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

Hardcover

ISBN 10: 3764364416 ISBN 13: 9783764364410

Publisher: Birkhäuser, 2001

Synopsis

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 fromthis 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.

About this title

Review

"...The book, indispensable for historians of mathematics, can be warmly recommended to every working mathematician."

--EMS Newsletter (on the first edition)

Synopsis

This is the second revised edition of the first volume of the outstanding collection of historical studies of mathematics in the nineteenth century compiled in three volumes by A. N. Kolmogorov and A. P. Yushkevich. This second edition was carefully revised by Abe Shenitzer, York University, Ontario, Canada. The historical period covered in this book extends from the early nineteenth century up to the end of the 1930s, as neither 1801 nor 1900 are, in themselves, turning points in the history of mathematics, although each date is notable fo a remarkable event: the first for the publication of Gauss' "Disquisitiones arithmeticae", the second for Hilbert's "Mathematical Problems." Beginning in the second quarter of the nineteenth century mathematics underwent a revolution as crucial and profound in its consequences for the general world outlook as the mathematical revolution in the beginning of the modern era. The main changes included a new statement of the problem of the existence of mathematical objects, particulary in the calculus, and soon thereafter the formation of non-standard structures in geometry, arithmetic and algebra.

The primary objective of the work has been to treat the evolution of mathematics in the nineteenth century as a whole; the discussion is concentrated on the essential concepts, methods, and algorithms.

Edition details

• Publisher: Birkhäuser
• Publication date: 2001
• Language: English
• ISBN 10: 3764364416
• ISBN 13: 9783764364410
• Binding: Hardcover
• Edition number: 2
• Number of pages: 322
• Editor: Kolmogorov A.N., Yushkevich A.P.