Mathematics - the science of quantitative relations and spatial forms of the real world. In close connection with demands of technology and science supply quantitative relations and spatial forms, which is studying math, is constantly expanding, so this is a common definition of mathematics is filled with all the rich content. A clear understanding of the independent status of mathematics as a special science became possible only after the accumulation of large enough factual material and first appeared in ancient Greece. Development of mathematics up to that time naturally attributed to the period of inception of mathematics. During these first two periods of mathematical research deal almost exclusively with very limited stock of basic concepts that have arisen even in the very early stages of historical development in connection with the most simple requests of economic life. The first task of mechanics and physics could still be met by the same margin of the basic mathematical concepts. In 17th century new demands of science and technology forcing mathematicians to focus on creating methods to mathematically study the motion, the process of changing variables, transformations of geometric figures. With the use of variables in analytic geometry and the establishment of differential and integral calculus begins during math variables. Further extension of the quantitative relations and spatial forms, he studied mathematics, has resulted in the early 19 century. The need to treat the process of expanding the object of mathematical research deliberately setting himself the task of a systematic study with a rather general point of view of the possible types of quantitative relations and spatial forms.