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The Poincare Conjecture: In Search of the Shape of the Universe
 
 
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The Poincare Conjecture: In Search of the Shape of the Universe (Hardcover)

by Donal O'Shea (Author) "Revolutions in mathematics are quiet affairs ..." (more)
3.4 out of 5 stars See all reviews (5 customer reviews)
RRP: £17.99
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Product details

  • Hardcover: 304 pages
  • Publisher: Allen Lane (26 April 2007)
  • Language English
  • ISBN-10: 1846140129
  • ISBN-13: 978-1846140129
  • Product Dimensions: 21.8 x 14 x 3.2 cm
  • Average Customer Review: 3.4 out of 5 stars See all reviews (5 customer reviews)
  • Amazon.co.uk Sales Rank: 301,313 in Books (See Bestsellers in Books)

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Product Description

Martin Gardner, Author of The Annotated Alice
"Donal O'Shea has written a truly marvellous book"

Keith Devlin, Author of The Millenium Problems
"The History of the Poincare Conjecture is the story of one of the
most important areas of modern mathematics. Donal O'Shea tells that story
in a delightful and informative way - the concepts, the issues, and the
people who made everything happen. I recommend it highly"

See all Product Description
Inside This Book (Learn More)
First Sentence
Revolutions in mathematics are quiet affairs. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

5 Reviews
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Average Customer Review
3.4 out of 5 stars (5 customer reviews)
 
 
 
 
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11 of 11 people found the following review helpful:
2.0 out of 5 stars A bit too historic, 9 Aug 2008
By P. O'sullivan "pjosull" (Southampton) - See all my reviews
(REAL NAME)   
I have read a book called `The Poincare Conjecture'. I understood the book, I even enjoyed the book; yet I am none the wiser on the actual Conjecture from where I set out.

I am not sure why D. O'Shea avoided the hard bits. There is no risk of an unsuspecting member of the public picking this up in an airport bookstore before boarding a long haul expecting a Tom Clancy novel.

This book is too focused on historical topics behind the Conjecture and associated topics in topology that make light reading. If you are seeking to learn more about the specifics of the 'Poincare Conjecture' this is not good enough.

A great deal of this book, say 50%, is centered on the evolution of Euclidian to non-Euclidian Geometry. Only about 2/3's of the way in are we actually dealing with the conjecture.
A massive amount of this book focuses on the golden period of mathematics at Göttingen. A fairer title for this book would have been 'Topics in the history of Geometry'.

In fairness, the mathematics behind Perelman's solution are pretty much inaccessible and even the conjecture itself is difficult to understand properly.

This book will not satisfy anyone who is seriously interested in the conjecture nor will it deepen anyone's understanding who wishes to understand it more.
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38 of 42 people found the following review helpful:
2.0 out of 5 stars Not quite what I expected..., 22 Aug 2007
By Paulo Monteiro (Porto, Portugal) - See all my reviews
(REAL NAME)   
There are some magnificent books about mathematics, and in particular on the history of some mathematical breakthrough, like that of Simon Singh on fermat last theorem, which I read more than once. (Simon Singh has a physics degree, if I recall).
This book of Donald O'Shea is not very well written. First of all, I think the book is not well structured. He doesn't conduct the story simply from a to b, he retains himself in too many subjects a bit off topic, not relevant, or doesn't seem quite pertinent to the main subject, which is the poincaré conjecture, (although some are interesting); what's the relevance of the second world war, or the history of united states mathematics and it's universities. He turns back and forth some times, like forgetting something behind. The prose is unpleasant, except maybe in the lasts chapters. The author spent several chapters in the beginning, talking about the shape of the earth, coulumbus travels, history of maps, defining manifolds of dimension 2, pitagoras and euclid elements, euclidian geometry, the fifth postulate, and suddenly jumps over almost every pertinent concept to understand the poincaré conjecture and the solution by perelman. That is, if he starts the book writing to a public with no knowledge on mathematics, he ends it as writing to a professional mathematician. Everyone that buys a book of this sort, obviously knows what a surface is (or even what is a manifold, or have some knowledge on calculus) don't see the point in explaining that. On the other hand, in the end of the book he says something like: "the complements of two knots could be homeomorphic without the knots being isotopic to each other or their mirror image" with no explanation whatsoever. Let me detail a bit more: for example, in page 131 alone O'Shea introduces several fundamental concepts in topology, see how he does:

about "betti numbers", and "homologies":
-Betti associated numbers with manifolds and poincaré reinterpreted this numbers by introducing equations between submanifolds of a manifold called homologies on a manifold that expressed the relation of bounding within the manifold;

about the "fundamental group":
-Poincaré associated a completely new algebraic object with each manifold which e called the fundamental group.
Sure, as I know from the beginning, that all this terms are associated with topology somehow!

In spite of being a mathematician, Donald O'Shea doesn't seem to think like one, he presents concepts, and tries to define them, in a confusing way. There are some mistakes, but not serious: "..a spherical piece of cloth that would fit perfectly on the top of your head. (...) The cloth would have to have less area inside a circle of fixed radius than there would be on a bedsheet."(page 96) Defines at least 2 times wrongly the number pi, as: "the ratio of the diameter of a circle to its radius"(page 208). These are 2 examples. Distractions of course, but nevertheless, doesn't look nice for a mathematician.
If you want to know the recent story about the poincaré conjecture and some facts about perelman's solution, you just need to read the last 3 chapters. And of course, you won't get any clear idea how perelman did it!
Many facts revealed, for example, in the article "Manifold Destiny" published in The New Yorker, important as they are to understand the circumstances of the solution, and all the complications that emerged around it, are simply ignored!!
The book has one good thing though, has lots of references, articles, books and websites.
For a mathematician who took a whole sabbatical to investigate and write this 200 page story, Donald O'Shea, in my view, did quite a miserable job.
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1 of 1 people found the following review helpful:
5.0 out of 5 stars What about mathematics ?, 16 Dec 2008
By Frans Peters (Eindhoven, Netherlands) - See all my reviews
(REAL NAME)   
Only few people have an idea on what mathematicians active at the frontiers of research try to achieve.

If you want to get a glimpse: read this book. No mathematical background is needed (if you nevertheless do have some background then the notes contain interesting material). The book describes the development of mathematical theories (in words, not in formulas) starting with Euclid's fifth postulate, via non-euclidian geometries to the Poincaré Conjecture and its solution by Grigory Perelman in 2003. It does so by introducing the people involved, describing their characters and their ways of living and presenting their contribution to the theory being developed.

The book also gives a clear account of the interaction of mathematics with other sciences.

The book is well written.

I recommend the book to every-one who wants to know what mathematicians do and why that is of importance. By the way the book is also interesting for people with a mathematical background who want to know what the Poincaré Conjecture is about.


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Most Recent Customer Reviews

4.0 out of 5 stars Fascinating topic
I found this book absorbing, in the same way as Simon Singh's "Big Bang" - he explains how human understanding of a topic increases with time. Read more
Published 2 months ago by blackanchorage

4.0 out of 5 stars Good historical review
Unlike John Derbyshire's books on the history of mathematics, this book does not contain much mathematics apart from concepts in topology, but it does contain a good history of... Read more
Published 6 months ago by Carolyn H

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