Supplementary mathematics/Pure mathematics

Pure mathematics is the study of mathematical concepts independent of any application outside of mathematics. These kinds of concepts may originate in real-world concerns, and the results obtained may later be highly useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the attraction is attributed to the intellectual challenge and the aesthetic beauty of working to the logical consequences of underlying principles.

While pure mathematics as an activity has existed at least since ancient Greece and has made effective progress, of course, these concepts can be seen in ancient Iran, ancient Egypt, ancient Babylon,And even in the golden period of Islam, etc. This concept was carried out around 1900, after the introduction of theories with counterintuitive features (such as non-Euclidean geometries and the theory of infinite contour sets) and complex concepts of calculus, and the theory was explained. The discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable and Russell's paradox) was also discussed as an example in the scientific field. It introduced the need to renew the concept of mathematical precision and rewrite all mathematics based on it, with the systematic use of axiomatic methods. This led many mathematicians to focus on complete mathematics for its own sake, i.e. pure mathematics.

It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference rather than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians.