About the book: 1983 / Over the last century, one of the central bridges in mathematical science has been occupied by the theory of infinite sets created by the German mathematician G. Cantor, the concepts of which reflect the most general properties mathematical objects. However, a number of paradoxes were revealed in this theory, which caused many prominent scientists to doubt the validity of its foundations. This book sets out in a popular form the paths that human thought took in trying to understand the idea of ​​​​infinity both in physics and mathematics, talks about the main concepts of set theory, the history of the development of this science, the contribution of Russian scientists to it. The book is intended for a wide range of readers who want to know how the idea of ​​infinity has changed, what set theory does and what is the current state of this theory.