Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics
Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics (Modern Birkhäuser Classics) Detlef Laugwitz, A. Shenitzer (Translator)
Publisher: Birkhäuser Boston
ISBN: 0817647767
DDC: 500
Edition: Paperback; 2008-01-21
Summary:
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 Riemann’s work. Einstein’s theory of gravitation would
be unthinkable without Riemannian geometry. In number theory,
Riemann’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 Riemann’s scientific work from a single unifying
perspective. Laugwitz describes Riemann’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 — for mathematics and
physics alike — 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 Riemann’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 throughout… 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 contemporaries… Laugwitz’s expertise on historical
matters is most impressive… Thanks are due to both author and
translator for making it much easier to enter into the literature on
Riemann." —MAA Online "...the author has succeeded
admirably...stating the technical details clearly and correctly while
writing an engaging and readable account of Riemann’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." —Bulletin of the AMS
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