The book is devoted to the place of mathematics in life, the applicability of abstract mathematical structures to the modeling of real-world phenomena. Much attention is paid to the formation of mathematics as an abstract science; details are given about the modern school of Nicola Bourbak and about its attitudes. A number of specific algebraic structures, as well as mathematical models of some linguistic and genetic phenomena are considered. The book is intended for a wide range of specialists - engineers, biologists, philosophers, linguists and all those who are interested in the problems of modern mathematics.