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. ( )

A thoroughly researched, but easily accessible story of the (very likely satisfactory) solution of a very difficult problem in mathematics called the Poincare Conjectue. Donal O'Shea takes a subject that the vast majority of the world's mathematicians do not understand and makes it real to the non-mathematician reader. His approach describes the historic development of almost endless new math methods which resulted from the many attempts over more than 100 years to prove an obscure conjecture made in 1904 by Henri Poincare. He also shows that almost every new result in math builds on previous works and ideas. Poincare's conjecture has very likely been solved, finally, by a Russian Mathematician Grigory Perlman. Perlman has been awarded the highest award in mathematics (the Fields Medal) which he declined to accept and and long as his proof stands for 2 years will win $1,000,000 from the Clay Mathematics Institute. There is considerable speculation about whether he will accept the money. O'Shea's book proivdes some insight into the minds of those we call mathematicians, and the extremely complex relationships between their individual work , the work of their peers and those who preceeded them. ( )

The history of the Poincaré Conjecture and the way it was probably solved by a Russian genius are ingredients for a science thriller. Unfortuntely the author missed the opportunity. ( )