Critical reflection of the system approach to the study of formal logic and justification for mathematics interaction

It should be noted that many modern works on logical research use a complex technical apparatus, which can only be understood by a well-prepared logic, it is impossible without studying mathematics. On the other hand, feedback from logic in the study of mathematics is important, since logical principles are intrinsically present in the basis constructions of mathematics and in mathematical logic. The principles of logic are adopted in mathematics in order to develop mathematical thinking through critical reflection, although formal logical analysis does not always reflect the real rules of mathematical argumentation. Understanding this contributes to the fundamentality of university mathematical education, as well as the need for a systematic approach to justification for mathematics.