Whistler 245 "Angling may be said to be so like the mathematics that it can never be fully learnt." -- Izaak Walton 246 "Mathematics is the science which draws necessary conclusions." -- Benjamin Peirce 247 "Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics." -- Leonardo da Vinci 248 "Mathematics, rightly viewed, possesses not only truth, but supreme beauty." -- Bertrand Russell 249 "Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform." -- Bertrand Russell 250 "The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty." -- Sir D'Arcy Wentworth Thompson 251 "Numerical precision is the very soul of science." -- Sir D'Arcy Wentworth Thompson 252 "All the mathematical sciences are founded on the relations between physical laws and laws of numbers." -- James Clerk Maxwell 253 "I have hardly ever known a mathematician who was capable of reasoning." -- Plato 254 "Histories make men wise; poets witty; the mathematics, subtile; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend." -- Francis Bacon 255 "A few honest men are better than numbers." -- Oliver Cromwell 256 "Q.E.D. (Quod Erat Demonstrandum: Which was to be proven.)" -- Euclid 257 "Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio." -- Thomas Robert Malthus 258 "The theory of probabilities is at bottom nothing but common sense reduced to calculus." -- Pierre de La Place 259 "Now don't be sad, 'cause two out of three ain't bad." -- Meatloaf 260 "Statistics means never having to say you're certain." 261 "Without geometry life is pointless." 262 "The work of a teacher -- exhausting, complex, idiosyncratic, never twice the same -- is at its heart, an intellectual and ethical enterprise. Teaching is the vocation of vocations..." -- William Ayres 263 "Beauty is the first test: there is no permanent place in the world for ugly mathematics." -- Godfrey Harold Hardy, A Mathematician's Apology (1940) 264 "We think it's about little techniques and tricks, but techniques only take you so far. We need teachers who care about kids, who care about what they teach, and who can communicate with kids." -- Parker I. Palmer in The Courage to Teach. 265 "Physicists defer only to mathematicians, and mathematicians defer only to God." 266 "Biologists think they are biochemists, Biochemists think they are Physical Chemists, Physical Chemists think they are Physicists, Physicists think they are Gods, And God thinks he is a Mathematician." 267 "Old math teachers never die –- they just lose their functions." 268 "Ganas is all you need." [Ganas is Spanish for passion, guts, determination, desire] -– Jaime Escalante 269 "I do not believe in the gifted. If [the students] have ganas [Spanish for desire], I can make them do it." -– Jaime Escalante 270 "Genius is one per cent inspiration, ninety-nine per cent perspiration." -- Thomas Alva Edison 271 "To teach is to learn." 272 "To learn, you must want to be taught." – Proverbs 12:1 273 "Failure is the opportunity to begin again, more intelligently." -- Henry Ford 274 "To infinity and beyond."" – Buzz Lightyear 275 "I think, therefore I laugh." -- John Allen Poulos 276 "I do not think -- therefore I am not." 277 "Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives." 278 "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 279 "The lottery is a tax on people who are bad at math." 280 "With an absurd oversimplification, the "invention" of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part." -- Richard Courant and Herbert Robbins 281 "The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers." -- Keith Devlin 282 "It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid." -- W. S. Jevons 283 "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 284 "But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not." -- Johann Bernoulli 285 "You live your life between your ears." -- Bebe Moore Campbell 286 "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 287 "Education is the key to unlock the golden door of freedom." -- George Washington Carver 288 "Infinity converts the possible into the inevitable." -- Norman Cousins 289 "Education is learning more than it 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. 290 "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 291 "How many pizzas are consumed each year in the United States? How many words have you spoken in your life? How many different peoples names appear in the New York Times each year? How many watermelons would fit inside the U.S. Capitol building? What is the volume of all the human blood in the world? -- John A. Paulos 292 "[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 293 "We must say that there are as many squares as there are numbers." -- Galileo Galilei 294 "The study of mathematics is apt to commence in disappointment." -- Alfred North Whitehead 295 "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 296 "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 297 "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 298 "Education is indoctrination if you're white; subjugation if you're black." -- James Baldwin 299 "The purpose of education...is to create in a person the ability to look at the world for himself, to make his own decisions." -- James Baldwin 300 "No set of principles can guarantee a recipe for good practice (in teaching)." -- D. Ball and T. Schroeder 301 "All of us are slaves to the prejudices of our own dimension." -- Thomas Banchoff (in introduction to Flatland) 302 "The calculus is the story this [the Western] world first told itself as it became the modern world." -- David Berlinski 303 "The definition of a limit is essentially his [Cauchy"s] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon." -- David Berlinski 304 "Everything tries to be round." -- Black Elk 305 "Somebody came up to me after a talk I had given, and said, 'You make mathematics seem like fun.' I was inspired to reply, 'If it isn't fun, why do it?'" -- Ralph P. Boas 306 "Major paradoxes provide food for logical thought for decades and sometimes centuries." -- Nicholas Bourbaki 307 "Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself." -- Claude Bragdon 308 "The schools are a great theater in which we play out the conflicts in the culture." -- David Cohen and Barbara Neufeld 309 "Learning without thought is labor lost; thought without learning is perilous." -- Confucius 310 "Starting in the seventeenth century, the general theory of extreme values -- maxima and minima -- has become one of the systematic integrating principles of science." -- Richard Courant and Herbert Robbins 311 "Every new body of discovery is mathematical in form, because there is no other guidance we can have." -- Charles Darwin 312 "One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories." -- P.J. Davis 313 "Common integration is only the memory of differentiation..." -- A. De Morgan 314 "I see it, but I don't believe it." [On Cantor's proof that the points in the unit interval were in one-to-one correspondence with points in the unit square.] -- Richard Dedekind 315 "Numbers are the free creation of the human mind." -- Richard Dedekind 316 "The linear-programming was -- and is -- perhaps the single most important real-life problem." -- Keith Devlin 317 "There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another." -- Keith Devlin 318 "Failure is instructive. The person who really thinks learns quite as much from his failures as from his successes." -- John Dewey 319 "Education is not a preparation for life, education is life itself." -- John Dewey 320 "One of the most important concepts in all of mathematics is that of function." -- T.P. Dick and C.M. Patton 321 "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 322 "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 323 "you got to look outside- your eyes- you got to think outside- your brain- you got to walk outside- your life- to where the neighborhoods change." -- Ani DiFranco 324 "A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical." -- P.A.M. Dirac 325 "Success isn't permanent, and failure isn't fatal." -- Mike Ditka 326 "If there's no struggle, there's no progress." -- Frederick Douglass 327 "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 328 "Education must not simply teach work - it must teach life." -- W.E.B. DuBois 329 "How is it that little children are so intelligent and men so stupid? It must be education that does it." -- Alexandre Dumas 330 "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 331 "Proof is an idol before which the mathematician tortures himself." -- Sir Arthur Eddington 332 "There ain't no rules around here! We're trying to accomplish something!" -- Thomas Edison 333 "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." -- Albert Einstein 334 "It is the supreme art of the teacher to awaken joy in creative expression and knowledge." -- Albert Einstein 335 "The series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences." -- Albert Einstein 336 "I have no particular talent. I am only inquisitive." -- Albert Einstein 337 "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 338 "The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms." -- Albert Einstein 339 "The value of an education ... is not the learning of many facts but the training of the mind to think something that cannot be learned from textbooks." -- Albert Einstein 340 "Every great and commanding moment in the annals of the world is the triumph of some enthusiasm." -- Ralph Waldo Emerson 341 "It will be another million years, at least, before we understand the primes." -- Paul Erdos 342 "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 boderline between the two respective domains." -- M.C. Escher 343 "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 344 "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 345 "After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential." -- Leonhard Euler 346 "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. Fehr 347 "On the other hand, it is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as a sum of two fourth powers or, in general for any number which is a power greater than the second to be written as a sum of two like powers. For this I have discovered a truly wonderful proof, but the margin is too small to contain it." -- P. Fermat 348 "The journey for an education starts with a childhood question." -- David L. Finn 349 "Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." -- Joseph Fourier 350 "The deep study of nature is the most fruitful source of mathematical discoveries." -- Jean-Baptist-Joseph Fourier 351 "What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?" -- Benjamin Franklin 352 "A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?" -- Martin Gardner 353 "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 354 "The most important outcome of education is to help students to become independent of formal education." -- Paul E. Gray 355 "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 356 "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 357 "The purpose of computing is insight, not numbers!" -- R. W. Hamming 358 "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 359 "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 360 "The struggle to become a better teacher begins all over again with the advent of each new class." -- Martin Henley 361 "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 362 "The discoveries of Newton have done more for England and for the race, than has been done by whole dynasties of British monarchs." -- Thomas Hill 363 "The infinite in mathematics is alway unruly unless it is properly treated." -- Edward Kasner and James Newman 364 "Where there is matter, there is geometry." -- Johannes Kepler 365 "The greater our knowledge increases, the greater our ignorance unfolds." -- John F. Kennedy 366 "...it is the greatest achievement of a teacher to enable his students to surpass him." -- John Kemeny 367 "The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education." -- Martin Luther King, jr 368 "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 369 "The Mandelbrot set is the most complex mathematical object known to mankind." -- B. Mandelbrot 370 "The teacher who is attempting to teach without inspiring the pupil to learn is hammering on cold iron." -- Horace Mann 371 "God created infinity, and man, unable to understand infinity, had to invent finite sets." -- Gian Carlo Rota 372 "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 373 "Three passions ... have governed my life: the longing for love, the search for knowledge, and the unbearable pity for the suffering of mankind." -- Bertrand Russell 374 "Zeno was concerned with three problems...These are the problem of the infinitesimal, the infinite, and continuity." -- Bertrand Russell 375 "You get what you settle for." -- Louise Sawyer, from the movie Thelma and Louise 376 "Think! Think and wonder. Wonder and think. How much water can 55 elephants drink?" -- Dr. Seuss 377 "If you hold yourself up to your children, hold yourself up as an object lesson and not as an example." -- George Bernard Shaw 378 "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 379 "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 guid to this growth is not calculation and formulas, but an open ended search for pattern." -- Lynn A. Steen 380 "What humans do with the language of mathematics is to describe patterns..." -- Lynn A. Steen 381 "There is a difference between not knowing and not knowing yet." -- Shelia Tobias 382 "Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it." -- Tolstoy 383 "Out of the public schools comes the greatness of the nation." -- Mark Twain 384 "Calculators can only calculate - they cannot do mathematics." -- John A. Van de Walle 385 "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 386 "Truth is much too complicated to allow anything but approximations." -- John von Neumann 387 "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 388 "I don't know if I should care for a man who made life easy; I should want someone who made it interesting." -- Edith Wharton 389 "If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy." -- Alfréd Rényi 390 "A mathematician's reputation rests on the number of bad proofs he has given." -- A. S. Besicovitch 391 "Statistics: the mathematical theory of ignorance." -- Morris Kline 392 "Poetry is as exact a science as geometry." -- Gustave Flaubert 393 "God is a child; and when he began to play, he cultivated mathematics. It is the most godly of man's games." -- V. Erath 394 "There still remain three studies suitable for free man. Arithmetic is one of them." -- Plato 395 "Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state." -- Plato 396 "In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection. -- Hugo Rossi" 397 "Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin 398 "With me everything turns into mathematics." -- Descartes 399 "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 400 "God not only plays dice. He also sometimes throws the dice where they cannot be seen. " -- Stephen Hawking 401 "One should always generalize." -- Carl Jacobi 402 "The greatest unsolved theorem in mathematics is why some people are better at it than others." -- Adrian Mathesis 403 "Logic doesn't apply to the real world." -- Marvin Lee Minsky 404 "You know we all became mathematicians for the same reason: we were lazy." -- Max Rosenlicht 405 "Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be." -- Bertrand Russell 406 "If you would make a man happy, do not add to his possessions but subtract from the sum of his desires." -- Seneca 407 "We think in generalities, but we live in details." -- Alfred North Whitehead 408 "Learning to solve problems is the principal reason for studying mathematics." -- National Council of Teachers of Mathematics 409 "High achievement always takes place in the framework of high expectation." -- Jack Kinder 410 "To state a theorem and then to show examples of it is literally to teach backwards." -- E. Kim Nebeuts 411 "Man can not discover new oceans unless he has the courage to lose sight of the shore." -- Andre Gide 412 "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 413 "It's not the situation ... it's your reaction to the situation." -- Robert Conklin 414 "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 415 "Success does not consist in never making mistakes, but in never making the same one a second time." -- George Bernard Shaw 416 "Millions saw the apple fall, but Newton asked why." -– Bernard Baruch 417 "In the book of life, the answers aren't in the back." -- Charlie Brown (Charles Schulz) 418 "The symbolism of algebra is its glory. But it also is its curse." -- William Betz 419 "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 420 "If we couldn't laugh, we just would go insane. If we weren't all crazy, we would go insane." -- Jimmy Buffett 421 "We use only 10% of our brains… Imagine how smart we would be if we used the other 60%!" -- Ellen DeGeneres 422 "The most powerful single idea in mathematics is the notion of a variable." -– K. Dewdney 423 "Home computers are being called upon to perform many new functions, including the consumption of homework formerly eaten by the dog." -- Doug Larson 424 "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. –- Albert Einstein 425 "You can not feed the hungry on statistics." -- Heinrich Heine 426 "A word to the wise ain't necessary -- it's the stupid ones that need our advice." -- Bill Cosby 427 "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 428 "Start every day off with a smile and get it over with." -- W.C. Fields 429 "I refuse to join any club that would have me as a member." -- Groucho Marx 430 "Hardware -- the parts of a computer that can be kicked." -- Jeff Pesis 431 "He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever." -– Confucius 432 "Do the math: Count your blessings." 433 "Students learn more when they complete homework that is graded, commented upon, and discussed by their teachers. The teacher's feedback -- reinforcing what has been done correctly and re-teaching what has not -- is key." -- Nancy Protheroe 434 "If one puts an infinite number of monkeys in front of typewriters, and lets them clap away, there is a certainty that one of them will come out with an exact version of the 'Iliad.'" -- Nassim Nicholas Taleb 435 "A math student's best friend is BOB (the Back Of the Book), but remember that BOB doesn't come to school on test days." -- Josh Folb 436 "The surest sign of wisdom is constant cheerfulness." -- Montaigne 437 "Do math and you can do anything. " -- N.C.T.M. slogan 438 "A mathematician is a device for turning coffee into theorems." -- Paul Erdos 439 “The pursuit of learning is not a piece of content that can be taught. It is a value that teachers model. Only teachers who are avid, internally motivated learners can truly teach their students the joy of learning.” -- Martin Haberman 440 “It isn't enough just to learn -- one must learn how to learn, how to learn without classrooms, without teachers, without textbooks. Learn, in short, how to think and analyze and decide and discover and create. -- Michael Bassis 441 “It isn't that they can't see the solution. It is that they can't see the problem.” -- G. K. Chesterton 442 “Mathematics is an independent world created out of pure intelligence.” -- Wordsworth, William 443 “Read Euler: he is our master in everything.” -- Pierre-Simon de Laplace 444 “I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors.” -- James Caballero 445 Charlie Chaplin once allegedly said to Albert Einstein: "The people applaud me because everyone understands me, and they applaud you because no one understands you."