The Role of Mathematical Methods in the Formation of Scientific Concepts (Elementary and Mathematics)

It is known that mathematical justification, with all its rigor and in accordance with the reality being studied, attests to the role of mathematical methods in the formation of scientific concepts. Any analysis of the idea of elementarity that claims to be adequate must take into account the fact that in real scientific knowledge, we never encounter the concept of an elementary object—be it a material point, a point event, or a process as such—but always within a system of specific knowledge (scientific theories, models, hypotheses) used to solve well-defined scientific problems. Such an analysis must consider the inextricable connection between certain ideas about elementarity and fundamental methodological principles of a systemic nature, such as simplicity, symmetry, invariance, and correspondence. In this study, an attempt was made to identify the methodological role of mathematical methods in the formation of scientific concepts.