The book is an extended version of a lecture delivered at a meeting of the student lecture hall of the Moscow Mathematical Society. The main goal is to show what meaning is given to the concept of number in modern mathematics. The basic concepts of p-adic and non-standard analysis are outlined, what is a quaternion and Cayley numbers are explained. The presentation leads the reader to the concept of von Neumann algebras, as well as to the idea of ​ ​ "supermathematics" - the calculus of anticommuting variables. For undergraduate, graduate and academic students interested in applications of mathematics.