These famous papers, with their characteristic
mixture of deep insight and inevitable confusion, are here presented
complete and in English for the first time, with a commentary by their
translator, John Stillwell, that guides the reader into the heart of
the subject. One of the finest works of one of the great
mathematicians is now available anew for students and experts
alike.
—Jeremy Gray
The AMS and John Stillwell have made an
important contribution to the mathematics literature in this
translation of Poincaré. For many of us, these great papers on the
foundations of topology are given greater clarity in
English. Moreover, reading Poincaré here illustrates the ultimate
in research by successive approximations (akin to my own way of
mathematical thinking).
— Stephen Smale
I am a proud owner of the original complete
works in green leather in French bought for a princely sum in Paris
around 1975. I have read them extensively, and often during
topology lectures I refer to parts of these works. I am happy that
there is now the option for my students to read them in
English.
—Dennis Sullivan
The papers in this book chronicle Henri Poincaré's journey in
algebraic topology between 1892 and 1904, from his discovery of the
fundamental group to his formulation of the Poincaré
conjecture. For the first time in English translation, one can follow
every step (and occasional stumble) along the way, with the help of
translator John Stillwell's introduction and editorial comments.
Now that the Poincaré conjecture has finally been proved, by
Grigory Perelman, it seems timely to collect the papers that form the
background to this famous conjecture. Poincaré's papers are in
fact the first draft of algebraic topology, introducing its main
subject matter (manifolds) and basic concepts (homotopy and
homology). All mathematicians interested in topology and its history
will enjoy this book.
This volume is one of an informal sequence of works within the
History of Mathematics series. Volumes in this subset,
“Sources”, are classical mathematical works that served as
cornerstones for modern mathematical thought.
Readership
Undergraduates, graduate students, and research mathematicians
interested in topology and the history of topology.