Mathematics: abstraction and reality. A sketch toward deeper analysis

Abstract

This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into "pure" and "applied" mathematics is artificial. The criterion of creativity and applicability outside of the original context is used as a litmus test. It is emphasized that great societies and cultural environments produce great mathematics and individual mathematicians.