Quotations

Why can't somebody give us a list of things that everybody
thinks and nobody says, and another list of things that
everybody says and nobody thinks?
                                      Oliver Wendell Holmes


Nothing puzzles me more than time and space; and yet nothing
troubles me less, as I never think about them.
                                       Charles Lamb


The system of Descartes... seemed to give a plausible reason 
for all those phenomena; and this reason seemed more just, as 
it is simple and intelligible to all capacities. But in 
philosophy, a student ought to doubt of the things he fancies 
he understands too easily, as much as of those he does not 
understand.
                                         Voltaire


A marveilous newtrality have these things mathematicall, and
also a strange participation between things supernaturall
and things naturall.
                                        John Dee


Like the ski resort full of girls hunting for husbands 
and husbands hunting for girls, the situation is not as
symmetrical as it might seem.
                                        Alan MacKay


Everything of importance has been said before, by someone
who did not discover it.
                                     Alfred North Whitehead


And Lucy, dear child, mind your arithmetic...  What would 
life be without arithmetic, but a scene of horrors?
                                       Syndey Smith, 1835


Then assuredly the world was made, not in time, but
simultaneously with time.
                                       St. Augustine


There was more imagination in the head of Archimedes than
in that of Homer.
                                        Voltaire


In science one tries to tell people, in such a way as to be 
understood by everyone, something that no one ever knew before. 
But in poetry, it's the exact opposite.
                                           Paul Dirac


To Thales the primary question was not 'What do we know?'
but 'How do we know it?'.
                                        Aristotle


Time and again an entirely new philosophical movement arises
which finally unmasks the old philosophical problems as pseudo-
problems, and which confronts the wicked nonsense of philosophy
with the good sense of meaningful, positive, empirical science.
And time and again do the despised defenders of 'traditional
philosophy' try to explain to the leaders of the latest
positivistic assault that the main problem of philosophy is
the critical analysis of the appeal to the authority of
'experience' - precisely that 'experience' which every latest
discoverer of positivism is, as ever, artlessly taking for
granted.
                                         Karl Popper, 1935


Certainly he who can digest a second or third fluxion need
not, methinks, be squeamish about any point in divinity.
                                       George Berkeley, 1734


If a little knowledge is dangerous, where is the man who has
so much as to be out of danger?
                                 Thomas Henry Huxley, 1877


I never came across one of Laplace's "Thus it plainly appears"
without feeling sure that I had hours of hard work before me to 
fill up the chasm and find out how it plainly appears.
                                   Nathanial Bodwitch, 1838


Ignorance is always ready to admire itself.  Procure yourself
critical friends.
                                      Nicolas Boileau, 1674


Everyone is free to set up an opinion and to adduce proofs in
support of it. Whether, though, a scientist shall find it worth 
his while to enter into serious investigations of opinions so
advanced is a question which his reason and instinct alone can 
decide. If these things, in the end, should turn out to be true,
I shall not be ashamed of being the last to believe them.
                                       Ernst Mach, 1883


I do not see, Sir, that it is reasonable for a man to be angry at 
another, whom a woman has preferred to him; but angry he is, no 
doubt; and he is loath to be angry at himself.
                                          Samuel Johnson, 1763


The mind of man is more intuitive than logical, and comprehends
more than it can coordinate.
                                        Vauvenargues, 1746


Never express yourself more clearly than you think.
                                               Niels Bohr


The mathematician knows some things, no doubt, but not those things
one usually wants to get from him.
                                            Albert Einstein


To guess what to keep and what to throw away takes considerable
skill.  Actually it is probably merely a matter of luck, but it
looks as if it takes considerable skill.
                                       Richard Feynman, 1965


Nothing is more dangerous than an idea, when it is the only
idea we have.
                                        Alain, 1908


The vain presumption of understanding everything can have no
other basis than never having understood anything.  For anyone
who had ever experienced just once the perfect understanding 
of one single thing, and had truly tasted how knowledge is 
accomplished, would recognize that of the infinity of other 
truths he understands nothing.
                                          Galileo, 1630


A circumstance which has always appeared wonderful to me, is 
that such sublime discoveries should have been made by the 
sole assistance of a quadrant and a little arithmetic.
                                              Voltaire


Ignoramus, n. A person unacquainted with certain kinds of
knowledge familiar to yourself, and having certain other kinds
that you know nothing about.
                                      Ambrose Bierce, 1890


Do I contradict myself?  Very well then I contradict myself.
I am large, I contain multitudes.
                                      Walt Whitman, 1870


Examinations are formidable even to the best prepared, for 
the greatest fool may ask more than the wisest man can answer.
                                  Charles Caleb Colton, 1825


General and abstract ideas are the source of the greatest 
errors of mankind.
                                        Rousseau, 1762


Hope deceives more men than cunning does.
                                     Vauvenargues, 1746


The second law of thermodynamics holds, I think, the supreme 
position among the laws of Nature. If someone points out to you 
that your pet theory of the universe is in disagreement with 
Maxwell's equations - then so much the worse for Maxwell's
equations. If it is found to be contradicted by observation, 
well, these experimentalists do bungle things sometimes. But 
if your theory is found to be against the second law of 
thermodynamics I can give you no hope; there is nothing for 
it but to collapse in deepest humiliation.
                                             Arthur Eddington


There is frequently more to be learned from the unexpected
questions of a child than the discourses of men, who talk
in a road, according to the notions and prejudices of their
education.
                                     John Locke, 1693


I do hate sums.  There is no greater mistake than to call
arithmetic an exact science.  There are hidden laws of number
which it requires a mind like mine to perceive.  For instance,
if you add a sum from the bottom up, and then again from the
top down, the result is always different.
                                   Mrs. La Touche, 19th c.


A Composition on the Piano
                                     J. S. Bach


From Alexander the Platonic, not frequently nor without necessity 
to say to any one, or to write in a letter, that I have no leisure; 
nor continually to excuse the neglect of duties required by our 
relation to those with whom we live, by alleging urgent occupations.
                                     Marcus Aurelius, Meditations


The intellectuals' chief cause of anguish are one another's works.
                                        Jacques Barzun, 1959


all ignorance toboggans into know
and trudges up to ignorance again.
                                       e.e.cummings, 1959


The test of interesting people is that subject matter doesn't
matter.
                                  Louis Kronenberger, 1954


The perplexity of life arises from there being too many
interesting things in it for us to be interested properly
in any of them.
                                     G. K. Chesterton, 1909


He who serves two masters has to lie to one.
                                    Portuguese Proverb


That knowledge which stops at what it does not know, is the
highest knowledge.
                                   Chuang Tzu, 4th c. B.C.


Intelligence is characterized by a natural incomprehension
of life.
                                        Henri Bergson, 1907


Knowledge is two-fold, and consists not only in the affirmation
of what is true, but in the negation of that which is false.
                                    Charles Caleb Colton, 1825


If I cannot brag of knowing something, then I brag of not
knowing it.
                                     R. W. Emerson, 1866


Human beings take more pleasure in their representation than in 
the thing, or rather we must say: Human beings take pleasure in 
a thing only insofar as they conceive it. It must suit their turn
of mind. And try as they may to raise their way of conceiving 
things ever so high above the common run, try as they may to 
purify it ever so much, it nevertheless commonly remains but one
way of conceiving things: that is, an attempt to bring many objects
into a certain comprehensible relation that, strictly speaking, 
they do not have, and hence the inclination to hypotheses, theories,
terminologies, and systems - which we cannot condemn, since they 
must necessarily spring from the organization of our being.
                                  Johann Wolfgang von Goethe


Education is an admirable thing, but it is well to remember
from time to time that nothing worth knowing can be taught.
                                      Oscar Wilde, 1891


The first mark of intelligence, to be sure, is not to start
things; the second mark of intelligence is to pursue to the
end what you have started.
                                    Panchatantra, c. 5th c.


The sole cause of all human misery is the inability of people
to sit quietly in their rooms.
                                     Blaise Pascal, 1670


Although to penetrate into the intimate mysteries of nature
and thence to learn the true causes of phenomena is not allowed
to us, nevertheless it can happen that a certain fictive 
hypothesis may suffice for explaining many phenomena.
                                     Leonhard Euler, 1748


The shortest path between two truths in the real domain
passes through the complex domain.
                                     Jacques Hadamard


Such is the advantage of a well-constructed language that
its simplified notation often becomes the source of profound
theories.
                                       P. S. Laplace


6accdae13eff7i3l9n4o4qrr4s8t12ux.
                                       Isaac Newton, 1676


I hope that posterity will judge me kindly, not only as to 
the things which I have explained, but also as to those 
which I have intentionally omitted so as to leave to others
the pleasure of discovery.
                                       Rene Descartes, 1637


It is easier to square a circle than to get round a 
mathematician.
                                       A. De Morgan, 1840


There is no excellent beauty that has not some strangeness
in the proportion.
                                          Francis Bacon


In conclusion I wish to say that in working at the problem
here dealt with I have had the loyal assistance of my friend
and colleague M. Besso, and that I am indebted to him for
several valuable suggestions.
                                    Albert Einstein, 1905


You had, by the way, overestimated the meaningfulness of my
observations again: I was not aware that they had the meaning
that an energy tensor for gravitation was dispensable. If I
understand it correctly, my inadvertent statement now implies
that planetary motion would satisfy conservation laws just by
chance, as it were. What is certain is that I was not aware of
this consequence of my comments and cannot grasp the argument
even now.
                                    Michele Besso, 1918


I see I have made myself a slave to Philosophy, but if I get
free of Mr. Linus's business I will resolutely bid adew to it
eternally, excepting for what I do for my private satisfaction
or leave to come out after me.  For I see a man must either
resolve to put out nothing new or to become a slave to defend it.
                                     Isaac Newton, 1677


There wanted not some beams of light to guide men in the
exercise of their Stocastick faculty.
                                        John Owen, 1662


I should consider that I know nothing about physics if I were 
able to explain only how things might be, and were unable to 
demonstrate that they could not be otherwise.
                                      Rene Descartes, 1640


Of all the communities available to us there is not one that
I would devote myself to, except for the society of true 
searchers, which has very few living members at any time.
                                     Albert Einstein, 1949


The description of right lines and circles, upon which
geometry is founded, belongs to mechanics.  Geometry does
not teach us to draw these lines, but requires them to
be drawn.
                                       Isaac Newton, 1687


I am coming more and more to the conviction that the
necessity of our geometry cannot be demonstrated...geometry
should be ranked, not with arithmetic, which is purely
aprioristic, but with mechanics.
                                        Carl Gauss, 1817


Among the great men who have philosophized about [the action
of the tides], the one who surprised me most is Kepler.  He
was a person of independent genius, [but he] became interested 
in the action of the moon on the water, and in other occult 
phenomena, and similar childishness.
                                        Galileo,  1632


Taking mathematics from the beginning of the world to the time 
of Newton, what he has done is much the better half.
                                    Gottfried Leibniz, 1688


I will sette as I doe often in woorke use, a paire of paralleles, 
or [twin] lines of one lengthe, thus  = ,  bicause noe 2. thynges,
can be moare equalle.
                                     Robert Recorde, 1557


That, if a straight line falling on two straight lines makes
the interior angles on the same side less than two right angles,
the two straight lines, if produced indefinitely, meet on that
side on which the angles are less than two right angles.
                                       Euclid, c. 300 B.C.


One of the chief peculiarities of this treatise is the doctrine 
that the true electric current, on which the electromagnetic 
phenomena depend, is not the same thing as the current of conduction,
but that the time-variation of the electric displacement must 
[also] be taken into account...
                                       James Clerk Maxwell, 1873


Your manuscript is both good and original.  However, that which
is good is not original, and that which is original is not good.
                                              Samuel Johnson


"That is another of your odd notions," said the Prefect, who had
the fashion of calling everything 'odd' that was beyond his 
comprehension, and thus lived amid an absolute legion of 'oddities'.
                                             Edgar Allan Poe


I knew when seven justices could not take up a quarrel, but when 
the parties were met themselves, one of them thought but of an If, 
as, 'If you said so, then I said so;' and they shook hands and 
swore brothers. Your If is the only peacemaker; much virtue in If.
                                                  Shakespeare


I have made this letter longer than usual because I lack the 
time to make it shorter.
                                                Blaise Pascal


A work of art is never finished, merely abandoned.
                                         Leonardo da Vinci


S'io credessi che mia risposta fosse
a persona che mai tornasse al mondo,
questa fiamma staria senza piu scosse.
Ma per cio che giammai di questo fondo
non torno vivo alcun, s'i'odo il vero,
senza tema d'infamia ti rispondo.
                                       Dante, 1302

Return to MathPages Main Menu