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Abstrakt

Marxism requires that even when creating the conception of mathematics we must not forget basic historical connections. In the paper ceartain philosophic-methodological aspects of the development of mathematics, its relation to practice and to other sciences, the development of the relation of the theoretical and applied orientation in mathematics, etc. are analyzed. The author outlines the procedure from a simple mathematical abstraction through multi-level specific (mathematical) idealizations to mathematical formalisms and from there the reverse motion through semantic and empirical interpretations which represents the reduction of the complex logical genesis of mathematics to its relatively simple form. Theories of concrete sciences become the source of new impulses for mathematics when certain antithetical relations between objects of mathematical theory are able to produce quite new mathematical objects, new mathematical concepts in order to become immediately the mediators of mutually fruitful relations between new substantial and formal mathematical theories on the one hand and theories of concrete sciences on the other hand. The last part of the paper deals with the relation of mathematics and dialectical materialism.