The Poincare Conjecture: In Search of the Shape of the Universe | 
 enlarge | Author: Donal O'shea
Publisher: Walker & Company
Category: Book
List Price: $15.95
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Rating:  20 reviews
Sales Rank: 214069
Media: Paperback
Edition: First Edition
Number Of Items: 1
Pages: 304
Shipping Weight (lbs): 0.6
Dimensions (in): 8.2 x 5.4 x 0.9
ISBN: 0802716547
Dewey Decimal Number: 500
EAN: 9780802716545
Publication Date: December 26, 2007
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Product Description
“O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman.”—Wall Street Journal
In 1904, Henri Poincare, a giant among mathematicians who transformed the fledging area of topology into a powerful field essential to all mathematics and physics, posed the Poincare conjecture, a tantalizing puzzle that speaks to the possible shape of the universe. For more than a century, the conjecture resisted attempts to prove or disprove it. As Donal O’Shea reveals in his elegant narrative, Poincare’s conjecture opens a door to the history of geometry, from the Pythagoreans of ancient Greece to the celebrated geniuses of the nineteenth-century German academy and, ultimately, to a fascinating array of personalities—Poincare and Bernhard Riemann, William Thurston and Richard Hamilton, and the eccentric genius who appears to have solved it, Grigory Perelman. The solution seems certain to open up new corners of the mathematical universe.
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| Customer Reviews: Read 15 more reviews...
 The first solution to one of the Millenium problems August 1, 2007
3 out of 3 found this review helpful
Lee Carlson's review casts some doubt about the validity of Perelman's proof, but this is not what the mathematical community of experts is saying. Even the people who have filled in the details of Perelman's proof agree that all the merit is his. As this book shows, Morgan clearly states in his address in the ICM in Madrid that Perelman proved the Poincare's conjecture and much more (Thurston's conjecture) and introduced new methods that will be used by many mathematicians in the coming years.
O'Shea's book is a good complement to Szpiro's. O'Shea is more encompassing and starts the history of the conjecture going back as far as Babylonic mathematics. It only gives the biography of Poincare in page 111 and misses some of the details of the controversy provoked by Yau and explained in detail in an article in New Yorker and also in the book by Szpiro. It also has some more technical details, but both books are good reading for a mathematically educated reader.
A wonderful book! July 13, 2007
2 out of 2 found this review helpful
This is a delightful, passionate book, written in an easily readable style (I read it in one busy week). It does a wonderful job explaining the significance of Perelman's achievement amidst the background of mathematical history. O'Shea moves from Pythagoras and Euclid through Gauss, Riemann, and Klein and finally to Thurtson and Hamilton and the present day. He has wisely chosen to keep it to 200 pages plus extensive endnotes (which you should not skip). The reader should be forewarned that at most 20 of these 200 pages are specifically on Perelman's proof, so you get more of a sense of the accomplishment as embedded in history than you do of the specific techniques employed. However, one cannot help but learn a lot of (a) history, (b) geometry, and (c) Perelman-lore, and therefore the trip is most definitely worth it.
A great popular math book September 9, 2007
2 out of 2 found this review helpful
Donal O'Shea has written a wonderful book. He successfully conveys that we are living currently in the greatest age of mathematics ever seen. He does this by highlighting the recent solution of the Poincare Conjecture by Perelman. If you already know about the Poincare Conjecture and want to know the proof, this is not the book for you. O'Shea is aiming for those who have possibly never even heard of the Poincare Conjecture (in other words, most of humanity). He shows, primarily by recounting a lot of mathematical history, how mathematics is far more conceptual than computational. In particular I liked how he emphasized the profound influence of Riemann in shifting how people do mathematics. One word of warning for readers who were not math majors in college (a warning that should be applied to almost all mathematically oriented books): be willing to skim sections that are too complicated on first reading. This is what most of the pros do. This is a great book.
Brain twisting adventure August 11, 2007
0 out of 1 found this review helpful
A very well written story of human ingenuity.
It is a very good example of what human race capable of.
A stunning book July 10, 2007
1 out of 1 found this review helpful
This stunning book pushed me into new ways of thinking. In two hundred pages, the author tells the story of one of the most beautiful, complicated, and significant mathematical achievements of all time. The narrative blends social history, mathematical exposition and biography, and is supplemented by detailed notes, two glossaries and two indexes, all carefully done and full of unexpected delights. But it is the mathematics that takes center stage, and O'Shea writes in a way that allows you to understand the central mathematical ideas. And what ideas these are!! The universe can, like the surface of earth, have no walls and yet be finite. Angles on triangles need not sum to 180 degrees and only do on surfaces and in spaces that are flat. High school geometry is only a tiny piece of a larger, more satisfying story (no wonder it made so little sense for me). The same surface can carry different geometries and a donut can be flat. Geometric notions such as angles, parallel lines, and distance are separate from topological notions such as dimension, finiteness and how an object connects up.
I have never felt more respected by an author. O'Shea clearly believes, and quietly demonstrates, that the Poincare conjecture and the mathematics that underlies its statement lie within the grasp of every individual. There is no waffling and no purple prose. If he uses a word, he tells you what it means. By the end, you understand why individuals spent their life trying to prove the Poincare conjecture, and why the solution matters so much and the money so little. The mathematical ideas unfold against the main historical events of their time, and a reader who skipped all the mathematics would still be treated with to an unusually lively, and I think important, intellectual history. Passages in the text reflect on, among other things, the rise of the modern university, the American research establishment, nationalism and war, and the nature of mathematical knowledge and proof. The numerous biographical and historical sketches are first rate and the individuals come across as real people.
My only caution is that the author's prose style is deceptive: many passages are lovely, but each page contains a *lot* of information. Read ten pages in a sitting, and you find yourself approaching information overload. The book is accessible, but more demanding than a quick perusal would suggest. Treat it as you would a very rich meal - carefully, without consuming too much too quickly. The force of the narrative and the sheer power and reach of the ideas leave one both sated and longing for more.
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