Mathematics of the 19th Century: Mathematical Logic Algebra Number Theory Probability Theory

by A.N. Kolmogorov (Editor), A.P. Yushkevich (Editor)

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics from antiquity to the early nineteenth century, published in three volumes from 1970 to 1972. 1 For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as well. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe­ matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Through an anal­ ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition.

308 pages, Paperback

Published June 1, 1992

About the author

Dr. Andrey Nikolaevich Kolmogorov, Ph.D. (Moscow State University, 1929; Russian: Андре́й Никола́евич Колмого́ров) was a Soviet mathematician and professor at the Moscow State University where he became the first chairman of the department of probability theory two years after the 1933 publication of his book which laid the modern axiomatic foundations of the field. He was a Member of the Russian Academy of Sciences and winner of many awards, including the Stalin Prize (1941), the Lenin Prize (1965), the Wolf Prize (1980), and the Lobachevsky Prize (1986).