The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction.... Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
Alfred North WhiteheadRelated topics
abstraction example fish instance mathematics moving point pure rid talking thought colours stonesRelated quotes
Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists.
Freeman Dyson
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
Remember it is essential to reach ever more of our folk with the message of racial survival. I wish you all the very best. You are dealing with pure, malignant evil, with devils incarnate. You will be targeted by the Federals, as their goal is your extinction. They will demonize you and your beliefs to deflect attention away from their own crimes. Go to the struggle with absolute defiance and accept what the Norns decree in likewise manner.
David Lane (white nationalist)
The important task of all art is to destroy the static equilibrium by establishing a dynamic one. Non-figurative art demands an attempt of what is a consequence of this task, the destruction of particular form and the construction of a rhythm of mutual relations, of mutual forms, or free lines.... the law of the denaturalization of matter is of fundamental importance. In painting, the primary color that is as pure as possible realizes this abstraction of natural color.
Piet Mondrian
The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features. This fundamental principle of generalization by abstraction was enunicated by the eminent American mathematician E. H. Moore more than thirty years ago. It is the purpose of the pages that follow to work out its implication for theoretical and applied economics.
Paul Samuelson