内容简介：
The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemanna (TM)s work. Einsteina (TM)s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemanna (TM)s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemanna (TM)s scientific work from a single unifying perspective. Laugwitz describes Riemanna (TM)s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle a " for mathematics and physics alike a " to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemanna (TM)s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics. "There is excellent referencing throughouta ] Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporariesa ] Laugwitza (TM)s expertise on historical matters is most impressivea ] Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann." a "MAA Online ..".the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemanna (TM)s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended." a "Bulletin of the AMS