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Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles | 
 enlarge | Author: George G. Szpiro
Publisher: Plume
Category: Book
List Price: $15.00
Buy New: $4.95
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Rating:  13 reviews
Sales Rank: 916942
Media: Paperback
Edition: Reprint
Pages: 320
Number Of Items: 1
Shipping Weight (lbs): 0.5
Dimensions (in): 8.1 x 5.5 x 0.7
ISBN: 0452289645
Dewey Decimal Number: 510.76
EAN: 9780452289642
Publication Date: July 29, 2008
Availability: Usually ships in 1-2 business days
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Product Description
The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it
In the tradition of Fermat s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincare developed the Poincare Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
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| Customer Reviews: Read 8 more reviews...
 interesting book May 17, 2008
Michael R. Chernick (Holland PA)
40 out of 40 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!
A story began by one of the best mathematicians of the 20th century and finished by a genius of the 21st August 1, 2007
Jaume Puigbo Vila (Barcelona, Spain)
9 out of 9 found this review helpful
A delightful story of one of the major problems in mathematics and the numerous people, many Field medalists, that have intervened to solve it. Even if you are not an expert in topology you will get a feeling of the path to the proof via Thurston's geometrization conjecture and Hamilton's Ricci flow to the surgery of Perelman.
The general educated reader will enjoy the stories of Smale in Copacabana and Hamilton's string of girlfriends which contrasts with the ascetism of Perelman and the political manouvering of Yau. In short, mathematics is a human endeavour and its practitioners are mortals which have similar passions, defects and excentricities as the rest of us, only they are extremely brilliant and passionate about the Queen of Sciences.
Compared with a similar book by O'Shea this goes more directly to the point, whereas O'Shea introduces Poincare only in page 111 after a very interesting but long detour from Babylon to Klein. Both books are worth reading and complement each other
A Gold Mind for the Mathematician August 10, 2007
Avid Reader (Franklin, Tn)
7 out of 9 found this review helpful
I read this book while enjoying my coffee and cinnamon roll at Borders. It describes the famous "Poincare puzzle" that is harder to explain than it is to imagine. To put it simply, is it possible to prove that a sphere is the only three-dimensional object without holes? Both the question and the solution relate to topology, interestingly a branch of mathematics developed almost single-handedly by Poincare.
Well, the puzzle was solved by Gregory Perelman, a Russian mathematician but he went far beyond the mere proof of this one problem and actually provided an explanation for the more difficult Geometrisation Conjecture proposed by William Thurston (every 3-dimensional object can be divided into pieces, all of which have geometric structure). Strangely, he devised the explanation and then refused to acknowledge or accept the huge cash prize for his efforts.
An excellect overview of mathematics and a wonderful (though brief) biography of the great Poincare and his unbelievable genius is provided as well as attending detail into the strange world of mathematical theory. I recomment this book wholeheartedly!
A gripping story that is marvelously told September 23, 2007
Gran Lector (Denver, USA)
2 out of 2 found this review helpful
This book is highly recommended for anyone who is interested to know how the proof of one of the most vexing mathematical conjectures of recent times came about. Mr. Szpiro easily walks the reader through complex and esoteric concepts in algebraic topology without assuming any previous background in the subject. Of course, if you have some familiarity with this field of mathematics, then the more you will get out of this book. What makes this book so engaging is that the author weaves into the story some details of the lives and the idiosyncrasies of the major mathematicians who were involved in the effort to prove the Poincare Conjecture. The writing style just right: it is concise and to the point, which is probably due to the fact that the author is a journalist and mathematician.
Brilliant analogies explain technical mathematics June 29, 2007
Frank Morgan (Williams College)
8 out of 11 found this review helpful
I'm impressed and delighted at the way that Szpiro has been able to use analogy to provide appealing and memorable mental pictures of some of the deep and technical mathematical ideas. Here's a short excerpt from Chapter 12:
"To prove Thurston's Geometrizaton Conjecture, Perelman described a process that would allow...surgery infinitely often for endless time. ... Let us consider the manifold to be the mythological multiheaded Hydra. ... Whenever he chops off a head, the Hydra keeps growing new ones. ... Had she just sprouted heads, Perelman would not have had a problem because spheres eventually go 'pop.' However, he really need to prevent the Hydra from sprouting extra bodies."
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