Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles [Mass Market Paperback]

George G. Szpiro (Author)

Book Description

Publication Date: July 29, 2008

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 Poincaré developed the Poincaré 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.

--This text refers to the Kindle Edition edition.

Editorial Reviews

From Booklist

*Starred Review* Imagine Oedipus solving the riddle of the Sphinx only then to refuse the crown offered as the reward for his triumph. A modern version of such an improbable event forms the spine of Szpiro's remarkable narrative. Himself an accomplished mathematician, Szpiro recounts the story of how a geometrical puzzle worthy of the most voracious sphinx finally yielded to an eccentric Russian genius who has since refused the honors and million-dollar prize proffered by an astonished world. The mathematical puzzle, readers learn, originated with the French polymath Henri Poincaré, whose revolutionary topology generated a tantalizing conjecture about how multidimensional bodies might all be transformed into spheres. Only specialists can fully understand this famous conjecture, but Szpiro translates its essential features into remarkably accessible analogies—rubber bands wrapped around a bagel, for instance. Readers learn much not only about the conjecture but also about the many scholars consumed by passion to prove—or disprove—it. Readers meet, among others, the radical but gentlemanly "Papa" Papakyriakopoulos and the playboy windsurfer Richard Hamilton. However, Szpiro accords pride of place to Grigori Perelman, the reclusive titan who finally pierced the mystery—and then spurned the awards. Never has mathematics provided more fascinating human drama! Christensen, Bryce
Copyright © American Library Association. All rights reserved --This text refers to an out of print or unavailable edition of this title.

Review

“[Szpiro] turns the abstract mathematics of spheres into a lucid, lovely romantic odyssey.”
—Sylvia Nasar, author of A Beautiful Mind

“A wonderful history of a great breakthrough.”
—Bud Mishra, professor, Courant Institute of Mathematical Sciences, New York University --This text refers to an out of print or unavailable edition of this title.

See all Editorial Reviews

Product Details

• Reading level: Ages 18 and up
  
• Mass Market Paperback: 309 pages
• Publisher: Plume; Reprint edition (July 29, 2008)
• Language: English
• ISBN-10: 0452289645
• ISBN-13: 978-0452289642
• Product Dimensions: 7.9 x 5.3 x 0.9 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (25 customer reviews)
• Amazon Best Sellers Rank: #1,198,571 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

49 of 49 people found the following review helpful:

5.0 out of 5 stars interesting book, May 17, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles (Hardcover)

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!

27 of 27 people found the following review helpful:

4.0 out of 5 stars lively history; many math errors; where are the pictures?, December 21, 2007

By 

Nim Sudo - See all my reviews

This review is from: Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles (Hardcover)

This book gives a nice account of the history of the various attempts to solve the Poincare conjecture, culminating with its recent proof by Perelman. Compared to the book by O'Shea, the history here seems more interesting and relevant. (Although here too the history is occasionally rambling and boring, at least we aren't subjected to a treatise on the rise of the German university system in the 19th century etc.) We get to meet lots of colorful characters and read many interesting stories about them. The author did an excellent job of interviewing all available people. The human side of mathematical research is very well presented here.

As for the math, although nice analogies are used to describe abstract concepts to the layman, the details are often garbled. Some of the basic mathematical statements made in the book are blatantly wrong. For example, the book states that the Poincare homology 3-sphere is the only homology 3-sphere other than the 3-sphere. (In fact, there are infinitely many different homology 3-spheres, and these comprise an intricate structure which is still being explored in present-day research.) We also learn in this book that the fundamental group of a genus 2 surface is Z^3, and the fundamental group of a genus 3 surface is Z^4. (Any student in an undergraduate topology class should know better.) The list goes on. I suppose that a layperson won't notice these mistakes, and will at least get an idea of what the math is like, modulo details. However there are other mathematical statements which, while not quite wrong, don't make any sense without more explanation. (Oh, and he keeps referring to three-dimensional manifolds as "floating in four-dimensional space", which really muddies the waters.) The description of Ricci flow at the end is quite a bit better than the math in the rest of the book; the acknowledgments indicate that the help of Christina Sormani played a big role here.

The most glaring omission in the book is the pictures. There aren't any. That's right, 300 pages of geometry without a single picture. Granted, professional mathematicians often write research articles in geometry with no pictures, only equations. But there the intended audience has enough knowledge to see the pictures in their mind. For a popular book on geometry to have no pictures is really disappointing. Maybe they were in a rush to get into print.

Conclusion: if you are a layperson who would like to learn about the Poincare conjecture, O'Shea's book is good for the math (which, while difficult to understand at times, is at least correct) and this book is good for the history.

17 of 17 people found the following review helpful:

5.0 out of 5 stars A story began by one of the best mathematicians of the 20th century and finished by a genius of the 21st, August 1, 2007

By 

Jaume Puigbo Vila "cosmos fan" (Barcelona, Spain) - See all my reviews
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Amazon Verified Purchase

This review is from: Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles (Hardcover)

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 Poincaré only in page 111 after a very interesting but long detour from Babylon to Klein. Both books are worth reading and complement each other