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# The Poincare Conjecture

by
Donal O'Shea

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.
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ebook, 304 pages

Published
May 26th 2009
by Walker Books Ltd
(first published 2007)

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## Community Reviews

(showing 1-30)

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

*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.

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 ...more

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

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

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 ...more

In fact, the best part of ...more

Il libro è abbastanza divulgativo, ma ci vogliono nozioni di topologia per comprendere appieno di che cosa si stia parlando.

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.

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.

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.

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?

Really digging this book!

Bolyai & Reimann section stood out to ...more

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

Ne ...more

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 ...more

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 ...more

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“The willingness to reexamine lifelong beliefs because of conflicting data takes enormous courage, and contrasts sharply with recent examples of public discourse in which our political, cultural, and religious leaders have fit data to preconceived theories.”
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“Sadly, we know almost nothing about Euclid (c. 325-c. 265 BCE).32 We know even less about him than we do about Pythagoras, and what little we do know has been hotly contested by scholars. Euclid wrote at least ten books, only half of which have survived. A number of mutually consistent indications suggest that he lived after Aristotle and before Archimedes. He was one of the first mathematicians at the great library of Alexandria and there had gathered a group of talented mathematicians about him. Legends about him abound, many as (possibly apocryphal) insertions in other mathematicians' works. One tells that Ptolemy asked Euclid for a quick way to master geometry and received the reply, "There is no royal road to geometry." Another tells of a student who, after encountering the first proposition in the Elements, asked Euclid what practical use studying geometry could have. The mathematician allegedly turned to his slave and replied dismissively, "Slave, give this boy a threepence, since he must make gain of what he learns.”
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