Mathematics (Study, science) – the science of the structure, order and relations that historically formed on the basis of counting, measuring, and describing the shape of objects. Mathematical objects are created by idealizing the properties of real or other mathematical objects and writing these properties in the formal language. Mathematics does not belong to the natural sciences, but is widely used in them both for the exact formulation of their content, and for obtaining new results. Mathematics is a fundamental science that provides (general) language means of other sciences; thus, it reveals their structural interrelationship and contributes to the finding of the most general laws of nature.
Idealized properties of investigated objects or formulated as axioms, or are recalculated in the definition of relevant mathematical objects. Then, according to the strict rules of the logical conclusion of these properties, other real properties (theorems) are derived. This theory collectively forms a mathematical model of the object being studied. Thus, first, based on spatial and quantitative relations, mathematics receives more abstract relationships, the study of which is also the subject of modern mathematics .
Traditionally, mathematics is divided into theoretical, which performs in-depth analysis of intramethematic structures, and applied, which gives its models to other sciences and engineering disciplines, and some of them occupy the boundary position with mathematics. In particular, formal logic can be considered as part of philosophical sciences, and as part of mathematical sciences; mechanics – both physics and mathematics; informatics, computer technologies and algorithmics relate both to engineering, to mathematical sciences, etc. In the literature, many different definitions of mathematics were proposed.