Mathematical Objects, Definitions, Diagrams

Abstract

The aim of this chapter is to give answer to the question: What is mathematics about? The chapter maintains that, being problem solving by the analytic method, mathematics is about objects which are hypotheses human beings make to solve mathematical problems. Therefore, mathematical objects exist only in the minds of the mathematicians who hypothesize them, and in the minds of the people who make use of them. Like mathematical objects, the mathematical definitions by which mathematical objects are introduced are hypotheses human beings make to solve mathematical problems by the analytic method. Mathematical diagrams also fit in the analytic method, since they are important tools to solve problems by that method.