Product Description

With a reclusive and eccentric hero, dramatic turns, and a million-dollar payoff, Poincaré’s Prize is the stuff of great fiction. Amazingly, the story unveiled in it is true.

In the world of math, the Poincaré 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 Poincaré 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 Poincaré sought to solve.

In fact, Poincaré 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 Poincaré 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.

Product Details

• Amazon Sales Rank: #433731 in Books
• Published on: 2007-06-21
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 320 pages

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

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

About the Author
George G. Szpiro is a mathematician and prizewinning journalist with an M.B.A. from Stanford and a Ph.D. in mathematical economics from the Hebrew University in Jerusalem. He has taught at the of Pennsylvania’s Wharton School, Hebrew University, and the of Zurich, and, along with a monthly popular math column, has published numerous articles. His previous book, Kepler’s Conjecture, was published in five languages to international critical acclaim.

Customer Reviews

interesting book
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!

lively history; many math errors; where are the pictures?
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.

A story began by one of the best mathematicians of the 20th century and finished by a genius of the 21st
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