Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles | 
| Author: George G. Szpiro
Publisher: Dutton Adult
Category: Book
List Price: $24.95
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Avg. Customer Rating:  13 reviews
Sales Rank: 279087
Media: Hardcover
Number Of Items: 1
Pages: 320
Shipping Weight (lbs): 0.9
Dimensions (in): 8.2 x 5.7 x 1.2
ISBN: 0525950249
Dewey Decimal Number: 510.76
EAN: 9780525950240
ASIN: 0525950249
Publication Date: June 21, 2007
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Condition: Brand New! May have ink mark on book edge and/or very light shelf wear
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Product Description
With a reclusive and eccentric hero, dramatic turns, and a million-dollar payoff, Poincares Prize is the stuff of great fiction. Amazingly, the story unveiled in it is true. In the world of math, the Poincare Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize. George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincare formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincare sought to solve. In fact, Poincare thought he had solved it back at the turn of the twentieth century, but soon realized his mistake. After four more years work, he gave up. Across the generations from China to Texas, great minds stalked the solution in the wilds of higher dimensions. Among them was Grigory Perelman, a mysterious Russian who seems to have stepped out of a Dostoyevsky novel. Living in near poverty with his mother, he has refused all prizes and academic appointments, and rarely talks to anyone, including fellow mathematicians. It seemed he had lost the race in 2002, when the conjecture was widely but, again, falsely reported as solved. A year later, Perelman dropped three papers onto the Internet that not only proved the Poincare Conjecture but enlightened the universe of higher dimensions, solving an array of even more mind-bending math with implications that will take an age to unravel. After years of review, his proof has just won him a Fields Medal, the "Nobel of math," awarded only once every four years. With no interest in fame, he refused to attend the ceremony, did not accept the medal, and stayed home to watch television. Perelman is a St. Petersburg hero, devoted to an ascetic life of the mind. The story of the enigma in the shape of space that he cracked is part history, part math, and a fascinating tale of the most abstract kind of creativity.
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| Customer Reviews: Read 8 more reviews...
 A Moving and Engaging Story October 15, 2008
This semester, I'm taking a course on topology, just for fun. Hence, I've grown more and more interested in stories about mathematicians who work in the field of topology, and no tale is grander than the race to prove the Poincare Conjecture!
Math enthusiasts will know that it is no longer a conjecture, but a theorem now. It was finally proven for n=3 by Grigori Perelman, an odd Russian genius who chose seclusion and anonymity over fame and glory. The book "Poincare's Prize" is full of stories about mathematicians who succeeded in proving the conjecture for certain dimensions (Smale proved n>4, and Freedman proved n=4), and others who spent the better part of their lives searching for one.
As if the writing wasn't enough, the lives of these mathematicians keep the reader engaged. The story of some of these mathematicians will bound to make the reader smile (people like Stephen Smale), some will evoke unlimited sympathy (all those who failed to find a proof), some will leave the reader angry (like Yau Shing Tung), and finally there is one person who will force the reader to imagine the unconstrained capabilities of the human mind, and that person is Grigori Perelman.
Perelman is the shining star of the book, his ultimate triumph and his withdrawal from mathematics and the media's attention not only makes for a potential Hollywood movie, but also forces the reader to think about the meaning of accolades and prizes, more importantly to ponder the underlying drive to find truth.
 Where are the Pictures? August 6, 2008
A story that I wanted to love. Unfortunately, the complete lack of illustrations left me increasingly in the dark. I'm very surprised that an editor would not have insisted on their inclusion in a book clearly marketed to the great unwashed.
interesting book May 17, 2008
39 out of 39 found this review helpful
I am a mathematician/statistician and thoroughly enjoyed the book. The author George Szpiro writes a great story that is fascinating reading. Szpiro is a very well-qualified person to write this book as he holds a masters degree from Stanford and a PhD in mathematical economics from the Hebrew University. Dr. Grigori Perelman is generally created with solving a 100 year old problem that is eligible for the Clay Prize and actually had a great deal to do with his being awarded a Field's medal. Although this is about high level theoretical mathematics it is a historical account written for the general public and very understandable to general audiences.
As he usually does Dr. Lee Carlson has given a very detailed review on amazon for this book and discuss in length issues about whther or not Perelman's work really proves the conjecture. But Perelman is an odd character. He has divorced himself from the mathematical community and refuses to publish his work which is a requirement for th 1 million dollar Clay Prize! It is hard to understand why he won't do it. But then again it is also difficult to understand why he is the first and only recipient of the Field's Medal to refuse it! I believe that Szpiro believes as do most mathematicians that the Poincare conjecture is now a theorem and the Perelman is deserving of the Clay Prize. I think Dr. Carlson is a little too harsh in his assessment.
The story also tells of the life and works of Henri Poincare a mathematical genius who lived in the late nineteenth and early twentieth centuries. Poincare's accomplishments are impressive and his conjectures about the n body problem came out of his work that won him the first and only King Oscar award for his solution of the 3 body problem. Poincare's proof had a flaw in it that only he discovered. It was missed by the referee's of the entries in the competition. In the correcting his work and arriving at an interesting and different area, Poincare actually opened the door to Chaos theory and the mathematical subdiscipline of algebraic topology.
I also found very interesting the description of Poincare's earlier work as a mining engineer, a job he apparently like. His first work in that area was to determine the cause of a mining explosion that had cost several coal miners their lives. This was a field that Poincare was soon to abandon for his greater interest in mathematical research.
This is a beautifully written book that is hard to put down once you start it!
 good biographies and imaginative analogies April 3, 2008
This is a book about Poincare's Conjecture, the efforts to establish it as true
or demonstrate its falsity, and the mathematicians involved in those efforts.
The mathematical domain involved is called topology, previously analysis situs.
In two dimensions it is sometimes called rubber sheet geometry. It is about what
is true if the medium is bent, stretched, or compressed, but not torn or glued.
While early work in the field was concrete and easily visualized, such as walking
tours that satisfied various constraints, and relationships between the number
of surfaces, edges, and vertices of a solid, the subject quickly became very
abstract and dealt with things in more than 3 dimensions.
The book contains biographies of many mathematicians that worked on the problem.
Some are brief, and some are the size of magazine articles. Even if you are a
fan of mathematical history, you will probably meet many interesting people you
did not know about, or probably that you have not heard of. Many are noble and
many have feet of clay. Especially in recent decades there are many controversies.
I know none of the facts, but Szpiro seems to be an unbiased and accurate observer.
Many pairs of participants are linked by the PhD advisor to student relation.
This link seems to have led to some of the dubious behavior described. You can find
more such links on the web at the Mathematics Genealogy Project, a joint venture
of North Dakota State University and the American Mathematical Society.
The biographies are intertwined with a description of the problem and the techniques
used on it. This is not a math book. The mathematical descriptions are by
analogy. I did not enjoy the attempted explanations as much as the biographies,
perhaps because of my math degree. But you might disagree. In any case, I won't
blame the author for weak analogies. They are generally imaginative, and as
accurate as I can imagine. The problem is the problem domain. Most of us can not
imagine things like five dimensional bagels.
Overall, the book is good enough that I will try another of Szpiro's works,
and the chances that I'll try to learn more topology were increased by it.
Chronicle of a Conjecture February 16, 2008
1 out of 1 found this review helpful
In 1904, Henri Poincare published a paper in which he asked: " Is it possible that the fundamental group of a manifold be trivial and yet the manifold not be homeomorphic to a sphere ? " and added that " this question would lead us too far astray."
For the next hundred years, mathematicians from different parts of the world chased a solution , sometimes even sacrificing their own careers.
The author begins with the International Congress of Mathematicians that took place in Madrid, Spain on August 22, 2006. It is an occasion when the Fields Medal (equivalent to the Nobel Prize) is awarded to selected brilliant mathematicians. Gregori Perelman, who was one of the medalists for his solution of the Poincare Conjecture, did not show up. The king of Spain had to wait in vain.
Perelman "spent the festive day hidden away in the modest apartment that he shared with his mother in a drab neighborhood of St. Petersburg."
We learn that Perelman is concerned about the ethics in the mathematics community. He says: " Even those who are more or less honest tolerate those who are not."
In the final chapter, the author tells about the million dollar prize by the Clay Institute for anyone who solves the Poincare Conjecture. Will Perelman be awarded ? will he accept ?
The second chapter is about the perception of dimensions. An ant crawling on a basketball thinks that the surface is completely flat. The sailors of Christopher Colombus were afraid they might fall off the edge of what they believed to be a flat world. A ball is a three-dimensional object and its surface is two dimensional. A gentle introduction.
In the next two chapters we get to know more about Poincare. He was trained as a mining engineer. His analytical mind came handy when he investigated a tragic accident in a coal mine, where sixteen people had been killed. Later, Poincare became a professor of math and won an Oscar Prize ( named after king Oscar II of Sweden ) for working on the three-body problem (the stability of the solar system is at stake !).
As I learned from other sources , Poincare was also a president of the Bureau of Longitudes and helped draw the world map for the colonies of the French empire. It is a puzzle that he did not come up with relativity theory after his intensive work on space, time and electrodynamics. One explanation is that he wanted to repair tradition and believed in such things as ether. The anti-authoritarian Einstein succeeded in defeating the Newtonian empire.
The next chapter "Geometry without Euclid" tells us about the origins and the purpose of topology. How to cross all the bridges (once each) of the town Koenigsburg ; how to classify objects according to their cavities , tunnels and twists. What are the betti numbers of pretzels, bagels and balls ?
The rest of the book is about the chronicle of the conjecture. The author tries to help the reader visualize the images of the objects. Manifolds can be imagined as flying carpets in the sky. As Poincare said : " Geometry is the art of reasoning well with badly made figures."
Two objects are topologically equivalent (homeomorphic), if they can be deformed to each other by pulling and creasing and crumpling , without tearing and gluing. A carpet is equivalent to a quilt but not to a poncho.
The Poincare Conjecture can help us figure out the shape of the universe. Are we living on a ball , a bagel or a pretzel ?
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