What, in fact, is mathematics doing? Why was it the least popular of all sciences for a long time, despite the fact that all human culture has a genuine basis for mathematical sciences? How does she play that outstanding role in our culture, which actually fell to her lot? What is the essence of mathematics? These and other issues are considered in the book of the German scientist devoted to the essence of mathematics, including from the point of view of the historical development of this science. The book is addressed to scientists - mathematicians and philosophers, graduate students and university students, everyone who is interested in the history and methodology of mathematics.