Mathematics: abstraction and reality. A sketch toward deeper analysis

TL;DR

This paper explores the dual nature of mathematics as both an abstract and concrete science, challenging the traditional division between pure and applied mathematics through a discussion on creativity and societal influence.

Contribution

It proposes that the distinction between pure and applied mathematics is artificial, emphasizing societal and cultural factors in mathematical development.

Findings

The division into pure and applied mathematics is artificial.

Societies with rich cultural environments produce greater mathematical achievements.

Creativity and applicability are key criteria for mathematical significance.

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.