ABSTRACT
Progress in mathematics has always been connected with the growth in the abstractness of its concepts and theories. Modern mathematics uses ever deeper abstractions to study, not only the quantitative, but also the more complex structural relations, the traditional quantitative relations among magnitudes happen to be a constituent part of these more complex relations. In contrast to the static concept of a set, the principal attention is turned towards the character of representations, which retain the definite structural specificity of the objects, and thereby the active, constructive aspect of mathematical knowledge is underlined. With the emergence of the new abstract divisions of mathematics, a structural approach towards the objects of mathematical investigations took shape; it became ever more clear that the subject-matter of mathematics is not limited to the study of the properties and relations obtainable among magnitudes and spatial figures.
