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

This book is about a part of mathematics called topology (the word topology goes back to the 1850s, but when I was young, a century ago, it was not used: the disciplin of topology was still part of "geometry"). The good news is that you can understand the book, because I did.
Despite the subtitle "In search of the shape of the universe," it is not about physics or astronomy at all, it is a book about an interesting mathematical problem. The author Donal O'Shea succombed to the influence of his friends and tried to interest us in the subject by showing that it can be useful. Math is math: often it is useful, sometimes it is not, sometimes it becomes useful centuries after a mathemematical discovery. We got to live with that. Math is interesting in itself, like games and puzzles: it gives the brain jolts of pleasure, even if you are not a mathematician.
O'Shea does a terrible job at making topology look useful: the idea that with everything we knew about maps at the time of Columbus, we could have concluded (but we did not) that the earth is a doughnut is irritating and ludicrous. It does not help. You can skip the first chapters and start at page 21 and get to the meaty part of the thing.
What I like about the book:
1. It is a neat problem
2. I understand what the author says
3. It has a compassionate look on the fate of mathematicians, and the history part is very well done. ( )

Very well written story of the history of mathematics leading up to topologies, geometries, manifolds, and of course the Poincare Conjecture regarding topological spheres. The text is interesting and lucid, with no equations outside of the footnotes, and very few even there. This could be because this form of mathematics lends itself to descriptions more than most other mathematics. An excellent book for the mathematically curious. ( )

Donal O'she explains complicated mathematics in a way the simple reader can not only understand but also enjoy. Additionally, the book is spiced up with very interesting and detailed historic background. Both the specialists and the general audience will find the Poincare Conjecture an interesting book. ( )

The Poincare conjecture is a statement in topology about the shape of certain types of manifolds, or mathematical spaces. It took most of the book to describe enough topology to even begin to understand its significance, and why the solution of the problem was important. There is a good deal of mathematics and history in the book, but I did not gain clarity on the concepts, possibly because they are too hard and I do not recall enough geometry. I had time in a car ride to concentrate on the book, and it went quickly. ( )

In The Poincaré Conjecture, Donal O’Shea explains a conjecture in topology from 1904 that had remained unsolved for nearly a century. Aside from its importance in topology, the conjecture also has implications on determining the shape of our own universe. It is also one of the seven Millennium Prize problems listed by the Clay Institute in 2000, with a one million dollar reward for a correct solution. It was finally solved in 2002 by Grigory Perelman and since then his solution has been accepted. He may be eligible for the Millennium Prize but does not appear to be interested. In 2006, he was awarded the Fields medal—the highest honor for mathematicians and which also carries a monetary reward—for his work but he declined the award.

In this book, O’Shea takes us through the history of the conjecture and the attempts at solving it, and also takes some time to give us the historical context along the way by describing the social and political climate surrounding each mathematician that has sought to prove the conjecture. He does a good job of providing relatively clear and simple explanations of the complex ideas in topology and non-Euclidean geometry involved, but the book does move at a fairly brisk pace (minus the notes at the end the main text is only 200 pages long) so some work is still required to follow along, but I never felt completely lost. This book contains a nice mix of mathematical ideas and history for a general audience, and it managed to keep my interest throughout. ( )