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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Papers on Fuchsian Functions (Hardcover, 1985 ed.)
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Papers on Fuchsian Functions (Hardcover, 1985 ed.)
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by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian
and Kleinian I1'OUps are of Il'eat interest from at least two
points of view: history, of course, but also as an inspiration for
further mathematical proll'ess. The papers are historic as the
climax of the ceometric theory of functions initiated by Riemann,
and ideal representatives of the unity between analysis, ceometry,
topololY and alcebra which prevailed during the 1880's. The rapid
mathematical prOll'ess of the 20th century has been made at the
expense of unity and historical perspective, and if mathematics is
not to disintell'ate altogether, an effort must sometime be made to
find its , main threads and weave them tocether 81ain. Poincare's
work is an excellent example of this process, and may yet prove to
be at the core of a . new synthesis. Certainly, we are now able to
gather up , some of the loose ends in Poincare, and a broader
synthesis seems to be actually taking place in the work of
Thurston. The papers I have selected include the three Il'eat
memoirs in the first volumes of Acta Math. -tice, on* Fuchsian
groups, Fuchsian , functions, and Kleinian groups (Poincare [1882
a,b,1883]). These are the papers which made his reputation and they
include many results and proofs which are now standard. They are
preceded by an , unedited memoir written by Poincare in May 1880 at
the height of his , creative ferment.
General
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