Enlarging the Scope of Applicability of Successful Techniques for Automated Reasoning in Mathematics

Abstract

AbstractIn mathematics sometimes methods from one area can be fruitfully applied for getting results in another area, occasionally looking very remote from the other area. A well-known example is given by analytic geometry that enables us, besides proving “elementary” geometrical theorems, to establish otherwise untractable results like unsolvability of the problems of angle trisection and doubling the cube by compass and straightedge and to reduce calculation of the kissing numbers of spheres to verification of a first-order formula about real numbers (and that could be done, in principle, by Tarski algorithm).