Wednesday, November 26, 2014

The Poincare Conjecture

Henri Poincare was a mathematician in the late nineteenth early twentieth century. He revolutionized the field of topology--the study of geometric configurations that are unchanged by stretching or twisting. Poincare's conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. His conjecture is one of the seven millennium problems that carries a one million dollar reward for the person who discovers the solution. Gregory Perelman has offered a proof for this conjecture. O'Shea explores the Poincare conjecture, and what led up to Perelman's proof of this conjecture.

This book was recommended to me by my husband. Wanting to understand more about his work as a topologist, I agreed to read this book. I found it very interesting. I liked learning about the history of this conjecture, and how Perelman came up with his proof. I found most of the information presented in a way that allowed for a non-mathematician to understand what was being discussed. I admit, some of the math was beyond me, but on the whole, it was understandable. While I preferred the history portion of the book, I thought there was a good balance between the history and the math used to explain the conjecture.

I liked the way O'Shea explained the math. I thought he did a decent job making it understandable to the average reader without making it seem too dumbed down or over the top popular science. I found much of the material interesting, and I liked that it would bring up a lot of fascinating thought and discussion points. There is also a great section of notes in the back if you desire to learn more about some of the topics discussed in the book.

If you are interested in the Poincare conjecture, math, or know a topologist, I recommend reading this book.

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