 |
 | ""I think you"re begging the question," said Haydock, "and I can see
looming ahead one of those terrible exercises in probability where six men
have white hats and six men have black hats and you have to work it out by
mathematics how likely it is that the hats will get mixed up and in what
proportion. If you start thinking about things like that, you would go
round the bend. Let me assure you of that!"" | |
 |
Agatha Christie
|
|
| "... it is interesting to note that the original problem that started
my research is still outstanding - namely the problem of planning or
scheduling dynamically over time, particularly planning dynamically under
uncertainty. If such a problem could be successfully solved it could
eventually through better planning contribute to the well-being and
stability of the world." | |
|
George Dantzig
|
|
| "... Newton was an unquestioning believer in an all-wise creator of
the universe, and in his own inability ? like the boy on the seashore ? to
fathom the entire ocean in all its depths. He therefore believed that there
were not only many things in heaven beyond his philosophy, but plenty on
earth as well, and he made it his business to understand for himself what
the majority of intelligent men of his time accepted without dispute (to
them it was as natural as common sense) ? the traditional account of the
creation." | |
|
Sir Isaac Newton
|
|
| "... the science of calculation also is indispensable as far as the
extraction of the square and cube roots: Algebra as far as the quadratic
equation and the use of logarithms are often of value in ordinary cases:
but all beyond these is but a luxury; a delicious luxury indeed; but not
to be in indulged in by one who is to have a profession to follow for his
subsistence." | |
|
Thomas Jefferson
|
|
| "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." | |
|
Count Leo Nikolaevich Tolstoy
|
|
| "A mathematician is a blind man in a dark room looking for a black
cat which isn"t there." | |
|
Charles Robert
|
|
| "A mathematician is a device for turning coffee into theorems." | |
|
Paul Erdos
|
|
| "A mathematician of the first rank, Laplace quickly revealed himself
as only a mediocre administrator; from his first work we saw that we had
been deceived. Laplace saw no question from its true point of view; he
sought subtleties everywhere; had only doubtful ideas, and finally carried
the spirit of the infinitely small into administration." | |
|
Napoléon Bonaparte
|
|
| "About Thomas Hobbes: He was 40 years old before he looked on
geometry; which happened accidentally. Being in a gentleman"s library,
Euclid"s Elements lay open, and "twas the 47 El. libri I" [Pythagoras"
Theorem]. He read the proposition "By God", sayd he, "this is impossible:"
So he reads the demonstration of it, which referred him back to such a
proposition; which proposition he read. That referred him back to another,
which he also read. Et sic deinceps, that at last he was demonstratively
convinced of that truth. This made him in love with geometry." | |
|
John Aubrey
|
|
| "Anyone who cannot cope with mathematics is not fully human. At best
he is a tolerable subhuman who has learned to wear shoes, bathe, and not
make messes in the house." | |
|
Robert Anson Heinlein
|
|
| "Can the difficulty of an exam be measured by how many bits of
information a student would need to pass it? This may not be so absurd in
the encyclopedic subjects but in mathematics it doesn"t make any sense
since things follow from each other and, in principle, whoever knows the
bases knows everything. All of the results of a mathematical theorem are
in the axioms of mathematics in embryonic form, aren"t they?" | |
|
Alfréd Rényi
|
|
| "Don"t talk to me of your Archimedes" lever. He was an absentminded
person with a mathematical imagination. Mathematics commands all my
respect, but I have no use for engines. Give me the right word and the
right accent and I will move the world." | |
|
Joseph Conrad
|
|
| "Einstein is an analytical mathematician seeking to give a physical
interpretation to the conclusions of his mathematical process. In this he
is hampered by a load of contradictory and absurd assumptions of the
school that he follows, which throws him in to all manner of difficulty.
Einstein has such a faculty for embracing both sides of a contradiction
that one would have to be of the same frame of mind to follow his thought,
it is so peculiarly his own. The whole Relativity theory is as easy to
follow as the path of a bat in the air at night." | |
|
Father Jeremiah Joseph Callahan
|
|
| "For a smart material to be able to send out a more complex signal it
needs to be nonlinear. If you hit a tuning fork twice as hard it will ring
twice as loud but still at the same frequency. That"s a linear response.
If you hit a person twice as hard they"re unlikely just to shout twice as
loud. That property lets you learn more about the person than the tuning
fork." | |
|
Neil Gershenfeld
|
|
| "For the things of this world cannot be made known without a
knowledge of mathematics." | |
|
Roger Bacon
|
|
| "God exists since mathematics is consistent, and the Devil exists
since we cannot prove it." | |
|
Andre Weil
|
|
| "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." | |
|
Wystan Hugh Auden
|
|
| "I don"t believe in mathematics." | |
|
Albert Einstein
|
|
| "I had a feeling once about Mathematics ? that I saw it all. Depth
beyond depth was revealed to me ? the Byss and Abyss. I saw ? as one might
see the transit of Venus or even the Lord Mayor"s Show ? a quantity passing
through infinity and changing its sign from plus to minus. I saw exactly
why it happened and why the tergiversation was inevitable ? but it was
after dinner and I let it go." | |
|
Sir Winston Churchill
|
|
| "I have hardly ever known a mathematician who was capable of
reasoning." | |
|
Plato
|
|
| "If others would but reflect on mathematical truths as deeply and as
continuously as I have, they would make my discoveries." | |
|
Karl Friedrich Gauss
|
|
| "If the entire Mandelbrot set were placed on an ordinary sheet of
paper, the tiny sections of boundary we examine would not fill the width
of a hydrogen atom. Physicists think about such tiny objects; only
mathematicians have microscopes fine enough to actually observe
them." | |
|
John Ewing
|
|
| "In mathematics you don"t understand things. You just get used to
them." | |
|
John Louis von Neumann
|
|
| "In my opinion, a mathematician, in so far as he is a mathematician,
need not preoccupy himself with philosophy -- an opinion, moreover, which
has been expressed by many philosophers." | |
|
Henri Lebesgue
|
|
| "In the World of Reality there is no self, There is no
other-than-self." | |
|
|
|
| "It is India that gave us the ingenious method of expressing all
numbers by means of ten symbols, each symbol receiving a value of position
as well as an absolute value; a profound and important idea which appears
so simple to us now that we ignore its true merit. But its very simplicity
and the great ease which it has lent to computations put our arithmetic in
the first rank of useful inventions; and we shall appreciate the grandeur
of the achievement the more when we remember that it escaped the genius of
Archimedes and Apollonius, two of the greatest men produced by
antiquity." | |
|
Pierre Simon de Laplace
|
|
| "Life is good for only two things, discovering mathematics and
teaching mathematics." | |
|
Siméon Poisson
|
|
| "Mathematicians are like lovers. Grant a mathematician the least
principle, and he will draw from it a consequence which you must also
grant him, and from this consequence another." | |
|
Bernard Le Bovier de Fontenelle
|
|
| "Mathematicians boast of their exacting achievements, but in reality
they are absorbed in mental acrobatics and contribute nothing to
society." | |
|
Sorai Ogyu
|
|
| "Mathematicians do not study objects, but relations between objects.
Thus, they are free to replace some objects by others so long as the
relations remain unchanged. Content to them is irrelevant: they are
interested in form only." | |
|
Jules Henri Poincaré
|
|
| "Mathematicians have tried in vain to this day to discover some order
in the sequence of prime numbers, and we have reason to believe that it is
a mystery into which the human mind will never penetrate." | |
|
Leonhard Euler
|
|
| "Mathematics has beauties of its own ? a symmetry and proportion in
its results, a lack of superfluity, an exact adaptation of means to ends,
which is exceedingly remarkable and to be found only in the works of the
greatest beauty. When this subject is properly ... presented, the mental
emotion should be that of enjoyment of beauty, not that of repulsion from
the ugly and the unpleasant." | |
|
J. W. A. Young
|
|
| "Mathematics is not a careful march down a well-cleared highway, but
a journey into a strange wilderness, where the explorers often get lost.
Rigour should be a signal to the historian that the maps have been made,
and the real explorers have gone elsewhere." | |
|
W. S. Anglin
|
|
| "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
|
|
| "Mathematics seems to endow one with something like a new
sense." | |
|
Charles Robert Darwin
|
|
| "Mathematics, the non-empirical science par excellence ... the
science of sciences, delivering the key to those laws of nature and the
universe which are concealed by appearances." | |
|
Hannah Arendt
|
|
| "Medicine makes people ill, mathematics makes them sad, and theology
makes them sinful." | |
|
Martin Luther
|
|
| "Most of the arts, as painting, sculpture, and music, have emotional
appeal to the general public. This is because these arts can be
experienced by some one or more of our senses. Such is not true of the art
of mathematics; this art can be appreciated only by mathematicians, and to
become a mathematician requires a long period of intensive training. The
community of mathematicians is similar to an imaginary community of
musical composers whose only satisfaction is obtained by the interchange
among themselves of the musical scores they compose." | |
|
Cornelius Lanczos,
|
|
| "On Ramanujan: I remember once going to see him when he was lying ill
at Putney. I had ridden in taxi cab number 1729 and remarked that the
number seemed to me rather a dull one, and that I hoped it was not an
unfavorable omen. "No," he replied, "it is a very interesting number; it
is the smallest number expressible as the sum of two cubes in two
different ways."" | |
|
Godfrey H. Hardy
|
|
| "One is hard pressed to think of universal customs that man has
successfully established on earth. There is one, however, of which he can
boast the universal adoption of the Hindu-Arabic numerals to record
numbers. In this we perhaps have man"s unique worldwide victory of an
idea." | |
|
Howard W. Eves
|
|
| "Perhaps the most surprising thing about mathematics is that it is so
surprising. The rules which we make up at the beginning seem ordinary and
inevitable, but it is impossible to foresee their consequences. These have
only been found out by long study, extending over many centuries. Much of
our knowledge is due to a comparatively few great mathematicians such as
Newton, Euler, Gauss, or Riemann; few careers can have been more
satisfying than theirs. They have contributed something to human thought
even more lasting than great literature, since it is independent of
language." | |
|
E. C. Titchmarsh
|
|
| "Proof is the idol before whom the pure mathematician tortures
himself." | |
|
Sir Arthur Stanley Eddington
|
|
| "Since you are now studying geometry and trigonometry, I will give
you a problem. A ship sails the ocean. It left Boston with a cargo of
wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is
broken, the cabin boy is on deck, there are 12 passengers aboard, the wind
is blowing East-North-East, the clock points to a quarter past three in the
afternoon. It is the month of May. How old is the captain?" | |
|
Gustave Flaubert
|
|
| "Study reveals that 5 out of 4 Americans have trouble with
fractions." | |
|
Unknown
|
|
| "The different branches of Arithmetic ? Ambition, Distraction,
Uglification, and Derision." | |
|
Lewis Carroll
|
|
| "The errors of definitions multiply themselves according as the
reckoning proceeds; and lead men into absurdities, which at last they see
but cannot avoid, without reckoning anew from the beginning." | |
|
Thomas Hobbes
|
|
| "The fraction of life can be increased in value not so much By
increasing your numerator as by lessening your denominator. Nay, unless my
Algebra deceives me, unity itself divided by zero will give
infinity." | |
|
Thomas Carlyle
|
|
| "The good Christian should beware of mathematicians, and all those
who make empty prophecies. The danger already exists that the
mathematicians have made a covenant with the devil to darken the spirit
and to confine man in the bonds of Hell." | |
|
Saint Augustine of Hippo
|
|
| "The mathematical life of a mathematician is short. Work rarely
improves after the age of twenty-five or thirty. If little has been
accomplished by then, little will ever be accomplished." | |
|
Alfred Adler
|
|
| "The most painful thing about mathematics is how far away you are
from being able to use it after you have learned it." | |
|
James R. Newman
|
|
| "The traditional mathematics professor of the popular legend is
absentminded. He usually appears in public with a lost umbrella in each
hand. He prefers to face the blackboard and to turn his back to the class.
He writes a, he says b, he means c; but it should be d. Some of his sayings
are handed down from generation to generation. "In order to solve this
differential equation you look at it till a solution occurs to you." "This
principle is so perfectly general that no particular application of it is
possible." "Geometry is the science of correct reasoning on incorrect
figures." "My method to overcome a difficulty is to go round it." "What is
the difference between method and device? A method is a device which you
used twice."" | |
|
George Polyá
|
|
| "The union of the mathematician with the poet, fervor with measure,
passion with correctness, this surely is the ideal." | |
|
William James
|
|
| "There are no sects in geometry." | |
|
Francois Voltaire
|
|
| "There is nothing mysterious, as some have tried to maintain, about
the applicability of mathematics. What we get by abstraction from
something can be returned." | |
|
R. L. Wilder
|
|
| "This seems to be one of the many cases in which the admitted
accuracy of mathematical processes is allowed to throw a wholly
inadmissible appearance of authority over the results obtained by them.
Mathematics may be compared to a mill of exquisite workmanship, which
grinds your stuff to any degree of fineness; but, nevertheless, what you
get out depends on what you put in; and as the grandest mill in the world
will not extract wheat flour from peascods, so pages of formulae will not
get a definite result out of loose data." | |
|
Thomas Henry Huxley
|
|
| "Time was when all the parts of the subject were dissevered, when
algebra, geometry, and arithmetic either lived apart or kept up cold
relations of acquaintance confined to occasional calls upon one another;
but that is now at an end; they are drawn together and are constantly
becoming more and more intimately related and connected by a thousand
fresh ties, and we may confidently look forward to a time when they shall
form but one body with one soul." | |
|
J.J. Sylvester
|
|
| "To be a scholar of mathematics you must be born with talent,
insight, concentration, taste, luck, drive and the ability to visualize
and guess." | |
|
Paul R. Halmos
|
|
| "To be an abstraction does not mean that an entity is nothing. It
merely means that its existence is only a factor of a more concrete
element of nature." | |
|
Alfred North Whitehead
|
|
| "We come finally, however, to the relation of the ideal theory to
real world, or "real" probability. If he is consistent a man of the
mathematical school washes his hands of applications. To someone who wants
them he would say that the ideal system runs parallel to the usual theory:
"If this is what you want, try it: it is not my business to justify
application of the system; that can only be done by philosophizing; I am a
mathematician". In practice he is apt to say: "try this; if it works that
will justify it". But now he is not merely philosophizing; he is
committing the characteristic fallacy. Inductive experience that the
system works is not evidence." | |
|
J. E. Littlewood
|
|
| "We lay down a fundamental principle of generalization by
abstraction: "The existence of analogies between central features of
various theories implies the existence of a general theory which underlies
the particular theories and unifies them with respect to those central
features...."" | |
|
Eliakim Hastings Moore
|
|
| "We often hear that mathematics consists mainly of "proving
theorems." Is a writer"s job mainly that of "writing sentences?"" | |
|
Gian-carlo Rota
|
|
| "What does this desire and this inability of ours proclaim to us but
that there was once in man a genuine happiness, of which nothing now
survives but the mark and the empty outline; and this he vainly tries to
fill from everything that lies around him, seeking from things that are
not there the help that he does not get from those that are present? Yet
they are quite incapable of filling the gap, because this infinite gulf
can only be filled by an infinite and immutable object - that is, God,
Himself. He alone is man"s veritable good, and since man has deserted Him
it is a strange thing that there is nothing in nature that has not been
capable of taking His place for man: stars, sky, earth, elements, plants,
cabbages, leeks, animals, insects, calves, serpents, fever, plague, war,
famine, vices, adultery, incest. And since he has lost the true good,
everything can equally appear to him as such - even his own destruction,
though that is so contrary at once to God, to reason, and to
nature." | |
|
Blaise Pascal
|
|
| "What is algebra exactly; is it those three-cornered things?" | |
|
Sir James Matthew Barrie
|
|
| "When I am violently beset with temptations, or cannot rid myself of
evil thoughts, [I resolve] to do some Arithmetic, or Geometry, or some
other study, which necessarily engages all my thoughts, and unavoidably
keeps them from wandering." | |
|
Jonathon Edwards
|
|
| "When you have mastered numbers, you will in fact no longer be
reading numbers, any more than you read words when reading books. You will
be reading meanings." | |
|
Harold Geneen
|
|
| "Without the concepts, methods and results found and developed by
previous generations right down to Greek antiquity one cannot understand
either the aims or achievements of mathematics in the last 50 years. [Said
in 1950]" | |
|
Hermann Weyl
|
|
| "You know we all became mathematicians for the same reason: we were
lazy." | |
|
Max Rosenlicht
|
|
| "[The works of Archimedes] are without exception, monuments of
mathematical exposition; the gradual revelation of the plan of attack, the
masterly ordering of the propositions, the stern elimination of everything
not immediately relevant to the purpose, the finish of the whole, are so
impressive in their perfection as to create a feeling akin to awe in the
mind of the reader." | |
|
Sir Thomas Heath
|