ON THE METHODOLOGICAL ROLE OF MATERIALIST DIALECTICS IN MATHEMATICAL COGNITION THROUGH THE PRINCIPLE OF DEVELOPMENT AND THE PRINCIPLE OF UNIVERSAL INTERCONNECTION

Abstract

The principle of universal interconnection is a theoretical principle that considers objects and phenomena in objective reality as existing in mutual relationships and interactions. This principle requires a comprehensive perspective in the study of mathematics. When solving a geometry problem, a point or a line should be considered in relation to other points and lines, as well as in connection with the entire geometric figure. Similarly, when examining a mathematical problem, various methods from algebra, geometry, trigonometry, and other mathematical fields may be applied. The principle of development shows that the evolution of a mathematical theory, as well as mathematics as a whole, is an objective process that does not depend on any individual’s will. It is a process that resolves contradictions arising within mathematics itself and addresses the practical needs of reality. The principle of development is manifested through the three fundamental laws of dialectical materialist philosophy.