Mathematical Quotes - Page 11

• Seek simplicity, and distrust it.

  Alfred North Whitehead

  Creativity, Science, Simplicity

  The Concept of Nature ch. 7 (1920)

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• Only mathematics and mathematical logic can say as little as the physicist means to say.

  Bertrand Russell

  Mean, Science, Mathematical Logic

  Bertrand Russell (1992). “The Basic Writings of Bertrand Russell, 1903-1959”, p.626, Psychology Press

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• 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".

  John Edensor Littlewood

  Running, Real, School

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• How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

  Stephen Leacock

  Fall, Struggle, Math

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• Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

  G. H. Hardy

  Sensual, Technique, Taught

  "A Mathematician's Apology". Book by G. H. Hardy, 1941.

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• You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.

  Hermann Hesse

  Reality, Law, Yesterday

  Hermann Hesse (2002). “The Glass Bead Game: (Magister Ludi) A Novel”, p.168, Macmillan

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• Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.

  Gottfried Leibniz

  Math, Interesting, Important

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• I cannot do it without comp[u]ters.

  William Shakespeare

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• One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

  George Polya

  Teacher, Science, Opportunity

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

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• I am ill at these numbers.

  William Shakespeare

  Math, Numbers, Ill

  William Shakespeare, Samuel Weller Singer, Charles Symmons (1826). “Romeo and Juliet. Hamlet. Othello”, p.213

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• It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.

  George Santayana

  Song, Art, Math

  George Santayana (2014). “Some Turns of Thought in Modern Philosophy”, p.81, Cambridge University Press

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• The art of discovering the causes of phenomena, or true hypotheses, is like the art of deciphering, in which an ingenious conjecture often greatly shortens the road.

  Gottfried Leibniz

  Art, Math, Causes

  "New Essays Concerning Human Understanding with an Appealing". Transtated from the Original Latin, French and German Writeen,

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• It is possible for a mathematician to be "too strong" for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

  John Edensor Littlewood

  Strong, Rocks, Different

  John Edensor Littlewood, Béla Bollobás (1986). “Littlewood's Miscellany”, p.144, Cambridge University Press

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• The essential fact is that all the pictures which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.

  James Jeans

  Nature, Science, Facts

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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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• The moving power of mathematical invention is not reasoning but imagination.

  Augustus De Morgan

  Teacher, Moving, Math

  "The Life of Sir William Rowan Hamilton". Book by Robert Perceval Graves, Volume 3, p. 219, 1889.

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• In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.

  Roger Bacon

  Math, Men, Intellectual

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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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• Reverend Fathers, my letters did not usually follow each other at such close intervals, nor were they so long.... This one would not be so long had I but the leisure to make it shorter.

  Blaise Pascal

  Father, Math, Long

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• If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

  Carl Friedrich Gauss

  Truth, Science, Discovery

  "The World of Mathematics". Book by J. R. Newman, 1956.

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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, 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

  Teaching, Math, Challenges

  Morris Kline (1964). “Mathematics in Western Culture”, p.470, Oxford University Press

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• I feel engulfed in the infinite immensity of spaces whereof I know nothing, and which know nothing of me, I am terrified The eternal silence of these infinite spaces alarms me.

  Blaise Pascal

  Math, Space, Silence

  "The Thoughts of Blaise Pascal". Book by Blaise Pascal, published by Kegan Paul. Chapter "The Misery of Man Without God", 1885.

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• Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.

  Arthur Koestler

  Wisdom, Blessed, Power

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• In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

  George Polya

  Expression, Order, Two

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

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• Nature hides her secrets because of her essential loftiness, but not by means of ruse.

  Albert Einstein

  Nature, Mean, Math

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