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The Poincare Conjecture: In Search of the Shape of the Universe (Englisch) Taschenbuch – 26. Dezember 2007


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Produktinformation

  • Taschenbuch: 293 Seiten
  • Verlag: Frank R Walker Co (Il); Auflage: Reprint (26. Dezember 2007)
  • Sprache: Englisch
  • ISBN-10: 0802716547
  • ISBN-13: 978-0802716545
  • Größe und/oder Gewicht: 14,1 x 2,2 x 21,2 cm
  • Durchschnittliche Kundenbewertung: 3.5 von 5 Sternen  Alle Rezensionen anzeigen (2 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 284.982 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

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Produktbeschreibungen

Pressestimmen

Praise for The Poincaré Conjecture:

“O'Shea inspires readers to note the beauty, application, and humanity involved with this mathematical journey.”—Library Journal

O'Shea describes mind-bending structures in topology as clearly as most of us can “describe a cube…”—Publishers Weekly

“Accessible…. valiant nonnumerical clarity…”—Booklist
 
"Fascinating….[O'Shea] does a good job of explaining the mathematics involved in solving the conjecture…"—Wall St Journal

“A layman’s guide to this mathematical odyssey is long overdue, and this one will appeal to math whizzes and interested novices alike.”—Discover magazine

“O’Shea shows that, just like chasing ‘sensual passions,’ the single-minded, relentless pursuit of proof can be a creative process.”—Chicago Tribune

“O’Shea tells the whole story in this book, neatly interweaving his main theme with the history of ideas about our planet and universe. There is good coverage of all the main personalities involved, each one set in the social and academic context of his time.”—New York Sun
 
"Donal O’Shea has written a truly marvelous book. Not only does he explain the long-unsolved, beautiful Poincaré conjecture, he also makes clear how the Russian mathematician Grigory Perelman finally solved it. Around this drama O’Shea weaves a tapestry of elementary topology and astonishing concepts, such as the Ricci flow, that have contributed to Perelman’s brilliant achievement. One can’t read The Poincaré Conjecture without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us."—Martin Gardner, author of The Annotated Alice and Aha! Insight

"The history of the Poincaré conjecture is the story of one of the most important areas of modern mathematics. Donal O’Shea tells that story in a delightful and informative way—the concepts, the issues, and the people who made everything happen. I recommend it highly."—Keith Devlin, Stanford University, author of The Millennium Problems

"In The Poincaré Conjecture, Mr. O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman . . . Mr. O'Shea does a good job of explaining the mathematics involved in solving the conjecture . . . [He] avoids cliché (we're spared the usual reference to coffee cups turning into doughnuts as an explanation of how surfaces might stretch without closing holes), and he tries to keep things lively."—Amir D. Aczel, The Wall Street Journal

Synopsis

"The Poincare Conjecture" tells the story behind one of the world's most confounding mathematical theories. Formulated in 1904 by Henri Poincare, his Conjecture promised to describe the very shape of the universe, but remained unproved until a huge prize was offered for its solution in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O'Shea explains the maths behind the Conjecture and its proof, and illuminates the curious personalities surrounding this perplexing conundrum, along the way taking in a grand sweep of scientific history from the ancient Greeks to Christopher Columbus. This is an enthralling tale of human endeavor, intellectual brilliance and the thrill of discovery. -- Dieser Text bezieht sich auf eine andere Ausgabe: Taschenbuch .

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2 von 3 Kunden fanden die folgende Rezension hilfreich Von M. D. Migge am 21. November 2008
Format: Taschenbuch
Die Poincare-Vermutung ist eines der Millenium-Probleme für deren Lösung das Clay Institute im Jahre 2000 einen Preis von 1 Millionen Dollar ausschrieb. 2006 bewies der russische Mathematiker Gregory Perelman die Geometrisierungs-Vermutung - eine Verallgemeinerung der Poincare-Vermutung und löste damit eines der wichtigsten Probleme der Mathematik. Insofern ist es wichtig, dass es ein Buch gibt das dieses Problem auch Nicht-Mathematikern näher bringt. Donal O'Shea führt den Leser durch die lange Geschichte des Problems und seiner Lösung. Genau hier liegt aber der Schwachpunkt des Buches. Die geschichtlichen Abschnitte des Buches sind teilweise schwammig und ein roter Faden ist oft nicht erkennbar. Schade, denn O'Shea versteht es gut das komplexe mathematische Problem auch Laien zu veranschaulichen. Ich hätte mich gefreut, wenn Simon Singh sich dieses Themas angenommen hätte. Denn mit Fermat's Last Theorem hat er schon sehr erfolgreich einen populärwissenschaftlichen Zugang zu einem ähnlich wichtigen Problem geschaffen.
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Format: Taschenbuch Verifizierter Kauf
O'Shea hat ein gutes Buch zu einem überaus komplexen Thema abgeliefert. Da ich kein Laie bin, kann ich nur bedingt beurteilen, wie gut der Zugang sonst wäre. Ich habe allerdings schon Material aus dem Buch sehr gut verwendet, um Vorträge vor Laienpublikum (unter anderem sogar vor Schülern der 9. Klasse) zu halten. Die Resonanz war bis dato immer sehr gut.

O'Shea geht sehr detailliert auf die Geschichte der (algebraischen) Topologie ein. An einigen Stellen, wie ein anderer Rezensent das schon angemerkt hat, könnte man hier noch etwas raffen bzw. einen klareren roten Faden haben. Es ist an manchen Stellen nicht ganz ersichtlich, worauf O'Shea hinauswill.

Ein weiterer Kritikpunkt ist eher, dass das Buch zu kurz ist. Wegen mir hätte man noch viel mehr über Perelmans Beweis bzw. seine Beweistechniken schreiben können. Ich vermute, dass das allerdings den Rahmen deutlich sprengen würde.

Insgesamt ein gutes Buch --- ob es für ein ebenso breites Publikum geeignet ist wie andere Werke, bezweifle ich allerdings. Wer es an Eltern verschenken möchte: Einfach gemeinsam durchgehen. Hat meinen Eltern und mir viel Spaß gemacht, endlich mal zu verstehen, was der Sohn so den lieben Arbeitstag über treibt.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 31 Rezensionen
78 von 81 Kunden fanden die folgende Rezension hilfreich
beautiful mathematics 9. Mai 2007
Von Nim Sudo - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
The Poincare conjecture was one of the most beautiful and important unsolved problems in mathematics for the last century. It has recently been solved, in a remarkable story, with the final breakthrough due to Perelman, who was awarded the Fields medal for his work but declined to accept it. The Poincare conjecture concerns the possible shapes of three-dimensional spaces, such as the universe that we live in. This book explains what the Poincare conjecture says, and tells the history of its formulation and proof. There are no equations in the main text (and only a couple in the endnotes), so in principle anyone can read this.

The book does a nice job of motivating the Poincare conjecture, by first discussing the possibilities for the shape of the two-dimensional surface of the earth (before we had explored the whole earth and figured out that it is a sphere), and then discussing the possibilities for the shape of the three-dimensional universe (which is currently unknown). The book also does a good job of explaining what modern geometry is about and how this has drastically changed since Euclid.

There were three things about the book that I didn't like. (Bear in mind that I do topology for a living so I am maybe being too critical here.) First, there is a lot of history, not only of the people who worked on the Poincare conjecture, but also of the institutions and political environment in which they worked. A lot of this seemed to me to have little relevance to the Poincare conjecture and didn't hold my interest. Second, in between these historical asides, the mathematical sections often rush through too much material, in not enough detail to be really understandable to a lay reader. Third, the pictures were subpar. Many of them looked like they were drawn with MacPaint, and are reproduced so small and dark that they are hard to make out. At least one picture is mathematically incorrect: it shows a disc of paper with a wedge cut out being folded to produce a spherical cap, but really one would get a cone instead. This mistake is unfortunate since it contradicts the whole point of the chapter in which it appears. In short, if I were writing this book, I would want to trim the history, remove some of the mathematics, explain the rest of the mathematics in more detail, and improve the pictures.

Perelman's papers finishing off the Poincare conjecture were sketchy, and a lot of work by other mathematicians was required to turn his papers into a detailed proof. There was some (in my opinion silly and unfortunate) controversy in the media regarding how much credit should go to various people for this. The book does not go into this controversy, which I think is a good thing (although it gives some hints without fully explaining the situation). There is also no discussion of why Perelman made the unusual decision to decline the Fields medal. Maybe no one really knows.
79 von 86 Kunden fanden die folgende Rezension hilfreich
I'm Not Sure Who the Real Audience Is for This Book 21. Juli 2007
Von Steve Koss - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Describing some of Henri Poincare's work, author Donal O'Shea writes on page 132 that Poincare "produced an infinite family of closed three-dimensional manifolds that are not homeomorphic to one another and showed that one can have nonhomeomorphic manifolds with the same Betti numbers and, in fact, with the same Betti numbers as a sphere." Oh, so you don't know what a Betti number is? Well, O'Shea's Glossary of Terms describes it as "an integer counting that number of inequivalent manifolds of a given dimension in a manifold that do not bound a submanifold of one dimension higher." If this is not quite your cup of mathematical tea (as it is not quite mine, despite my B.S. in mathematics from a highly-regarded engineering school), then THE POINCARE CONJECTURE might just be a full teapot that you want to skip.

A fundamental rule of nonfiction is to identify and write for your intended audience, and it is difficult to imagine who O'Shea saw here as his audience. THE POINCARE CONJECTURE addresses a mathematically famous but publicly obscure hypothesis from the general field of topology, the study of shapes and curvature. Filled to overflowing with historical background, dating back to Euclid's original five postulates for plane geometry, the main body of O'Shea's book is exclusively textual. Even the hypercritical Ricci flow equation, the main vehicle through which Grigory Perelman achieved his landmark proof, is relegated in abbreviated form to the footnotes. All of this, combined with O'Shea's opening chapters attempting to explain topological manifolds, suggests a book targeted at nonmathematicians. Yet as the excerpt above demonstrates, the author seems too often not to have found the necessary nonmathematical explication to reach successfully a nonprofessional mathematical audience. Conversely, those who are sufficiently mathematically versed to follow O'Shea's elucidation will likely find it far too light in pure mathematical content.

In point of fact, author O'Shea defers even stating or describing the Poincare Conjecture until page 45: "...the assertion that any compact three-manifold on which any closed path can be shrunk to a point, is the same topologically as (that is, homeomorphic to) the three-sphere." What follows is 136 pages of interesting mathematical history tracing from Euclid through Gauss, Bolyai, and Lobachevsky to Riemann, Felix Klein, Poincare himself, and then on to David Hilbert, Smale, Thurston, Richard Hamilton, and finally, Perelman. The final eighteen pages attempt in some small way to capture the excitement behind Perelman's revelation of the solution to one of the Clay Institute's seven millennium problems (each with an accompanying million dollar prize), but the conclusion is disappointingly anticlimactic. Perelman being the professional hermit and cipher to which he apparently aspires, O'Shea gives us little sense of the man and his background and virtually no sense of his labors (and, presumably, travails) over this infamous hypothesis. Perelman appears in this book as he appeared before the mathematical community in 2003 - on the stage for too precious few moments and then whisked away, backed to self-selected obscurity in Russia. Compare this to Simon Singh's brilliant treatment of Andrew Wiles and his search for the proof of the so-called Fermat's Last Theorem.

In that same final eighteen pages, O'Shea returns to the "real world" question that his book's subtitle suggests would be answered as a result of proving Poincare's Conjecture: the shape of the universe. He devotes slightly over one page to revealing his answer -- that "the question...is still very much open." The teaser subtitle is just that, a teaser for the scientifically interested and inclined. Gee, thanks.

THE POINCARE CONJECTURE is long on the history of non-Euclidian geometry and the various subdisciplines of topology and unsatisfying short on the actual proof of its eponymous theorem, the peculiar man behind that proof, and the real world implications of the result. The text itself runs 200 pages but offers just short of 100 more space-filling pages larded with footnotes, glossary of terms, glossary of names, timeline, bibliography, further reading, art credits, acknowledgments, and an index. Frankly, the New Yorker's 14-page article about Perelman in August 2006 by Nasar and Gruber was more informative. For this book, a gentleman's 3 stars is the most I can muster.
9 von 9 Kunden fanden die folgende Rezension hilfreich
Proofread? 27. März 2008
Von J.D. WHITE - Veröffentlicht auf Amazon.com
Format: Taschenbuch
This book feels as if the author tried to edit it himself, complete with embarassingly frequent mistakes in grammar and punctuation, not to mention horribly botched illustrations.

While several of the reviewers here have stated that they weren't satisfied with the mathematical "meatiness" of this book, I represent the lay side that found plenty of challenge following the concepts here (most of which I was seeing for the first time). As such, the histories were welcome asides to the often very long, hard to follow, and dubiously worded (AND poorly illustrated) technical paragraphs.

Still, for someone who used this book as an introduction to topology, it was a fascinating read...in parts. If it ever sees another edition that allows for decent editing and proofreading, I imagine I would tack a fourth star onto the review.
11 von 12 Kunden fanden die folgende Rezension hilfreich
Ambitious, but Overreaching 4. Juni 2007
Von Simmoril - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
I myself am not a mathematician, but I am a fan of mathematics in general. I had been following Grigori Perelman's work in the news ever since he gave his lectures at MIT, and had been awaiting a book to cover this amazing story.

The book itself does quite a bit of leg work covering the history behind the Poincare Conjecture and the lives of the key contributors (Gauss, Riemann, Poincare, Klein, etc.). In the first few chapters, the author gives the reader a 'crash course' in topology (as well as talking about how the field of topology came to be), and in the last few chapters, talks about the failed attempts at proving the conjecture by various mathematicians, and finally, of course, the successful attempt by Perelman.

While making my way through this book, it felt like the author was attempting to do too much in too small a space. At exactly 200 pages of text (the last 90 pages or so are footnotes, appendices, and index), it's pretty much a featherweight when you consider the material the author is trying to cover. The book at once tries to be a history lesson, a treatise on the importance of mathematics (or learning in general depending on your interpretation), a short tutorial on topology, and a brief outline of the conjecture and it's proof. Each of these topics is covered in varying detail at the expense of brevity in others. I was shocked to see that talk about Perelman's proof occupied a scant 10 or so pages at the end of the book.

The history lesson, albeit very well researched and nicely written, shouldn't have been the main focus of the book. The author should have spent more time helping the reader gain a better understanding of topology, as well as helping to connect the dots between the various topics (how Perelman solved the problem of singularities in Ricci flows, how Ricci flows help prove Thurston's Geometrization Conjecture, and how Thurston's Geometrization Conjecture implies Poincare's Conjecture).

In all honesty, what I was hoping for was this book to be to Poincare's Conjecture what Simon's Singh's classic Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem was to Fermat's Last Theorem. Although a good try, it still falls short of my expectations.
10 von 11 Kunden fanden die folgende Rezension hilfreich
The first solution to one of the Millenium problems 1. August 2007
Von Jaume Puigbo Vila - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
Lee Carlson's review casts some doubt about the validity of Perelman's proof, but this is not what the mathematical community of experts is saying. Even the people who have filled in the details of Perelman's proof agree that all the merit is his. As this book shows, Morgan clearly states in his address in the ICM in Madrid that Perelman proved the Poincaré's conjecture and much more (Thurston's conjecture) and introduced new methods that will be used by many mathematicians in the coming years.

O'Shea's book is a good complement to Szpiro's. O'Shea is more encompassing and starts the history of the conjecture going back as far as Babylonic mathematics. It only gives the biography of Poincaré in page 111 and misses some of the details of the controversy provoked by Yau and explained in detail in an article in New Yorker and also in the book by Szpiro. It also has some more technical details, but both books are good reading for a mathematically educated reader.
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