This book presents William Clifford's English translation of
Bernhard Riemann's classic text together with detailed
mathematical, historical and philosophical commentary. The basic
concepts and ideas, as well as their mathematical background, are
provided, putting Riemann's reasoning into the more general and
systematic perspective achieved by later mathematicians and
physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the
basis of his seminal ideas. Following a historical introduction
that positions Riemann's work in the context of his times, the
history of the concept of space in philosophy, physics and
mathematics is systematically presented. A subsequent chapter on
the reception and influence of the text accompanies the reader from
Riemann's times to contemporary research. Not only mathematicians
and historians of the mathematical sciences, but also readers from
other disciplines or those with an interest in physics or
philosophy will find this work both appealing and insightful.
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