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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than any… - Nicholas Murray Butler
" "The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
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About Nicholas Murray Butler
Nicholas Murray Butler (April 2, 1862 – December 7, 1947) was an American philosopher, diplomat, and educator. Butler was president of Columbia University, president of the Carnegie Endowment for International Peace, and a recipient of the Nobel Peace Prize.
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Nicholas M. Butler
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Nicholas Butler
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Additional quotes by Nicholas Murray Butler
There was a time when philosophy might have been defined as the science of human activity, so all-comprehensive was it. The ambitious Greek who would attach his name to a philosophical system must include in his scheme all that could be known, done, and speculated about God, the world, and man. In the course of time and the specialization of the sciences this view of philosophy fell away, and was replaced by the more exact and narrower conception of modern times.
The United States is in sore need today of an aristocracy of intellect and service. Because such an aristocracy does not exist in the popular consciousness, we are bending the knee to the golden calf of money. The form of monarchy and its pomp offer a valuable foil to the worship of money for its own sake. A democracy must provide itself with a foil of its own and none is better or more effective than an aristocracy of intellect and service.
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1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.
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