Mathematics Quotes - Page 7

• If you had done something twice, you are likely to do it again.

  Brian Kernighan

  Done, Mathematical, Ifs

  Brian W. Kernighan, Rob Pike (1984). “The UNIX Programming Environment”, Prentice Hall

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• Everyone else would climb a peak by looking for a path somewhere in the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak.

  Donald J. Newman

  Shining, Mountain, Path

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• The very term 'combinatorial methods' has an oxymoronic character.

  Joel Spencer

  Character, Method, Mathematical

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• When I entered graduate school I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann's and Feynman's doors and asked them what they were currently doing. Murray wrote down the partition function for the three-dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman's answer was 'nothing'.

  Kenneth G. Wilson

  Father, Nice, School

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• The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.

  Eric Bell

  Moving, Math, Cowboy

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• With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.

  Ludwig Wittgenstein

  Philosophical, Math, Mountain

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

  George Santayana

  Art, Mathematical, Math And Science

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• The principle is so perfectly general that no particular application of it is possible.

  George Polya

  Knowledge, Math, Principles

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

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• A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.

  George Polya

  Real, Math, Tree

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• MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.

  Jim Propp

  Blah, Mathematical, Respectable

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• The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

  G. H. Hardy

  Appreciation, Math, People

  G. H. Hardy (1992). “A Mathematician's Apology”, p.86, Cambridge University Press

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• Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.

  Richard Askey

  Science, Germany, Analysis

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• Music is part of Number Theory. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed.

  Hendrik Lenstra

  Numbers, America, Way

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• Recreational number theory [...] is that part of number theory that is too difficult to study.

  Hendrik Lenstra

  Science, Numbers, Study

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• The simple equations that generate the convoluted Mandelbrot fractal have been called the wittiest remarks ever made.

  John Allen Paulos

  Simple, Made, Fractals

  John Allen Paulos (2008). “Once Upon A Number: The Hidden Mathematical Logic Of Stories”, p.61, Hachette UK

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• One geometry cannot be more true than another; it can only be more convenient.

  Henri Poincare

  Geometry, Convenient, Theorems

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.85, Modern Library

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• Induction makes you feel guilty for getting something out of nothing, and it is artificial, but it is one of the greatest ideas of civilization.

  Herbert Wilf

  Science, Civilization, Ideas

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• 1/r^2 has a nasty singularity at r=0, but it did not bother Newton-the Moon is far enough.

  Edward Witten

  Moon, Nasty, Newton

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• In order to solve this differential equation you look at it until a solution occurs to you.

  George Polya

  Math, Order, Looks

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• A set is a Many that allows itself to be thought of as a One.

  Georg Cantor

  "Infinity and the Mind". Book by Rudy Rucker, 1982.

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• A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

  John Edensor Littlewood

  Math, Mediocrity, Paper

  John Edensor Littlewood, Béla Bollobás (1986). “Littlewood's Miscellany”, p.24, Cambridge University Press

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• Mathematics is a dangerous profession; an appreciable proportion of us go mad.

  John Edensor Littlewood

  Mad, Proportion, Dangerous

  John Edensor Littlewood, Béla Bollobás (1986). “Littlewood's Miscellany”, p.103, Cambridge University Press

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• Nature's great book is written in mathematics.

  Galileo Galilei

  Book, Math, Science

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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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• ... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.

  Bertrand Russell

  Mean, Numbers, Long

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