Quotations collected below all reflect on perception of Mathematics by various people over a few hundred years history. (My own thoughts could be found in my Manifesto and the What is What? section of the site.)
Proclus (412-485) had this to say:
The Pythagoreans considered all mathematical sciences to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics (astronomy, A.B.) magnitude inherently moving.
Obviously, in the 2500 years since Pythagoras when music was still considered a mathematical science, both human perception of and our attitude towards, mathematics underwent a tremendous metamorphosis. Below I list several quotations - definitions of mathematics - but this is not a quotation page per se. Presenting different views with quotations appears to me less personal and more authoritative. Could you please check the boxes against those quotations you approve of and then press the Submit button at the bottom of the page.
Copyright © 1996-2018 Alexander Bogomolny