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The Poincaré Conjecture: In Search of the Shape of the Universe

3.85  ·  Rating details ·  767 ratings  ·  73 reviews
Henri Poincaré 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 Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the univers ...more
Hardcover, 304 pages
Published March 6th 2007 by Walker Books (first published 2007)
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Apr 21, 2015 rated it really liked it
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
Mar 29, 2007 rated it liked it
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
Dec 19, 2011 rated it did not like it  ·  review of another edition
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.
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.
Jun 24, 2008 rated it really liked it
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!
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.
Aug 15, 2007 rated it it was amazing
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.
Daniel Cunningham
Jan 10, 2014 rated it liked it
Shelves: library, popsci
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-
Jan 26, 2010 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
Apr 04, 2013 rated it really liked it
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.
Apr 24, 2008 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.
May 26, 2016 rated it it was ok
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.
May 03, 2009 rated it really liked it
Fun book. Made me want to read an introductory book on topology...
Jun 30, 2008 rated it liked it
p. 47: "absolute precision buys the freedom to dream meaningfully."
Kaushik Satapathy
Feb 11, 2018 rated it really liked it
Amazingly traces the development of topology over the years and it's culmination in the Poincare Conjecture. A must-read for any math enthusiast.
G.R. Reader
Apr 26, 2015 rated it did not like it
Puts the wanker into Poincaré conjecture. Too many cute biographical details, not enough Ricci flow.
Andrew Thibodeau
Oct 18, 2010 rated it really liked it
Shelves: mathematics
The universe is a infinite topologically bounded three dimensional manifold. Did I say that right?
Really digging this book!
May 01, 2009 rated it really liked it
Shelves: non-fiction
Fun book on history of topology and Poincare conjecture in particular.
May 09, 2018 rated it liked it
The goal of this book, as stated, was to outline the buildup to and eventual solution of the Poincare conjecture in a way that non-mathematicians would be able to follow. As someone who studied some graduate math, I feel comfortable saying that O'Shea partially achieved his goal. Definitely my passing familiarity with some of the topics mentioned made my reading of the book easier. Since even with that understanding I simply passed by some of the content, there are parts that a non-mathematician ...more
Mar 03, 2019 rated it it was amazing  ·  review of another edition
Shelves: mathematics
The book encapsulates the fascinating journey of mathematical development centered around topological concepts that led to a conjecture in the early 1900s by the great French mathematician Henri Poincaré. According to this conjecture , every simply connected closed 3 dimensional manifold is topologically similar to a 3-sphere. The author carefully presents the concepts and reiterates them wherever needed through out the book for laymen interested in mathematics. The author knits the socio-politi ...more
Al Maki
Notice that the subtitle is "in search of the shape of the universe," not "the shape of the universe". The book is about what mathematicians have been able to determine about the shape and that is not very specific: it's all connected, it's finite, it has no boundary. So even though it's finite and you could go anywhere in it, you would never get to the end of it. A counter-intuitive idea, but the book presents some comprehensible possibilities of how that might work. I very much enjoyed it for ...more
May 10, 2019 rated it really liked it
Shelves: history
very clean exposition
Monthir Zadjali
May 27, 2018 rated it liked it
Overall the book doesn't talk about math and physic. It has a lot of information that will in-light you for many things related to the shape of the universe.
Tom Gray
Aug 02, 2018 rated it it was amazing  ·  review of another edition
This book is a clear exposition of the Poincare Conjecture and teh research program in which it fits. it makes teh overall goal of topology clear and the reason why this is important
Yuganka Sharan
Too technical for a layman audience.
Eli Decker
Aug 18, 2018 rated it liked it
sometimes the concepts were explained in depth, sometimes no attempt was made. but very fascinating
Vinh Dang
Oct 29, 2018 rated it really liked it
Shelves: science, non-fiction
A very good introduction to the problem: there is no way to know the shape of the earth without a satellite. And the same for the universe.
Dec 28, 2015 rated it really liked it
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 me a
Oct 30, 2016 rated it liked it
I found this a somewhat approachable book about crazy difficult mathematics. There is plenty of easy reading about the lives and the history of math and an journalistic account of the story of the refusal of the million dollar prize when this conjecture was proven by 2006. I was a math major in college and I found topology very difficult and did not study non-Euclidian geometry either. These are two of the basic areas of study involved in the conjecture but the basic idea the author conveys is h ...more
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