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History of Mathematics
2010; 228 pp; softcover
List Price: US$59
Member Price: US$47.20
Order Code: HMATH/37
John Stillwell was the recipient of the Chauvenet Prize for Mathematical Exposition in 2005.
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.
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).
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 in 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.
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.
Undergraduates, graduate students, and research mathematicians interested in topology and the history of topology.
"The current book provides a skillful translation of his [Poincari's] breakthrough work in algebraic topology. . . . John Stillwell has done a marvelous job with his translations and editing. . . . Poincari's prose flows smoothly - he was a pretty good writer, after all - and it is a delight to read. . . . I found this a charming contrast to the impersonality of many modern texts."
-- Bill Satzer, MAA Reviews
"The English translation of Poincari's celebrated work Analysis situs, together with the series of "Compliments" he added between 1895 and 1904, makes available a remarkable resource to the non-francophone community. Darboux wrote of Poincari that "when he drafted a memoir, he drafted it in one go, limiting himself to some crossings out, without coming back to what he had written". Stillwell's translation admits us to this pouring forth of Poincari's ideas, and to their consequences as played out in the supplements. Not only do we get a glimpse of Poincari at work, but these papers contain the beginnings of the modern notions used in topology today and the connections they make with the ideas of the nineteenth century.
"Analysis situs and its supplements have earned their place as the source of many rich ideas that developed into the field of algebraic topology. At the end of the introduction to Analysis situs Poincari writes, "I do not think then that I have engaged in useless work in writing the present memoir". The reader more than a century later will find that he or she will not engage in useless work in reading Poincari's papers. We have Stillwell to thank for making such work easier with his translation."
-- John McCleary, Mathematical Reviews
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