Mathematics: subject, problems, applications

In this article some aspects of history and methodology of mathematics are considered. The history of development of mathematics is observed. Various approaches to mathematics, such as a logicism, an intuitionism, a formalism and set-theoretic approach are considered. Great mathematician, followers of various approaches, their opposition, mathematician efforts to create mathematics, and also the revealed contradictions are also in detail presented. Mathematics continues to develop and is effectively applied, so the value of applied mathematics is discussed. The contribution of the worked mathematicians who worked in both pure, and applied mathematics is observed. In mathematics there are a lot of areas which are not applied yet and can continue its independent, abstract development for a long time. Man created mathematics, the world of mathematics which is the mathematical model of various aspects of the physical world.