Math Quotes

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

Postby Giacomo on May 18th, 2008, 4:13 am 

Fractals



Mountains are not cones, clouds are not spheres, trees are not cylinders,
neither does lightening travel in a straight line. Almost everything around us
is non-Euclidean.


– Benoit Mandelbrot
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Postby Giacomo on May 18th, 2008, 4:13 am 

Functions



That flower of modern mathematical thought, the notion of a function.


– Thomas McCormack
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Postby Giacomo on May 18th, 2008, 4:14 am 

Genius



It takes immense genius to represent, simply and sincerely,
what we see right in front of us.


– Edmond Duranty


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


– David Hilbert


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
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Postby Giacomo on May 21st, 2008, 4:32 am 

Geometry



Everything in nature adheres to the cone, the cylinder and the cube.


– Paul Cezanne



Geometry is the right foundation of all painting.


– Albrecht Dürer



If a man is at once acquainted with the geometric foundation of things
and with their festal splendor, his poetry is exact and his arithmetic musical.


– Ralph Waldo Emerson



Mighty is geometry; joined with art, resistless.


– Euripides



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 Friedrich Gauss




Geometry is the only science that it hath pleased God hitherto to bestow on mankind.


– Thomas Hobbes



Where there is matter, there is geometry.


– Johannes Kepler



I believe the geometric proportion served the creator as an idea
when He introduced the continuous generation of similar objects
from similar objects.


– Johannes Kepler




Geometry enlightens the intellect and sets one’s mind right.


– Ibn Khaldun




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.


– Sir Isaac Newton



[Inscription above Plato's Academy:] Let no one ignorant of geometry enter here.

– Plato




Geometry existed before the creation.


– Plato




God ever geometrizes.


– Plato




Then, my noble friend, geometry will draw the soul towards truth,
and create the spirit of philosophy, and raise up that which is not
unhappily allowed to fall down.


– Plato

(Source: The Republic, VII. 522-528, “Quadrivium”)




Geometry is knowledge of the eternally existent.



– Pythagoras



There is geometry in the humming of the strings.



– Pythagoras



I regret that it has been necessary for me in this lecture
to administer such a large dose of four-dimensional geometry.
I do not apologize, because I am really not responsible for
the fact that nature in its most fundamental aspect is four-dimensional.
Things are what they are.



– Alfred North Whitehead
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Postby Giacomo on May 21st, 2008, 4:32 am 

Group Theory



The importance of group theory was emphasized very recently
when some physicists using group theory predicted the existence
of a particle that had never been observed before, and described
the properties it should have. Later experiments proved that
this particle really exists and has those properties.


– Irving Adler



Nowadays, group theoretical methods – expecially those
involving characters and representations, pervade all
branches of quantum mechanics.


– George Mackey



The theory of groups is a branch of mathematics in which
one does something to something and then compares the results
with the result of doing the same thing to something else, or
something else to the same thing.


– James Newman



The universe is an enormous direct product of
representations of symmetry groups.


– Hermann Weyl
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Postby Giacomo on June 5th, 2008, 3:50 am 

Analytical Theory of Heat



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




Heat, like gravity, penetrates every substance of the universe,
its rays occupy all parts of space. The object of our work is to
set forth the mathematical laws which this element obeys. The theory
of heat will hereafter form one of the most important branches of
general physics.



– Joseph Fourier
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Postby Giacomo on June 5th, 2008, 3:52 am 

History



From the time of Kepler to that of Newton, and from Newton to Hartley, not only all things
in external nature, but the subtlest mysteries of life and organization, and even of the
intellect and moral being, were conjured within the magic circle of mathematical formulae.



– Samuel Taylor Coleridge



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.



– Hermann Hankle



In these days of conflict between ancient and modern studies, there must surely be something
to be said for a study which did not begin with Pythagoras and will not end with Einstein,
but is the oldest and youngest of all.



– Godfrey Harold Hardy



The further a mathematical theory is developed, the more harmoniously and uniformly does
its construction proceed, and unsuspected relations are disclosed between hitherto separated
branches of the science.



– David Hilbert



Descartes commanded the future from his study more than Napoleon from the throne.



– Oliver Wendell Holmes



Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by
intuition rather than by rigorous proofs.



– Felix Klein



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.



– Pierre-Simon Laplace



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



– Gottfried Willhelm von Leibniz



There is nothing so troublesome to mathematical practice ... than multiplications, divisions,
square and cubical extractions of great numbers ... I began therefore to consider ...
how I might remove those hindrances.



– John Napier



To force the future of mathematics the true method is to study its history and its present state.



– Henri Poincaré



On the basis of my historical experience, I fully believe that mathematics of the twenty-fifth century
will be as different from that of today as the latter is from that of the sixteenth century.



– George Sarton



The idea of the continuum seems simple to us. We have somehow lost sight of the difficulties it implies ...
We are told such a number as the square root of 2 worried Pythagoras and his school almost to exhaustion.
Being used to such queer numbers from early childhood, we must be careful not to form a low idea of the
mathematical intuition of these ancient sages; their worry was highly credible.



– Erwin Schrödinger



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 forsee 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 Tiemann; 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.



– Edward Charles Titchmarsh
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Postby Giacomo on June 5th, 2008, 3:56 am 

Humor



In Samoa, when elementary schools were first established, the natives developed an absolute craze
for arithmetical calculations. They laid aside their weapons and were to be seen going about armed
with slate and pencil, setting sums and problems to one another and to European visitors.
The Honourable Frederick Walpole declares that his visit to the beautiful island was positively
embittered by ceaseless multiplication and division.



– T. Briffault




I had a feeling once about Mathematics – that I saw it all. Depth beyond depth was revealed to me –
the Byss and Abyss. But it was after dinner and I let it go.



– Winston Churchill




The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures
whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures,
but this was long ago; to this day a shape will occasionally appear which will fit into the garment as
if the garment had been made for it. Then there is no end of surprise and delight!



– Tobias Dantzig




A mathematician is a blind man in a dark room looking for a black cat which isn't there.



– Charles Darwin






Of all things, good sense is the most fairly distributed: everyone thinks he is so well
supplied with it that even those who are the hardest to satisfy in every other respect
never desire more of it than they already have.



– Rene Descartes




Perfect numbers like perfect men are very rare.



– Rene Descartes




There are three kinds of lies: lies, damned lies, and statistics.



– Benjamin Disraeli




A mathematician is a device for turning coffee into theorems.



– Paul Erdös




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 main mast 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




Mathematicians are like lovers ... Grant a mathematician the least principle, and he will
draw from it a consequence which you must grant him also, and from this consequence another.



– Bernard de Fontenelle




Mathematicians are a species of Frenchmen: if you say something to them they translate it
into their own language and presto! It is something entirely different.



– Johann Wolfgang Goethe




A diller, A dollar, A witless trig scholar
On a ladder against a wall.
If length over height
Gives an angle too slight,
The cosecant may prove his downfall.



– L. A. Grahm




Paul Erdos has a theory that God has a book containing all the theorems of mathematics
with their absolutely most beautiful proofs, and when he wants to express particular
appreciation of a proof he exclaims, “This is from the book!”



– Ross Hansberger




If I were to awaken after having slept for a thousand years, my first question would be:
Has the Riemann hypothesis been proven?



– David Hilbert




God exists since mathematics is consistent, and the devil exists since we cannot prove the consistency.



– Morris Kline




Statistics: the mathematical theory of ignorance.



– Morris Kline




Logic is the art of going wrong with confidence.



– Morris Kline




He uses statistics as a drunken man uses lamp posts – for support rather than illumination.



– Andrew Lang




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




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




Bridges would be safer if only people who knew the proper definition of a real number
were allowed to design them.



– David Norman Mermin




The theory of groups is a branch of mathematics in which one does something to something
and then compares the results with the result of doing the same thing to something else,
or something else to the same thing.




– James Newman




Circles to square and cubes to double
Would give a man excessive trouble.



– Matthew Prior





Black holes are where God divided by zero.



– Steven Wright
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Postby Giacomo on June 8th, 2008, 8:34 pm 

Infinity



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



– Bishop George Berkeley



And what are these same evanescent increments? They are neither finite quantities, nor quantities
infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?



– Bishop George Berkeley



Even as the finite encloses an infinite series,
And in the unlimited limits appear,
So the soul of immensity dwells in minuta
And in the narrowest limits, no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what Divinity!



– Jakob Bernoulli



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



– David Hilbert



The infinite! No other question has ever moved so profoundly the spirit of man.



– 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



I am so in favor of the actual infinite that instead of admitting that Nature abhors it,
as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to
show more effectively the perfections of its Author.



– Gottfried Willhelm von Leibniz


Source: Nouveaux Essais de l'Entendement humain




Man is equally incapable of seeing the nothingness from which he emerges and
the infinity in which he is engulfed.



– Blaise Pascal



I love mathematics ... principally because it is beautiful, because man has breathed
his spirit of play into it, and because it has given him his greatest game – the encompassing
of the infinite.



– Rozso Peter



The notion of infinity is our greatest friend; it is also the greatest enemy of our peace of mind.



– James Pierpont



The study of infinity is much more than a dry academic game. The intellectual pursuit of
the absolute infinity is, as Georg Cantor realized, a form of the soul’s quest for God.
Whether or not the goal is ever reached, an awareness of the process brings enlightenment.



– Rudy Rucker



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



The solution of the difficulties which formerly surrounded the mathematical
infinite is probably the greatest achievement of which our age has to boast.



– Bertrand Russell



I could be bounded in a nutshell and count myself a king of infinite space.



– William Shakespeare



An irrational number ... lies hidden in a cloud of infinity.



– Michael Stifel
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Postby Giacomo on June 8th, 2008, 8:35 pm 

Intuition




Intuition is the conception of an attentive mind, so clear, so distinct,
and so effortless that we cannot doubt what we have so conceived.



– Rene Descartes




Thus, in a sense, mathematics has been most advanced by those who distinguished themselves
by intuition rather than by rigorous proofs.



– Felix Klein



Mathematicians create by acts of insight and intuition.
Logic then sanctions the conquests of intuition.



– Morris Kline



Mathematical reasoning may be regarded rather schematically as the exercise of
a combination of two facilities, which we may call intuition and ingenuity.



– Alan Turing
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Postby Giacomo on June 16th, 2008, 3:54 am 

Knowledge



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



The charm [of mathematics] lies chiefly in the absolute certainty of its results;
for that is what, beyond all mental treasures, the human intellect craves for.
Let us be sure of something! More light, more light!



– Lewis Carroll



A good puzzle should demand the exercise of our best wit and ingenuity, and
although a knowledge of mathematics and of logic are often of great service
in the solution of these things, yet it sometimes happens that a kind of natural
cunning and sagacity is of considerable value.



– Henry Ernest Dudeny



Imagination is more important than knowledge.



– Albert Einstein



Door meten tot weten. (By measuring to knowing.)



– Heike Kammerling-Onnes



The science of mathematics presents the most brilliant example of how pure reason may
successfully enlarge its domain without the aid of experience.



– Emmanuel Kant



When you can measure what you are talking about and express it in numbers,
you know something about it.



– Lord Kelvin



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



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
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Postby Giacomo on June 16th, 2008, 3:56 am 

Learning



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



So if man’s wit be wandering, let him study the mathematics: for in demonstrations,
if his wit be called away never so little, he must begin again.



– Sir Francis Bacon



Students attend our lectures, not because the mathematics we teach ‘makes lots
of fun’ for us, but because they believe they can learn some essential knowledge
from us. And each of our young students has only one life to live. We should
therefore be able to justify ourselves to our listeners with respect to what
we teach them.



– H. Behnke



To appreciate the living spirit rather than the dry bones of mathematics,
it is necessary to inspect the work of a master at first hand. Textbooks
and treatises are an unavoidable evil... The very crudities of the first
attack on a significant problem by a master are more illuminating than all
the pretty elegance of the standard texts which has been won at the cost
of perhaps centuries of finicky polishing.



– Eric Temple Bell



In Samoa, when elementary schools were first established, the natives developed
an absolute craze for arithmetical calculations. They laid aside their weapons and
were to be seen going about armed with slate and pencil, setting sums and problems
to one another and to European visitors. The Honourable Frederick Walpole declares
that his visit to the beautiful island was positively embittered by ceaseless
multiplication and division.



– T. Briffault



Thus metaphysics and mathematics are, among all the sciences that belong to reason,
those in which imagination has the greatest role.



– Jean D’Alembert



Whoever despises the high wisdom of mathematics nourishes himself on delusion.



– Leonardo da Vinci



Each problem that I solved became a rule which served afterwards to solve other problems.



– Rene Descartes



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



– Bernard de Fontenelle



The essence of mathematics is not to make simple things complicated,
but to make complicated things simple.



– S. Gudder



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 Richard Halmos



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.



– Israel Nathan Herstein



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



– David Hilbert



The object of mathematics is the honor of the human spirit.



– Carl Jacobi



Everyone knows what a curve is, until he has studied enough mathematics to become confused
through the countless number of possible exceptions.



– Felix Klein



The tantalizing and compelling pursuit of mathematical problems offers mental absorption,
peace of mind amid endless challenges, repose in activity, battle without conflict, refuge
from the goading urgency of contingent happenings, and the sort of beauty changeless mountains
present to senses tried by the present-day kaleidoscope of events.



– Morris Kline



The mathematician who pursues his studies without clear views of this matter,
must often have the uncomfortable feeling that his paper and pencil surpass
him in intelligence.



– Ernst Mach



I keep the subject constantly before me and wait till the first dawnings
open little by little into the full light.



– Sir Isaac Newton



A child[’s] ... first geometrical discoveries are topological ...
If you ask him to copy a square or a triangle, he draws a closed circle.



– Jean Piaget



There is no more a math mind, than there is a history or an English mind.



– Gloria Steinem



The study of mathematics is apt to commence in disappointment ...
we are told that by its aid the stars are weighed and the billion
of molecules in a drop of water are counted. Yet, like the ghost
of Hamlet’s father, this great science eludes the efforts of our
mental weapons to grasp it.



– Alfred North Whitehead
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Postby Giacomo on June 29th, 2008, 3:00 pm 

Lectures



Students attend our lectures, not because the mathematics we teach ‘makes lots of fun’ for us,
but because they believe they can learn some essential knowledge from us. And each of our young
students has only one life to live. We should therefore be able to justify ourselves to our
listeners with respect to what we teach them.



– H. Behnke
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Postby Giacomo on June 29th, 2008, 3:02 pm 

Logic



Logic is invincible, because in order to combat logic it is necessary to use logic.



– Pierre Leon Boutroux



“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so,
it would be; but as it isn’t, it ain’t. That's logic.”



– Lewis Carroll



You can only find truth with logic if you have already found truth without it.



– Gilbert Keith Chesterton



A good puzzle should demand the exercise of our best wit and ingenuity,
and although a knowledge of mathematics and of logic are often of great
service in the solution of these things, yet it sometimes happens that
a kind of natural cunning and sagacity is of considerable value.



– Henry Ernest Dudeny



Logic, like whisky, loses its beneficial effect
when taken in too large quantities.



– Lord Dunsany



Pure mathematics is, in its way, the poetry of logical ideas.



– Albert Einstein



Mathematicians create by acts of insight and intuition.
Logic then sanctions the conquests of intuition.



– Morris Kline



Logic is the art of going wrong with confidence.



– Morris Kline



Logic is the anatomy of thought.



– John Locke



Logic is the hygiene the mathematician practices
to keep his ideas healthy and strong.



– Hermann Weyl
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Postby Giacomo on June 29th, 2008, 3:03 pm 

Mastery



To appreciate the living spirit rather than the dry bones of mathematics,
it is necessary to inspect the work of a master at first hand. Textbooks
and treatises are an unavoidable evil... The very crudities of the first
attack on a significant problem by a master are more illuminating than all
the pretty elegance of the standard texts which has been won at the cost
of perhaps centuries of finicky polishing.



– Eric Temple Bell
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Postby Giacomo on June 29th, 2008, 3:05 pm 

Mathematicians



How happy is 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



With me everything turns into mathematics.



– Rene Descartes



A mathematician is a device for turning coffee into theorems.



– Paul Erdös



Mathematicians are like lovers ... Grant a mathematician the least principle,
and he will draw from it a consequence which you must grant him also, and from
this consequence another.



– Bernard de Fontenelle



Every good mathematician is at least half a philosopher,
and every good philosopher is at least half a mathematician.



– Gottlob Frege



Mathematicians are a species of Frenchmen: if you say something to them they
translate it into their own language and presto! It is something entirely different.



– Johann Wolfgang Goethe



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 union of the mathematician with the poet, fervor with measure,
passion with correctness, this surely is the ideal.



– William James



Mathematicians create by acts of insight and intuition.
Logic then sanctions the conquests of intuition.



– Morris Kline



It is impossible to be a mathematician without being a poet in soul.



– Sophia Kovalevskaya



Number theorists are like lotus-eaters --
having once tasted of this food they can
never give it up.



– Leopold Kronecker



He is very intelligent but he is not a mathematician: this as you know is a great defect.



– Blaise Pascal

(Source: From a letter of Pascal to Fermat)



The mathematician, carried along on his flood of symbols, dealing apparently
with purely formal truths, may still reach results of endless importance for
our description of the physical universe.



– Karl Pearson



Mathematicians study structure independent of context, and their science is a voyage of
exploration through all the kinds of structure and order which the human mind is capable
of discerning.



– Charles Pinter



A scientist worthy of the name, above all a mathematician, experiences in his work the
same impression as an artist; his pleasure is as great and of the same nature.



– Henri Poincaré



Mathematicians do not study objects, but relations among objects; they are indifferent
to the replacement of objects by others as long as the relations don't change. Matter
is not important, only form interests them.



– Henri Poincaré



The future mathematician ... should solve problems, choose the problems which are in his line,
meditate upon their solution, and invent new problems. By this means, and by all other means,
he should endeavor to make his first important discovery: he should discover his likes and dislikes,
his taste, his own line.



– George Polya



To create a good philosophy you should renounce metaphysics but be a good mathematician.



– Bertrand Russell



Every mathematician worthy of the name has experienced ... the state of lucid exaltation
in which one thought succeeds another as if miraculously ... this feeling may last for
hours at a time, even for days. Once you have experienced it, you are eager to repeat it
but unable to do it at will, unless perhaps by dogged work....



– André Weil

(Source: The Apprenticeship of a Mathematician)



Let us grant that the pursuit of mathematics is a divine madness of the human spirit,
a refuge from the goading urgency of contingent happenings.



– Alfred North Whitehead
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Postby Giacomo on June 29th, 2008, 3:06 pm 

Mechanics



Mechanics is the paradise of the mathematical sciences,
because by means of it one comes to the fruits of mathematics.



– Leonardo da Vinci



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.



– Sir Isaac Newton
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Postby Giacomo on June 29th, 2008, 3:07 pm 

Mind



Either mathematics is too big for the human mind or the human mind is more than a machine.



– Kurt Gödel



There is no more a math mind, than there is a history or an English mind.



– Gloria Steinem
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Postby Giacomo on June 29th, 2008, 3:10 pm 

Mistakes



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



– Niels Bohr
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Postby Giacomo on June 30th, 2008, 1:33 am 

Music



Music is the pleasure the human mind experiences from
counting without being aware that it is counting.



– Gottfried Willhelm von Leibniz



There is geometry in the humming of the strings.



– Pythagoras



If all art aspires to the condition of music,
all the sciences aspire to the condition of mathematics.



– George Santayana



May not music be described as the mathematics of sense, mathematics as music
of the reason? The musician feels mathematics, the mathematician thinks music --
music the dream, mathematics the working life.



– James Joseph Sylvester



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
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Postby Giacomo on June 30th, 2008, 1:34 am 

Mysticism



I have often admired the mystical way of Pythagoras,
and the secret magic of numbers.



– Sir Thomas Browne
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Postby Giacomo on June 30th, 2008, 1:36 am 

Nature



One must do no violence to nature, nor model it in conformity to
any blindly formed chimaera.



– Janos Bolyai



The structures with which mathematics deals are more like lace,
the leaves of trees and the play of the light and shadow on a
human face than they are like buildings and machines, the least
of their representatives.



– Scott Buchanan



Everything in nature adheres to the cone, the cylinder and the cube.



– Paul Cezanne



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



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




– Joseph Fourier

(Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, New York, 1972)



Mathematical Analysis is as extensive as nature herself.



– Joseph Fourier



All the effects of nature are only mathematical results of a small number of immutable laws.



– Pierre-Simon Laplace



I am so in favor of the actual infinite that instead of admitting that
Nature abhors it, as is commonly said, I hold that Nature makes frequent
use of it everywhere, in order to show more effectively the perfections of its Author.



– Gottfried Willhelm von Leibniz

(Source: Nouveaux Essais de l'Entendement humain)



The latest authors, like the most ancient, strove to subordinate
the phenomena of nature to the laws of mathematics.



– Sir Isaac Newton



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



There is no more common error than to assume that, because prolonged and
accurate mathematical calculations have been made, the application of the
result to some fact of nature is absolutely certain.



– Alfred North Whitehead



I regret that it has been necessary for me in this lecture to administer
such a large dose of four-dimensional geometry. I do not apologize, because
I am really not responsible for the fact that nature in its most fundamental
aspect is four-dimensional. Things are what they are.



– Alfred North Whitehead
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Postby Giacomo on June 30th, 2008, 1:37 am 

Newton



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



– Gottfried Willhelm von Leibniz



[of Newton] ... from motion’s simple laws Could trace the secret hand of
Providence Wide-working through this universal frame.



– James Thompson



A monument to Newton! A monument to Shakespeare! Look up to heaven,
look into the Human Heart. Til the planets and the passions, the
affections and the fixed stars are extinguished their names cannot die.



– John Wilson
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Postby Giacomo on July 18th, 2008, 6:11 pm 

Conventional Wisdom


We associate truth with convenience, with what most closely accords with self-interest and personal well being or promises best to avoid awkward effort or unwelcome dislocation of life. We also find highly acceptable what contributes most to self-esteem..... economic and social behavior are complex, and to comprehend their character is mentally tiring. Therefore we adhere, as though to a raft, to those ideas which represent our understanding.

Kenneth Galbraith


So the conventional wisdom must be simple, convenient, comfortable, and comforting -- though not necessarily true.

Kenneth Galbraith


Kenneth Galbraith coined the phrase "conventional wisdom", but he did not consider it a compliment.
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Postby Giacomo on July 19th, 2008, 4:31 pm 

"Wir mussen wissen, wir werden wissen", which means "We must know, we will know."

David Hilbert's most famous quote
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Re: Math Quotes

Postby Existencebyproxy on June 5th, 2009, 5:46 am 

"Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude." Nietzsche
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Re: Math Quotes

Postby AnalynSarte on June 8th, 2009, 4:41 am 

"I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return." (Bertrand Russell, 1912)
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Re: Math Quotes

Postby Giacomo on August 20th, 2010, 2:03 pm 

A proof only becomes a proof after the social act of “accepting it as a proof”.

--- Yuri Manin
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Re: Math Quotes

Postby mem4 on March 4th, 2011, 1:28 pm 

I looked at the thermometer for outside…it read zero. My wife asked me what the temperature was…I said there wasn’t one.

Ron White
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Re: Math Quotes

Postby Alan Masterman on November 11th, 2012, 9:50 am 

Mathematicians really talk some fatuous nonsense when they venture outside their comfort zone, don't they? I mean, poor old G H Hardy:

"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"

Shakespeare might disagree; though he preceded Newton, his ideas have endured longer: Newton was proven wrong by Einstein.

As for Dirac... well, yes, why don't we ditch objectivity altogether, and just believe in the things that we find beautiful? What a wonderful world that would make!
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