Mathematics Quotes - Page 13

• What could be more general than 2, which can represent two galaxies or two pickles, or one galaxy plus one pickle (the mind doth boggle), or just 2 gently bobbing - where? It, like God, is an "I am" and many have thought that it must be a precipitate of ultimate reality.

  Alfred W. Crosby

  Reality, Numbers, Two

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• Now that practical skills have developed enough to provide adequately for material needs, one of these sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt, the priestly caste there having the leisure necessary for disinterested research.

  Aristotle

  Math, Skills, Egypt

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• To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.

  Hilda Phoebe Hudson

  Christian, Education, Math

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• And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics - nay, all realms of exact thought - are woven into the very fabric of our number system.

  Tobias Dantzig

  Art, Numbers, Two

  Tobias Dantzig (1954). “Number, the Language of Science: A Critical Survey Written for the Cultured Non-mathematician”

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• 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

  Years, Achievement, Greek

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• A generating function is a clothesline on which we hang up a sequence of numbers for display.

  Herbert Wilf

  Numbers, Clotheslines, Function

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• ...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

  Charles Sanders Peirce

  Dream, Math, Science

  Charles Sanders Peirce (1931). “Collected Papers of Charles Sanders Peirce”

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• Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...'

  John Updike

  Beautiful, Moving, Math

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• Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.

  Edward Kasner

  Math, Views, Common Sense

  Edward Kasner, James Newman (2013). “Mathematics and the Imagination”, p.8, Courier Corporation

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• A proof only becomes a proof after the social act of "accepting it as a proof".

  IU?. I. Manin

  Social, Accepting, Proof

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• Gel'fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel'fand found hedgehogs lurking in the rows of his spectral sequences!

  Dusa McDuff

  Math, Talking, Ideas

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• He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.

  Henry David Thoreau

  Life, Learning, Exercise

  Henry David Thoreau (2017). “Journeys, Adventures & Life in Harmony with Nature – 6 Book Collection (Illustrated): Including Walden, A Week on the Concord and Merrimack Rivers, The Maine Woods, Cape Cod, A Yankee in Canada & Canoeing in the Wilderness - North American Highlands Series”, p.270, e-artnow

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• There is no smallest among the small and no largest among the large, but always something still smaller and something still larger.

  Anaxagoras

  Smallest, Stills

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• To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.

  James R Newman

  Knowledge, Math, Talking

  James R. Newman (2000). “The World of Mathematics”, p.1200, Рипол Классик

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• It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 1:10. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely.

  John Edensor Littlewood

  Learning, Math, Past

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• Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.

  Jean le Rond d'Alembert

  Math, Men, Differences

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• Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.

  John Banville

  Math, Null, Mixtures

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• Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

  Eric Temple Bell

  Beauty, Spring, Math

  "The Development of Mathematics" by Eric Temple Bell, (p. 9), 1940.

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• Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.

  Louis J. Mordell

  Party, Science, Appreciate

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• Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, 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

  Art, Inspiration, Past

  Eric Temple Bell (1938). “The queen of the sciences”

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• The Mathematics are Friends to Religion; inasmuch as they charm the Passions, restrain the Impetuosity of Imagination, and purge the Mind from Error and Prejudice.

  John Arbuthnot

  God, Faith, Hope

  "An Essay on the Usefulness of Mathematical Learning: In a Letter from a Gentleman in the City, to His Friend at Oxford".

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• When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.

  Edward Kasner

  Home, Order, Interesting

  "Mathematics and the Imagination".

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• Thus the good christian should beware of mathematicians and all those who make false prophecies, however much they may in fact speak the truth; lest, being in league with the devil, they may deceive errant souls into making common cause.

  Saint Augustine

  Christian, League, Soul

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• I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the "Law of Frequency of Error." The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason.

  Francis Galton

  Math, Errors, Self

  Natural Inheritance Normal Variability (p. 66)

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• Waste not thy time in windy argument but let the matter drop.

  William Shakespeare

  Matter, Waste, Argument

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