The Poincaré Conjecture by Donal O'Shea

The Poincaré Conjecture

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 universe. The conjecture states that there is only one shape possible for a fini...

Details The Poincaré Conjecture

TitleThe Poincaré Conjecture
Release DateMar 6th, 2007
PublisherWalker Books
GenreScience, Mathematics, Nonfiction, History, Physics

Reviews The Poincaré Conjecture

  • Manny
    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 re...
  • 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...
  • 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.
  • 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.
  • 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!
  • 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.
  • Sean
    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
    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 domand...
  • 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 rius...
  • 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 insurmountabl...
  • Chris
    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 metri...
  • 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 ch...
  • 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 ab...
  • Katie
    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.
  • Richard
    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.
  • Nick
    p. 47: "absolute precision buys the freedom to dream meaningfully."
  • Andrew Thibodeau
    The universe is a infinite topologically bounded three dimensional manifold. Did I say that right?
  • G.R. Reader
    Puts the wanker into Poincaré conjecture. Too many cute biographical details, not enough Ricci flow.
  • Gus
    Fun book. Made me want to read an introductory book on topology...
  • Kaushik Satapathy
    Amazingly traces the development of topology over the years and it's culmination in the Poincare Conjecture. A must-read for any math enthusiast.
  • Richie
    Fun book on history of topology and Poincare conjecture in particular.
  • Van
    Really digging this book!
  • Nicholas
    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...
  • Arko
    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 intereste...
  • Tom Gray
    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
  • Monthir Zadjali
    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.
  • iri
    very clean exposition
  • Eli Decker
    sometimes the concepts were explained in depth, sometimes no attempt was made. but very fascinating
  • Vinh Dang
    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.