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The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth. J. B. Shaw, In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Mathematics has beauties of its own -- a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. When this subject is properly ... presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant. J. W. A. Young, In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful. Hermann Weyl, (1885 - 1955) In an obituary by Freeman J. Dyson in Nature, March 10, 1956.
The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance. J.J. Sylvester Presidential Address to British Association, 1869.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained. Arthur Cayley, In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Aristotle, Metaphysica, 3-1078b.
Mathematics, rightly viewed, posses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture. Bertrand Russell
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 (1883-1960)
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. Godfrey H. Hardy, (1877 - 1947) A Mathematician's Apology, London, Cambridge University Press, 1941.
I regard it as an inelegance, or imperfection, in quaternions, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to have recourse to x, y, z, etc.. [Sir] William Rowan Hamilton, (1805-1865) In a letter from Tait to Cayley.
Mathematics has beauties of its own -- a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. When this subject is properly ... presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant. J. W. A. Young, In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful. Hermann Weyl, (1885 - 1955) In an obituary by Freeman J. Dyson in Nature, March 10, 1956.
The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance. J.J. Sylvester Presidential Address to British Association, 1869.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained. Arthur Cayley, In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Aristotle, Metaphysica, 3-1078b.
Mathematics, rightly viewed, posses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture. Bertrand Russell
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 (1883-1960)
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. Godfrey H. Hardy, (1877 - 1947) A Mathematician's Apology, London, Cambridge University Press, 1941.
I regard it as an inelegance, or imperfection, in quaternions, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to have recourse to x, y, z, etc.. [Sir] William Rowan Hamilton, (1805-1865) In a letter from Tait to Cayley.
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