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.
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Attributed in Chaplin, Virginia. "Princeton & Mathematics: A Notable Record". Princeton Alumni Weekly (May 9, 1958).Marston Morse
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So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
Bertrand Russell
May she be granted beauty and yet not
Beauty to make a stranger’s eye distraught,
Or hers before a looking-glass, for such,
Being made beautiful overmuch,
Consider beauty a sufficient end,
Lose natural kindness and maybe
The heart-revealing intimacy
That chooses right, and never find a friend.William Butler Yeats
Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry.
Bertrand Russell
I think that one may contribute (ever so slightly) to the beauty of things by making one's own life and environment beautiful, as far as one's power reaches.This includes moral beauty, one of the qualities of humanity, though it seems not to appear elsewhere in the universe. But I would have each person realize that his contribution is not important, its success not really a matter for exultation nor its failure for mourning; the beauty of things is sufficient without him.
(An office of tragic poetry is to show that there is beauty in pain and failure as much as in success and happiness.)Robinson Jeffers
And the true order of going, or being led by another, to the things of love, is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these steps only, and from one going on to two, and from two to all fair forms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is.
Plato
Morse, Marston
Morse, Samuel F. B.
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