Math Quotes

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

Math Quotes

Postby Giacomo on May 2nd, 2008, 10:46 pm 

"A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data."

Paul Dirac
Giacomo
 


Postby Giacomo on May 3rd, 2008, 4:15 am 

"The generation of random numbers is too important to be left to chance."
Giacomo
 


Postby Giacomo on May 3rd, 2008, 4:16 am 

"Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."

John von Neumann
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:19 am 


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
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:20 am 


Earlier we considered the argument, ‘Twice two must be four,
because we cannot imagine it otherwise.’ This argument brings out
clearly the connexion between reason and imagination: reason is in
fact neither more nor less than an experiment carried out in the
imagination.


W. W. Sawyer
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:22 am 


It is better to solve one problem five different ways, than to solve
five problems one way.


George Polya
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:23 am 


Creative mathematicians play a lot; around any problem really
interesting they develop a whole cluster of analogies, of playthings.



David Hawkins
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:24 am 


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
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:27 am 


If we are to teach mathematics at all, real success is not possible
unless we know that the subject is beautiful as well as useful. Mere
utility of the moment without any feeling of beauty becomes
a hopeless bit of drudgery, a condition which leads to stagnation.

...What would mathematics have amounted to without the
imagination of its devotees—its giants and their followers? There
never was a discovery made without the urge of imagination—of
imagination which broke the roadway through the forest in order
that cold logic might follow.



David Eugene Smith
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:28 am 


You don’t understand anything until you learn it more than one way.



Marvin Minsky
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:29 am 


In mathematics, the art of asking questions is more valuable than solving problems.



Georg Cantor
Giacomo
 


Postby Giacomo on May 3rd, 2008, 5:30 am 

There is no Royal Road to Geometry.


Euclid
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:44 am 

Abstraction :



The longer mathematics lives the more abstract – and
therefore, possibly also the more practical – it becomes.


– Eric Temple Bell




We think of the number “five” as applying to
appropriate groups of any entities whatsoever –
to five fishes, five children, five apples, five days ...
We are merely thinking of those relationships between
those two groups which are entirely independent of
the individual essences of any of the members of either group.
This is a very remarkable feat of abstraction; and it must
have taken ages for the human race to rise to it.


– Alfred North Whitehead
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:45 am 

Algebra :




Algebra is generous; she often gives more than is asked of her.


– Jean D’Alembert




Algebra is the intellectual instrument which has been
created for rendering clear the quantitative aspects of
the world.


– Alfred North Whitehead
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:46 am 

Analysis :




Mathematical Analysis is as extensive as nature herself.


– Joseph Fourier
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:47 am 

Applied mathematics :




Mathematics is the tool specially suited for dealing
with abstract concepts of any kind and there is no
limit to its power in this field.


– Paul Dirac




There is no branch of mathematics, however abstract,
which may not someday be applied to the phenomena
of the real world.



– Nicolai Lobachevsky
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:48 am 

Arithmetic :



Arithmetic is one of the oldest branches, perhaps the
very oldest branch, of human knowledge; and yet
some of its most abstruse secrets lie close to its
tritest truths.




– Henry J.S. Smith
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:49 am 

Art :




A mathematician, like a painter or a poet, is a maker
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas.



– Godfrey Harold Hardy




The art of doing mathematics consists in finding that
special case which contains all the germs of generality.




– David Hilbert
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:50 am 

Beauty :




One’s intellectual and aesthetic life cannot be
complete unless it includes an appreciation of the
power and the beauty of mathematics. Simply put,
aesthetic and intellectual fullfillment requires that you
know about mathematics.




– J. P. King



The scientist does not study nature because it is useful;
he studies it because he delights in it, and he delights
in it because it is beautiful. If nature were not beautiful,
it would not be worth knowing, and if nature were not worth
knowing, life would not be worth living.



– Henri Poincaré



What is it indeed that gives us the feeling of elegance in a solution,
in a demonstration? It is the harmony of the diverse parts, their symmetry,
their happy balance; in a word it is all that introduces order, all that
gives unity, that permits us to see clearly and to comprehend at once both
the ensemble and the details.



– Henri Poincaré



Mathematics, rightly viewed, possesses not only
truth, but supreme beauty – a beauty cold and
austere, like that of sculpture, without appeal to any
part of our weaker nature, without the gorgeous
trappings of paintings or music, yet sublimely pure
and capable of a stern perfection such as only the
greatest art can show.



– Bertrand Russell
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:51 am 

Calculus :




The calculus is the greatest aid we have to the appreciation
of physical truth in the broadest sense of the word.



– William F. Osgood
Giacomo
 


Postby Giacomo on May 12th, 2008, 3:52 am 

Cantor :




No one will expel us from the paradise that Cantor has created for us.



– David Hilbert




(On Cantor’s set theory:) The finest product of mathematical genius and
one of the supreme achievements of purely intellectual human activity.



– David Hilbert




Zeno was concerned with three problems . . . These are
the problem of the infinitesimal, the infinite, and continuity ...
From his to our own day, the finest intellects of each generation
in turn attacked these problems, but achieved broadly speaking nothing ...
Weierstrass, Dedekind, and Cantor, ... have completely solved them. Their ...
solutions are so clear as to leave no longer the slightest doubt or difficulty.
This achievement is probably the greatest of which our age can boast.



– Bertrand Russell
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:04 am 

Proofs :



Proofs are to mathematics what spelling (or even calligraphy) is to poetry.
Mathematical works do consist of proofs, just as poems do consist of characters.


Vladimir Arnold
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:05 am 

Conjectures :



In mathematics the art of proposing a question must
be held of higher value than solving it.


– Georg Cantor


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


It is the first duty of a hypothesis to be intelligible.


– Thomas Henry Huxley
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:07 am 

Creativity :



Creative mathematicians now, as in the past, are
inspired by the art of mathematics rather than by any
prospect of ultimate usefulness.


– Eric Temple Bell



The creative principle resides in mathematics. In a
certain sense, therefore, I hold it true that pure thought
can grasp reality, as the ancients dreamed.


– Albert Einstein


‘Mathematizing’ may well be a creative activity of man,
like language or music, of primary originality . . .


– Hermann Weyl



The science of Pure Mathematics, in its modern developments,
may claim to be the most original creation of the human spirit.


– Alfred North Whitehead



Mathematics is an independent world created out of pure intelligence.


– William Wordsworth
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:07 am 

Differential equations



The differential equations of the propagation of heat express the most general conditions,
and reduce the physical questions to problems of pure analysis, and this is the proper object
of theory.


– Joseph Fourier
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:08 am 

Discovery :



Every new body of discovery is mathematical in form,
because there is no other guidance we can have.


– Charles Darwin



The profound study of nature is the most fertile source of mathematical discoveries.



– Joseph Fourier



Mathematical discoveries, small or great, are never born of spontaneous generation.
They always presuppose a soil seeded with preliminary knowledge and well prepared by
labour, both conscious and subconscious.


– Henri Poincaré


The real voyage of discovery consists not in seeking
new landscapes, but in having new eyes.



– Marcel Proust
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:09 am 

Education



An educated mind is, as it were, composed of all the minds of preceding ages.


– Bernard de Fontenelle



The mind is not a vessel to be filled, it is a fire to be kindled.


– Plutarch



This therefore is Mathematics:

She reminds you of the invisible forms of the soul;
She gives life to her own discoveries;
She awakens the mind and purifies the intellect;
She brings light to our intrinsic ideas;
She abolishes oblivion and ignorance which are ours by birth.


– Proclus Diadochus



Poor teaching leads to the inevitable idea that the subject (mathematics) is
only adapted to peculiar minds, when it is the one universal science and the
one whose ... ground rules are taught us almost in infancy and reappear in the
motions of the universe.


– Henry J.S. Smith


Besides language and music, [mathematics] is one of
the primary manifestations of the free creative powers
of the human mind, and it is the universal organ for
world-understanding through theoretical construction.
Mathematics must therefore remain an essential element
of the knowledge and abilities which we have to teach,
of the culture we have to transmit, to the next generation.



– Hermann Weyl
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:10 am 

EUCLID



Euclid alone has looked on Beauty bare.


– Edna St. Vincent Millay
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:11 am 

Experts



An expert is a man who has made all the mistakes,
which can be made, in a very narrow field.


– Niels Bohr
Giacomo
 


Postby Giacomo on May 18th, 2008, 4:12 am 

Formulae




If I am given a formula and I am ignorant of its meaning,
it cannot teach me anything, but if I already know it
what does the formula teach me?


– Saint Augustine of Hippo
Giacomo
 


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