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 ButlerRelated topics
anything calculus daring follow geometry history indispensable marvelous mathematics philosophy pure reason supremacy tool today gauss riemann leibniz lobachevsky newton descartes sciencesRelated quotes
[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are... two distinct categories of things of which an account must be given-the ideas or concepts of mathematics, and the propositions of mathematics. ...the great majority of writers on the subject have concentrated their attention on the explanation of one or the other... and erroneously supposed that a satisfactory explanation of the other would immediately follow.
Frank P. Ramsey
Phenomena of the external sense are examined and set forth in physics; those of the internal sense in empirical psychology. Pure mathematics considers space in geometry and time in pure mechanics. To these is to be added a certain concept, intellectual to be sure in itself, but whose becoming actual in the concrete requires the auxiliary notions of time and space in the successive addition and simultaneous juxtaposition of separate units, which is the concept of number treated in arithmetic.
Immanuel Kant
Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness.
Galileo Galilei
Newton and Descartes started to try and prove that God existed in the same way as they would try and prove something in the laboratory or with their mathematics ... And when you try and mix science and religion you get bad science and bad religion. The two are doing two different things. ... Science can give you a diagnosis of cancer. It can even cure your disease, but it cannot touch your grief and disappointment, nor can it help you to die well.
Karen Armstrong
...The subjects we study at school can be divided roughly into two groups-the sciences and the arts. The sciences include mathematics, geography, chemistry, physics, and so on. Among the arts are drawing, painting, modelling, needlework, drama, music, literature. The purpose of education is to fit us for life in a civilised community, and it seems to follow from the subjects we study that the two most important things in civilised life are Art and Science.
Anthony Burgess
