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“ The mathematician does not study pure mathematics because it is useful; he or she studies it because he or she delights in it and he or she delights in it because it is beautiful. “
Henri Poincare
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“If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy”
Alfred Renyi
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“The things of this world cannot be made known without the knowledge of mathematics”
Roger Bacon
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“...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know”
Henri Poincare
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“Mathematics rightly viewed possesses not only truth, but supreme beauty”
Bertrand Russell
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“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
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“...there is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics]”
J.J. Sylvester
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“The essence of mathematics is its freedom”
Georg Cantor
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“Mathematics seems to endow one with something like a new sense”
Charles Darwin
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“A scientist worthy of his or her name, above all a mathematician, experiences in his or her work the same impression as an artist; his or her pleasure is as great and of the same nature”
Henri Poincare
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“Anyone who cannot cope with mathematics is not fully human. At best he or she is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house”
Robert Heinlein
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“Life is only good for two things, discovering mathematics and teaching mathematics”
Simeon Poisson
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"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
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"It is here [in mathematics] that the artist has the fullest scope of his imagination"
Havelock Ellis
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"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity."
Howard W. Eves
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"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
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"Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country."
David Hilbert
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"The study of mathematics cannot be replaced by any other activity that will train and develop man's purely logical faculties to the same level of rationality."
C.O. Oakley
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“Where there is matter, there is geometry”
Johannes Kepler
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“Geometry enlightlens the intellect and sets one’s mind right”
Ibn Khaldun
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“might is geometry; joined with art, resistless”
Euripides
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“[Mathematics] is an independent world created out of pure intelligence”
William Wordsworth
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“it may be well doubted whether, in all the range of science, there is any field so fascinating to the explorer - so rich in hidden treasures - so fruitful in delightful surprises - as pure mathematics”
Lewis Carroll
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“What sciences can there be more noble, more excellent, more useful for people, more admirably high and demonstrative, than mathematics?”
Benjamin Franklin
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“Mathematics is the gate and key of the sciences... Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences or the things of this world”
Roger Bacon
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“In any particular theory there is only as much real science as there is mathematics”
Immanuel Kant
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“...for no human inquiry can be called science unless is pursues its path through mathematics exposition and demonstration”
Leonardo da Vinci
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“The mathematician has reached the highest rung on the ladder of human thought”
Havelock Ellis
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“There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world”
Lobachevsky
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“The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit”
A.N. Whitehead
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“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
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“This, therefore, is mathematics: she reminds you of the invisible form 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
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“Like the crest of a peacock so is mathematics at the head of all knowledge”
Indigenous saying
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“I often admired the mystical way of Pythagoras, and the secret magic of numbers”
Sir Thomas Browne
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“Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever”
Godfrey Hardy
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“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
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“Fractal geometry will make you see everything differently. ... Never again will your interpretation of [clouds, forests, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpets, bricks, and much else besides] be quite the same”
M.F. Barnsley
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“The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict...”
Morris Kline
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Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.”
Bertrand Russell
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“...treat Nature by the sphere, the cylinder and the cone...”
Paul Cezanne
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“Mathematics is not only real, but it is the only reality.”
Martin Gardner
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“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
John Adams
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“Pure mathematics is, in its way, the poetry of logical ideas.”
Albert Einstein
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“It is clear that the chief end of mathematical study must be to make the students think.”
John Wesley Young
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“Mathematics is no more computation than typing is literature.”
John Allen Paulos
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“Algebra is generous; she often gives more than is asked of her.”
D’Alembert
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“one’s work may be finished some day, but one’s education never.”
Alexandre Dumas
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“Not everything that counts can be counted.
Not everything that can be counted counts.”
Albert Einstein
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“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
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“One of the most important concepts in all of mathematics is that of function.”
T.P. Dick and C.M. Patton
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“A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical.”
P.A.M. Dirac
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It will be another million years, at least, before we understand the primes.”
Paul Erdos
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“The purpose of computing is insight, not numbers!”
R.W. Hamming
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“The Mandelbrot set is the most complex mathematical object known to mankind.
Benoit Mandelbrot
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“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
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“What humans do with the language of mathematics is to describe patterns...”
Lynn A. Steen
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“Mathematical knowledge adds vigour to the mind, frees it from prejudice, credulity, and superstition.”
John Arbuthnot
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“I have discovered such wonderful things that I was amazed... Out of nothing I have created a strange new universe.
Janos Bolyai
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“Indeed, nowadays no electical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.”
Keith Devlin
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“It’s not that I’m so smart, it’s just that I stay with problems longer.”
Albert Einstein
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“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 Hankel
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“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
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“Simply put, aesthetic and intellectual fulfillment requires that you know about mathematics.”
Jerry P. King
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“Mathematics is the abstract key which turns the lock of the physical universe.”
John Polkinghorne
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“Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.”
Alfred North Whitehead
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“The advancement and perfection of mathematics are intimately connected with the prosperity of the State”
Napolean I
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"In many cases, mathematics is an escape from reality. The mathematician finds his or her own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics."
Stanislaw Ulam
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