Quotations about Mathematics and Education

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  
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 

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 

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 
      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."