“Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth.”

— Marston Morse

Attributed in Princeton & Mathematics: A Notable Record, Chaplin, Virginia, Princeton Alumni Weekly, May 9, 1958 http://www.princeton.edu/~mudd/finding_aids/mathoral/pmcxpaw.htm,

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Marston Morse 2

American mathematician 1892–1977

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“The viewpoint of the formalist must lead to the conviction that if other symbolic formulas should be substituted for the ones that now represent the fundamental mathematical relations and the mathematical-logical laws, the absence of the sensation of delight, called "consciousness of legitimacy," which might be the result of such substitution would not in the least invalidate its mathematical exactness. To the philosopher or to the anthropologist, but not to the mathematician, belongs the task of investigating why certain systems of symbolic logic rather than others may be effectively projected upon nature. Not to the mathematician, but to the psychologist, belongs the task of explaining why we believe in certain systems of symbolic logic and not in others, in particular why we are averse to the so-called contradictory systems in which the negative as well as the positive of certain propositions are valid.”

L. E. J. Brouwer (1881–1966) Dutch mathematician and logician

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“Beauty, like truth, is a thing which is relative to the time in which one lives and to the individual capable of understanding it. The expression of the beautiful bears a precise relation to the power of perception acquired by the artist.”

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“The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age”

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Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5
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“Music is a mysterious mathematical process whose elements are part of Infinity. … There is nothing more musical than a sunset.”

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Context: Music is a mysterious mathematical process whose elements are part of Infinity. … There is nothing more musical than a sunset. He who feels what he sees will find no more beautiful example of development in all that book which, alas, musicians read but too little — the book of Nature.

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