A comprehensive exposition of mathematics, tracing the history and cultural significance of mathematical ideas from antiquity to the present day. Mathematics, which originated in antiquity in the needs of daily life, has developed into an immense system of widely varied disciplines. Like the other sciences, it reflects the laws of the material world around us and serves as a powerful instrument for our knowledge and mastery of nature. But the high level of abstraction peculiar to mathematics means that its newer branches are relatively inaccessible to nonspecialists. This abstract character of mathematics gave birth even in antiquity to idealistic notions about its independence of the material world. In recent years, many popular books about mathematics have appeared, but many of them have neglected the twentieth century, the undisputed "golden age" of mathematics. This book undertakes the ultimate task of mathematical exposition, outlining the history and cultural significance of mathematical ideas and their continuous development from the earliest beginnings of history to the present day.

This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated development.