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.

Nicholas Murray Butler

Tag: science reason philosophy philosophers scientists isaac-newton newton leibniz mathematics geometry descartes calculus sylvester supremacy gauss carl-friedrich-gauss gottfried-leibniz gottfried-wilhelm-leibniz analytical-geometry lobachevsky rene-descartes riemann

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Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.

W.W. Rouse Ball

Tag: science history scientists discovery isaac-newton newton mathematics calculus fermat johannes-kepler kepler barrow pierre-de-fermat cavalieri infinitesimal napier wallis

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