Platonism, intuition and the nature of mathematics

Abstract

Platonism is an essential aspect of mathematical method. Mathematicians are learned ability " t o l i v e " in the "world" of mathematical concepts. Here we have the main source of the creative power of mathematics, and of its surprising efficiency in natural sciences and technique. In this way, "living" (sometimes - for many years) in the "world"of their concepts and models, mathematicians are learned to draw a maximum of conclusions from a minimum of premises. Fixed system of basic principles is the distinguishing property of every mathematical theory. Mathematical model of some natural process or technical device is essentially a f i x e d m o d e l which can be investigated independently of its "original".