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The Poincare Conjecture

3.79  ·  Rating Details ·  556 Ratings  ·  62 Reviews
Henri Poincar was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincar conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. ...more
ebook, 304 pages
Published May 26th 2009 by Walker Books Ltd (first published 2007)
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Apr 22, 2015 Manny rated it really liked it  ·  review of another edition
Recommends it for: Anyone who wants to understand what math is really about
My meeting with this book fell considerably short of love at first sight. Not saw it on sale yesterday at a Melbourne bookstore and asked if I thought it might be interesting. I picked it up, glanced at the less-than-brilliant cover and leafed through it for a minute or two; the writing seemed lackluster and the first anecdote I found was one I'd seen before. I was about to put it back when I reconsidered. It cost $10 and was evidently an easy read. I'd always wondered what the deal was with the ...more
Aug 30, 2016 Jafar rated it liked it  ·  review of another edition
So – the shape of the universe. It’s a giant ball, right? Especially when you think of its beginning in a big bang. But that brings up the awkward question of what’s outside the ball. Space (universe) is not infinite. It’s believed to be finite, but without a boundary. It becomes easier to understand this if you consider two-dimensional beings living in a spherical (the two-dimensional surface of a ball) universe. Their universe is finite, but has no boundaries. There are no edges, and if they s ...more
Jul 15, 2008 Camille rated it really liked it  ·  review of another edition
Shelves: science-math
I've been interested in the Millennium problems since I first read about them several years ago. It was exciting to read about the first one to be solved. I never took topology in college, though, so I have to admit that much of this went right over my head. If you wanted to know without reading all the math, yes, the Poincare conjecture turned out to be true. Pretty cool stuff!
Dec 20, 2011 Steven rated it did not like it  ·  review of another edition
Shelves: mathematics, 2011
There was some explanation earlier in the book, but later explanation was poor. I came away with little understanding of how the Poincare conjecture was solved. The book was a disappointment, but did provide a reference to book by Jeffrey Weeks that might offer better layman-level explanations of topological concepts.
Vilém Zouhar
This book was in the 'mathematics' section in the library and I was expecting something more mathematics focused. Hence I was disappointed by the history lesson this book turned out to be. Except for the initial confusion, it was a nice read.
Daniel Wright
Why is this book not more widely read? It's at least as good as books like Fermat's Last Theorem, with far more mathematical content. If any layman wants a glimpse into the world of top-level mathematics, I cannot recommend a better book.
Aug 15, 2007 Sean rated it it was amazing  ·  review of another edition
Recommends it for: anyone who has ever asked me what "mathematical research" is
As a recent grad student in mathematics I found this book incredibly interesting. It made me want to go on and get my Ph.D. in manifold theory.
Marco Dal Pozzo
May 07, 2013 Marco Dal Pozzo rated it it was amazing  ·  review of another edition
Shelves: matematica, scienza
Henri Poincaré enuncio' una congettura: "E' possibile che il gruppo fondamentale di una varieta' sia l'identita', ma che la varieta' in questione non sia omeomorfa alla sfera tridimensionale?"

A chi non ha studiato matematica, tante delle parole presenti nella congettura di Poincaré - siamo a cavallo tra il 1800 e il 1900, non dicono niente. Ma sfido chiunque a non rintracciare in esse un qualche fascino.

Questa congettura e' legata ad una domanda che, se possibile, e' ancora piu' affascinante: "q
Daniel Cunningham
This was a decent book, but a bit of a hard read.

Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail; how one concept leads to another; how concepts fail to connect. For me, at least, this was difficult to follow. Granted, in order to truly understand what is being discussed, you would need to understand the mathematics; perhaps this is just an insurmountable problem in trying to translate high-level and di
Feb 15, 2010 Chris rated it it was ok  ·  review of another edition
Recommends it for: People who love math but have the patience to listen to someone poorly explain topology
Shelves: 2010-books
This book was about as painful as reading the book of Genesis: its pages mostly comprise a chronological list of mathematicians ("and so-and-so's work begot so-and-so's thesis"...) interspersed with definitions sans explanation or example (a group, a ring, etc.). The highlights were the only occasional example of geometry in mathematical physics or when the author found time to elaborate a little more on an interesting property of a certain metric or surface structure.

In fact, the best part of
Saggio interessante sulla risoluzione di uno dei 7 millennium problems (si vince un milione di dollari per la soluzione di ognuno). Lo scienziato che ha risolto la congettura, il russo Grigori Perelman, ha rifiutato sia il premio in denaro, sia la medaglia Fields, per la quale ogni matematico sulla faccia della terra penso sia disposto a uccidere.
Il libro è abbastanza divulgativo, ma ci vogliono nozioni di topologia per comprendere appieno di che cosa si stia parlando.
Tuệ Trần
Để bàn về vũ trụ, hãy nhìn về trái đất.

Trước khi quả quyết trái đất hình cầu, người ta cho rằng trái đất là một cái dĩa phẳng, và đâu đó tồn tại một "The end of the world".

Giờ đây chúng ta cũng có thể ngồi một chỗ mà tự tin phán rằng: trái đất không có nơi tận cùng. Nó không được giới hạn bởi bất kỳ một đường biên giới nào. Thế nhưng không vì thế mà nó không bị giới hạn bởi một diện tích vốn có, không cách chi thay đổi được.

Hình dạng vũ trụ cũng hứa hẹn một điều tương tự.

Katlego Makgoale
Apr 04, 2013 Katlego Makgoale rated it really liked it  ·  review of another edition
I enjoy books about mathematics. Not a daunting read, easily understood and very clear explainations.
Takes some imagination and thinking to get ones mind around the concepts discussed but all in all an awesome book. One of my favorite when it comes to popular science.

Its kind of like a "history of topology", "story of a frustrating problem and the journey to its solution" and discussion between you and the author about what topology really is about all wrapped into one book.
Jun 05, 2016 Katie rated it it was ok  ·  review of another edition
The conjecture from which the title comes doesn't make an appearance until 136 pages into this 200 page book. Poincare himself is only present for about 1/10th of the book. It's more of a very brief history of geometry and topology than a treatment of the problem.
Also, the resolutions of the images in the book are so poor it's as if the publisher printed out jpegs and made Xeroxes of them.
Sep 19, 2008 Richard rated it it was amazing  ·  review of another edition
Recommends it for: Nerds, history buffs, math geeks
Shelves: mathamatics
I originally purchased this book to learn more about Gregory Perelman and the fields medal he turned down, but over the course of the book you get such a detailed explanation of the history of math, that I spent just as much time in wikipedia as I did reading this book. Fantastic read, for every type of math fan out there, of every level of proficiency.
G.R. Reader
Apr 26, 2015 G.R. Reader rated it did not like it  ·  review of another edition
Puts the wanker into Poincaré conjecture. Too many cute biographical details, not enough Ricci flow.
Aug 04, 2008 Nick rated it liked it  ·  review of another edition
p. 47: "absolute precision buys the freedom to dream meaningfully."
Andrew Thibodeau
Oct 18, 2010 Andrew Thibodeau rated it really liked it  ·  review of another edition
Shelves: mathematics
The universe is a infinite topologically bounded three dimensional manifold. Did I say that right?
May 03, 2009 Gus rated it really liked it  ·  review of another edition
Fun book. Made me want to read an introductory book on topology...
May 01, 2009 Richie rated it really liked it  ·  review of another edition
Shelves: non-fiction
Fun book on history of topology and Poincare conjecture in particular.
Really digging this book!
Jan 02, 2016 Jake rated it really liked it  ·  review of another edition
Preview: I will preface this by saying that my knowledge of topology is limited. I am a computer science undergrad, who learned most of my topology from Tadashi Tokieda's set of lectures that can be found on African Institute for Mathematical Sciences' youtube page, various sources scattered on the internet and messing around in Wolfram Alpha with examples. I've found it incredibly useful in helping me understand proofs in other mathematical disciplines.

Bolyai & Reimann section stood out to
Jul 24, 2011 Pasteurisiert rated it it was amazing  ·  review of another edition
Wie falte ich Landkarten, die eine endliche Oberfläche darstellen jedoch noch Ränder haben, zu einer endlichen, randlosen sphärischen Oberfläche (=Globus) zusammen? Das kann man sich noch irgendwie vorstellen. Aber wie erzeuge ich aus zwei Kugeln (endliches Volumen mit Rand, nämlich der Kugeloberfläche) eine Dreisphäre, die ein endliches Volumen hat, aber keinen Rand???

Mit sowas und noch viiiel komplizierter befasst sich heute die Mathematik und unterstützt dabei die Physik und die Astronomie.

Maurizio Codogno
Quando Grigori Perelman rifiutò il milione di dollari che il Clay Institute gli aveva assegnato per la dimostrazione della Congettura di Poincaré, la notizia raggiunse le prime pagine di tutti i giornali. Non che la gente sapesse che diavolo fosse questa congettura, a dire il vero; ma l'idea di tutti quei soldi li stuzzicava. Fortunatamente ci sono stati alcuni matematici che hanno pensato non tanto di raccontare la dimostrazione quanto di riuscire a dare uno sguardo generale sui temi trattati, ...more
Feb 01, 2015 Whitney rated it it was amazing  ·  review of another edition
Shelves: math
This book was recommended to me by my husband. Wanting to understand more about his work as a topologist, I agreed to read this book. I found it very interesting. I liked learning about the history of this conjecture, and how Perelman came up with his proof. I found most of the information presented in a way that allowed for a non-mathematician to understand what was being discussed. I admit, some of the math was beyond me, but on the whole, it was understandable. While I preferred the history p ...more
Jan 07, 2012 Ron rated it liked it  ·  review of another edition
This is a terrific read. It must be read as a historical introduction to the subject, rather than an effective explanation for the nonmathematician. There are simply too many terms containing highly specialized jargon that are tossed about for a nonspecialist to follow effectively.That said, there is a very nice story spun here, about the commotion caused by the solution of a very hard problem in the math community. The origin of the problem, as well as the people involved, are brought to life w ...more
Jul 23, 2010 Scott rated it did not like it  ·  review of another edition
Shelves: sci-tech
This book was Donal O'Shea's first work for a popular audience. Unfortunately, his style does not get beyond what the popular audience might expect from an Ivy-League professor specializing in topology. His writing style alternated breezy sections on the personalities of mathematicians and the state of their contemporary world with dense, barely comprehensible (to the non-mathematical layman) sections describing the mathematics leading up to the Poincare Conjecture and its proof. I found it read ...more
Chelsea M
Jun 15, 2015 Chelsea M rated it liked it  ·  review of another edition
Shelves: non-fiction
I felt like the title was a little misleading. The Poincare conjecture is only mentioned in the last few chapters, and the majority of the book is taken up by going over the history of mathematics and topology. I've already read a number of books on mathematics, so I found this somewhat repetitive. However, I did like this book. It accomplishes what I consider to be the single most important goal of a book about a mathematical problem: making me understand what the problem actually is, and how i ...more
Dan Adelman
I think it'd be unfair of me to give this book a star rating, since I really had a hard time understanding it. That may be more a reflection of me than the book, and I wouldn't want to drag down its average.

I will say that I am pretty comfortable with math books written for a lay audience. I had no issues with Fermat's Last Theorem (Simon Singh), Journey through Genius (William Dunham), or the Golden Ratio (Mario Livio). So I'd say if you already have a little background in topology (which I do
Feb 28, 2015 Milad rated it did not like it  ·  review of another edition
The first quarter of the book gives you a lot of cool info on the shape of the universe, Grigori Perelman, and Poincare. But that's it! Because after that, it begins throwing some really unnecessary paragraphs (and chapters) on the biography of the people.

That's what I hate about this book: unnecessary information. Some sections are completely unneeded and even most of the times, it's somewhere you don't expect it to be, right in the middle of a serious work!

Perhaps it's because I'm a math majo
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