Loading... The Poincare Conjecture: In Search of the Shape of the Universeby Donal O'Shea
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Sign up for LibraryThing to find out whether you'll like this book. No current Talk conversations about this book. This is one of the most beautifully written popular science books I have ever encountered. It is simple and intuitive enough to be understood by someone not familiar with the field, but is also in depth enough to be fascinating to people with some mathematical background. It explores some of the basic concepts of topology all while placing the mathematics within the context of the fascinating story of the Poincare Conjecture. Absolutely brilliant. This is one of the most beautifully written popular science books I have ever encountered. It is simple and intuitive enough to be understood by someone not familiar with the field, but is also in depth enough to be fascinating to people with some mathematical background. It explores some of the basic concepts of topology all while placing the mathematics within the context of the fascinating story of the Poincare Conjecture. Absolutely brilliant. This book is about a part of mathematics called topology (the word topology goes back to the 1850s, but when I was young, a century ago, it was not used: the disciplin of topology was still part of "geometry"). The good news is that you can understand the book, because I did. Despite the subtitle "In search of the shape of the universe," it is not about physics or astronomy at all, it is a book about an interesting mathematical problem. The author Donal O'Shea succombed to the influence of his friends and tried to interest us in the subject by showing that it can be useful. Math is math: often it is useful, sometimes it is not, sometimes it becomes useful centuries after a mathemematical discovery. We got to live with that. Math is interesting in itself, like games and puzzles: it gives the brain jolts of pleasure, even if you are not a mathematician. O'Shea does a terrible job at making topology look useful: the idea that with everything we knew about maps at the time of Columbus, we could have concluded (but we did not) that the earth is a doughnut is irritating and ludicrous. It does not help. You can skip the first chapters and start at page 21 and get to the meaty part of the thing. What I like about the book: 1. It is a neat problem 2. I understand what the author says 3. It has a compassionate look on the fate of mathematicians, and the history part is very well done. Very well written story of the history of mathematics leading up to topologies, geometries, manifolds, and of course the Poincare Conjecture regarding topological spheres. The text is interesting and lucid, with no equations outside of the footnotes, and very few even there. This could be because this form of mathematics lends itself to descriptions more than most other mathematics. An excellent book for the mathematically curious. no reviews | add a review
References to this work on external resources. Wikipedia in English (2)Amazon.com Product Description (ISBN 080271532X, Hardcover)Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture. (retrieved from Amazon Thu, 12 Mar 2015 18:23:05 -0400) Conceived in 1904, the Poincaré conjecture, a puzzle that speaks to the possible shape of the universe and lies at the heart of modern topology and geometry, has resisted attempts by generations of mathematicians to prove or to disprove it. Despite a million-dollar prize for a solution, Russian mathematician Grigory Perelman, posted his solution on the Internet instead of publishing it in a peer-reviewed journal. This book "tells the story of the fascinating personalities, institutions, and scholarship behind the centuries of mathematics that have led to Perelman's dramatic proof." The author also chronicles dramatic events at the 2006 International Congress of Mathematicians in Madrid, where Perelman was awarded a Fields Medal for his solution, which he declined.… (more) |
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Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail; how one concept leads to another; how concepts fail to connect. For me, at least, this was difficult to follow. Granted, in order to truly understand what is being discussed, you would need to understand the mathematics; perhaps this is just an insurmountable problem in trying to translate high-level and difficult mathematics into lay-language.
Secondly, there are too many sections where names and dates and attempted proofs of such-and-such a conjecture/theory/etc. are listed; in these sections it very much feels like the only people who would be able to pull much meaning would be already quite familiar with the topics. There is much more of this in the last third or quarter of the book.
The middle 85% of the book isn't about the Poincare Conjecture per se. In this, I would describe the book as the history of mathematicians and mathematics, from ancient times to today, as told from the point of view of the Poincare Conjecture. An analogy might be something like a book that details the life of some famous figure by telling the history of their family/ancestry and the times and events their family lived through. ( )