ABSTRACT
The achievements of Mathematics over the centuries cannot fail to arouse the deepest admiration. There are but few mathematicians who feel impelled to reject any of the major results of Algebra, or of Analysis, or of Geometry and it seems likely that this will remain true also in the future. It is commonly accepted that the beginnings of Mathematics as a deductive science go back to the Greek world in the fifth and fourth centuries B.C. It is even more certain that in the course of many hundreds of years before that time people in Egypt and Mesopotamia had accumulated an impressive body of mathematical knowledge, both in Geometry and in Arithmetic. Euclid’s geometry was supposed to deal with real objects, whether in the physical world or in some ideal world. The fundamental importance of the advent of non-Euclidean geometry is that by contradicting the axiom of parallels it denied the uniqueness of geometrical concepts and hence, their reality.
