Quotes for math page
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"There is no Royal Road to Geometry." -- Euclid
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
"Your work is to discover your work and then with all
your heart to give yourself to it." -- Buddha
8
"A mind is a fire to be kindled, not a vessel to be
filled." -- Plutarch
9
"The greater part of our happiness or misery depends
on our dispositions, and not on our circumstances."
-- Martha Washington
10
"The world is not given to you by your parents. It is
loaned to you by your children." -- Kenyan proverb
11
"If a man hasn't found something he will die for, he
isn't fit to live." -- Martin Luther King, Jr.
12
"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
13
"What happens to you in life is not as important as
your attitude toward it."
14
"The secret of success is to have more good days than
bad days."
15
"The second most important job in the world, second
only to being a good parent, is being a good teacher."
-- S.G. Ellis
16
"Small deeds done are better than great deeds planned."
-- Peter Marshall.
17
"Forget committees. New, noble, world-changing ideas
always come from one person working alone."
-- H. Jackson Brown, Life's Little Instruction Book
18
"The most important questions in life are, for the
most part, really only problems of probability."
-- Pierre Simon de La Place
19
"I do not teach, I relate." -- Montaigne
20
"The more you know, the less sure you are." -- Voltaire
21
"Well done is better than well said." -- Ben Franklin
22
"Perfect numbers like perfect men are very rare."
-- Descartes
23
"Mathematics is a more powerful instrument of knowledge
than any other that has been bequeathed to us by human
agency." -- Descartes
24
"Cogito, Ergo Sum.
25
"The reading of all good books is like a conversation
with the finest people of past centuries." -- Descartes
26
"We make a living by what we get, but we make a life
by what we give." -- Winston Churchill
27
"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
28
"St. Augustine had good insight on the division of
labor between God and his children when he wrote that we
should work as if everything depended on our efforts and
pray as if everything depended on the Almighty."
29
"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
30
"Old principals never die, they just lose their
faculties."
31
"How you teach is more important than what you teach."
32
"Life is too short for long division."
33
"I hear and I forget.
I see and I remember.
I think, therefore I am."
-- Descartes
I do and I understand." -- Chinese Proverb.
34
"Any teacher that can be replaced by a computer
should be replaced by a computer."
35
"Old math teachers never die, they just tend to infinity."
36
"Old teachers never die; they just lose their class."
37
"Natural numbers are better for your health."
38
"Decimals have a point."
39
"Calculus has its limits."
40
"Geometry is just plane fun."
41
"Polar coordinates aren't just arctic fashions."
42
"The only time a question should be asked is when all other
possibilities of finding the answer for yourself have been
eliminated." -- Ben Franklin.
43
"A great memory does not make a mind, any more than
a dictionary is a piece of literature."
44
"Old math teachers never die; they just pass into another sphere."
45
"Knowledge exists to be imparted." -- Emerson
46
"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.
47
"Life is a ladder: Every step we take is either up or
down." -- Brewster
48
"Give a man a fish and you feed him for a day.
Teach a man to fish and you feed him for a lifetime."
49
"Give a man a fish and you feed him for a day.
Teach a man to fish and you will realize why some
people think golf is exciting."
50
"Small minds discuss persons. Average minds
discuss events. Great minds discuss ideas.
Really great minds discuss mathematics."
51
"There is no branch of mathematics, however abstract, which may not
someday be applied to the phenomena of the real world."
-- Nicolai Lobachevsky
52
"Logic is the anatomy of thought." -- John Locke;
53
"I tell them if they will occupy themselves with the study of
mathematics, they will find in it the best remedy against
the lusts of the flesh." -- Thomas Mann
54
"The mathematical rules of the universe are visible to men in
the form of beauty." -- John Michel
55
"It is easier to square a circle than to get round a
mathematician."
-- de Morgan
56
"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
58
"It is impossible to be a mathematician without being a poet in
soul.
-- Sophia Kovalevskaya
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
62
"I recoil with dismay and horror at this lamentable plague of
functions which do not have derivatives. -- Charles Hermite
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
65
"The object of mathematics is the honor of the human spirit."
-- C. Jacobi
66
"One person's constant is another person's variable."
-- Susan Gerhart
67
"People who don't count won't count." -- Anatole France
68
"An educated mind is, as it were, composed of all the minds of
preceding ages." -- de Fontenelle
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
76
"The advancement and perfection of mathematics are intimately
connected with the prosperity of the state." -- Napoleon
77
"The calculus is the greatest aid we have to the application of
physical truth in the broadest sense of the word." -- W. F. Osgood
78
"The notion of infinity is our greatest friend; it is also the
greatest enemy of our peace of mind." -- James Pierpont
79
"Numbers are the highest degree of knowledge. It is
knowledge itself." -- Plato
80
"Geometry existed before creation." -- Plato
81
"God ever geometrizes." -- 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
85
"The real voyage of discovery consists not in seeking new
landscapes but in having new eyes." -- Marcel Proust
86
"There is geometry in the humming of the string." -- Pythagoras
87
"What would life be without arithmetic but a scene of horrors?"
-- Sydney Smith
88
"A mathematician who is not also something of a poet will never
be a complete mathematician." -- Karl Weierstrass
89
"Mathematics is the science of definiteness, the necessary
vocabulary of those who know." -- W. J. White
90
"The pursuit of mathematics is a divine madness of the human
spirit."
-- Alfred North Whitehead
91
"Algebra is the intellectual instrument which has been created for
rendering clear the quantitative aspects of the world."
-- Alfred North Whitehead
92
"The science of Pure Mathematics, in its modern developments,
may claim to be the most original creation of the human spirit.
-- Alfred North Whitehead
93
"Black holes are where God divided by zero." -- Steven Wright
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
95
"Math class is tough." -- Barbie Doll (1992)
96
"After years of finding mathematics easy, I finally reached
integral calculus and came up against a barrier. I realized that
this was as far as I could go, and to this day I have never
successfully gone beyond it in any but the most superficial way."
-- Isaac Asimov
97
"It is clear that the chief end of mathematical study must be to
make the students think." -- John Wesley Young
98
"Only professional mathematicians learn anything from proofs.
Other people learn from explanations." -- Ralph Boas
99
"I must study politics and war that my sons may have liberty to
study mathematics and philosophy." -- John Adams
100
"Mathematics is not a spectator sport!"
101
"He who can properly define and divide is to be considered a god."
-- Plato
102
"The Good Lord made all the integers; the rest is man's doing."
-- Leopold Kronecker
103
"Medicine makes people ill, mathematics makes them sad, and
theology makes them sinful." -- Martin Luther
104
"There are two ways to do great mathematics. The first is to be
smarter than everybody else. The second way is to be stupider than
everybody else -- but persistent." -- Raoul Bott
105
"Mathematics is the life of the gods."
-- Novalis (Friedrich von Hardenberg)
106
"He is unworthy of the name of man who is ignorant of the fact that
the diagonal of a square is incommensurable with its side.
-- Plato
107
"Mathematics consists in proving the most obvious thing in the
least obvious way." -- George Polya
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
109
"How happy the lot of the mathematician. He is judged solely by his
peers, and the standard is so high that no colleague or rival can
ever win a reputation he does not deserve." -- W.H. Auden
110
"Obvious is the most dangerous word in mathematics." -- E.T. Bell
111
"Mathematics is written for mathematicians." -- Copernicus
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
116
"Everything that is really great and inspiring is created by the
individual who can labor in freedom." -- Albert Einstein
117
"Science without religion is lame; religion without science is
blind."
-- Albert Einstein
118
"The mathematician has reached the highest rung on the ladder of
human thought." -- Havelock Ellis
119
"Whenever you can, count." -- Sir Francis Galton
120
"Mathematics is a game played according to certain simple rules
with meaningless marks on paper." -- David Hilbert
121
"I'm very good at integral and differential calculus, I know the
scientific names of beings animalculous; in short, in matters
vegetable, animal, and mineral, I am the very model of the modern
Major General." -- W.S. Gilbert in the Pirates of Penzance
122
"Mathematics is the science of what is clear by itself."
-- Carl Jacobi
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
126
"All great therorems were discovered after midnight."
-- Adrian Mathesis
127
"In mathematics, you don't understand things. You just get used to
them."
-- Johann von Neumann
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
132
"There are no solved problems; there are only problems that are
more or less solved." -- Henri Poincare
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."
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."
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
--
Robert Frost
-- Peter J. Hilton
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."
155
"Numbers constitute the only universal language."
156
"To err is human, but to really foul things up requires a
computer."
157
"The essence of mathematics is in its freedom."
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
-- Galileo
--Nathanael West
-- Georg Cantor
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."
174
"Alcohol and Calculus Don't Mix;
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
-- Henry Clay
Never Drink and Derive."
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.
bring negative results."
203
Negative attitudes
"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
"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
206
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."
218
"A problem well stated is half-solved."
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
- Harold MacMillan
- John Dewey
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.
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."
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.
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
If you're
-- Jamie Byrnie Shaw"
It gives you the
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."
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
-- Bebe Moore Campbell
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."
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
-- Black Elk
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."
326
"If there's no struggle, there's no progress."
-- Frederick Douglass
-- Mike Ditka
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."
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
-- Johannes Kepler
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." -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
Louise Sawyer,
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."
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."
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."
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
-- Descartes
-- Carl Jacobi
--
Marvin Lee Minsky
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.
-- 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."
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
But it also is its curse."
-- Heinrich Heine
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:
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
Count your blessings."
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."
446
“Share knowledge, not answers.”
447
“Any fool can know. The point is to understand."
-- Albert Einstein
448
“It has been said that Newton was born in the same year that
Galileo died because God wanted someone of that caliber on Earth
at all times.”