The conceptual basis and its role in the formation of new sections of mathematics

Poberezhnyy I. A.

The article considers the state of the conceptual basis of mathematics in the historical and philosophical aspect. The genesis and evolution of some of the most ambiguous mathematical concepts are shown. The article describes how the evolution of concepts leads to the development of new scientific theories. On the other hand, the emergence of new directions in mathematics contributes to the renewal of its conceptual apparatus.

Keywords:history of mathematics, conceptual basis, irrational numbers, infinitesimal quantities, continuum, transfinite numbers.