The Poincare Conjecture
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The Poincare Conjecture

3.78 of 5 stars 3.78  ·  rating details  ·  360 ratings  ·  42 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 univers...more
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Published (first published 2007)
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Steven
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.
Camille
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!
Marco Dal Pozzo
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...more
Jafar
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
Chris
Feb 15, 2010 Chris rated it 2 of 5 stars  ·  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...more
Katlego Makgoale
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.
Richard
Sep 19, 2008 Richard rated it 5 of 5 stars  ·  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.
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...more
Sean
Aug 15, 2007 Sean rated it 5 of 5 stars  ·  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.
Andrew Thibodeau
The universe is a infinite topologically bounded three dimensional manifold. Did I say that right?
Richie
Fun book on history of topology and Poincare conjecture in particular.
Nick
p. 47: "absolute precision buys the freedom to dream meaningfully."
Gus
Fun book. Made me want to read an introductory book on topology...
Pasteurisiert
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.

Ne...more
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
Ron
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
Scott
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
Robert
An easy to read introduction to the historical and substantive background of one of the most important conjectures in mathematics. The Poincare Conjecture was proved by Grigori Perelman in 2002, who won a Millennium Prize, as well as the Fields Medal for his work. He rejected both awards. The "conjecture" (now a theorem) has important consequences regarding the shape of the universe. It states that a 3-dimensional manifold which is compact, has no boundary and is simply connected must be homeomo...more
Toby
A pretty good discussion of the Poincare Conjecture and its history. I found the historical discussions more interesting than the mathematical discussions since the mathematics is on the technical side, requiring the reader to remember a lot of technical terms. More pictures and examples would probably have helped.

I was also left wanting to know more about Perelman himself. As apparently most other people do, Donal O'Shea makes Perelman's reclusive personality part of the story, and this is wher...more
Chastity
I really enjoyed this book, but it dragged a little through some of the biographies of mathematicians. Also, if you have a feel for math you'll enjoy the book even if you didn't study a lot of mathematics in college. That also might make some of the explanations in the first half of the book a little too lengthy. Overall a well-written book on the history of math and the mathematicians that contributed to the knowledge that allowed such a conjecture to be formulated, and the ultimate ability to...more
Claudia
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.
Stefano Ottolenghi
Ma chi me lo fa fare, basta!
Leroy
Topology is a lot harder than it may seem to some. The second half of this book was completely over my head. I gave the book two stars because the ratings are based on my subjective personal experience in reading it ("it was ok"), but it is clearly an expertly written book on an extremely complex topic. I don't know whether it is possible to dumb it down, so to speak, to make these concepts more accessible, but I imagine I would enjoy such a book more.
William
Even though I graduated in Mathematics, I never really delved into topology. The book was a mixture of interesting pieces and portions that were hard to understand, but overall a good history of the evolution of mathematical thought. I'd probably rate it higher if I'd been able to read it in a few days -- unfortunately schedules were such that it took me four months to complete.
Dallas
Not many people can turn the pusuits of a reclusive Russian living with his mother in a bug-infested St. Petersburg apartment into a story of wonderment, but O'Shea gives a good development of the background leading up to Perelman's proof; the detail is what really makes this a good read. Now if only someone can figure out Riemann's hypothesis...
David
Despite being written for a non-mathematical audience, it was quite confusing. I enjoyed the history sections but got lost in most of the topology. I only finished it because I have a really hard time starting a book and not finishing it. Someone who doesn't have at least a basic interest in math will probably not enjoy this book.
Rob
A bit slow going at first, with what I guess was a necessary background for those that don't know what it means for an n-dimensional manifold to be homeomorphic to another n-dimensional manifold. However, once it got into the history of the development of topology and especially the life of Poincare it became much more interesting.
Kristin McPhillips
Inspiring. Picked this up at a used book store because I wanted to learn about the shape of the universe. Turns out its more about math history. I definitely have a better understanding of the poincare conjecture and it's proof, and it's a great story it's just not as sciency as I thought it would be
Haider A
This is a nice book that is about many thing, mostly geometry and the mathematical work of Poincare. Unfortunately, the title of the book is missleading, I have expected to read more about how the conjecture was proved, but I ended up trying to remember what the conjecture was all about.
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