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Perfect Rigor: A Genius And The Mathematical Breakthrough Of The Century

by Masha Gessen
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Product Details

  • Publisher: Houghton Mifflin Harcourt
  • Publishing date: 11/11/2009
  • Language: English
  • ISBN-13: 9780151014064
  • ISBN: 015101406X


Product Description
In 2006, an eccentric Russian mathematician named Grigori Perelman solved one of the world's greatest intellectual puzzles. The Poincare conjecture is an extremely complex topological problem that had eluded the best minds for over a century. In 1998, the Clay Institute in Boston named it one of seven great unsolved mathematical problems, and promised a million dollars to anyone who could find a solution. Perelman will likely be awarded the prize this fall, and he will likely decline it. Fascinated by his story, journalist Masha Gessen was determined to find out why.

Drawing on interviews with Perelman's teachers, classmates, coaches, teammates, and colleagues in Russia and the US--and informed by her own background as a math whiz raised in Russia--she set out to uncover the nature of Perelman's genius. What she found was a mind of unrivalled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength has turned out to be his undoing: such a mind is unable to cope with the messy reality of human affairs. When the jealousies, rivalries, and passions of life intruded on his Platonic ideal, Perelman began to withdraw--first from the world of mathematics and then, increasingly, from the world in general. In telling his story, Masha Gessen has constructed a gripping and tragic tale that sheds rare light on the unique burden of genius.

A Q&A with Masha Gessen, Author of Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century

Q: Grigory Perelman doesn't talk to journalists. How did you write this book?

A: Actually, at this point he really talks to no one. When I first started researching the book, he was still speaking to his lifelong math tutor, his competition coach and, in many ways, the architect of his life, Sergei Rukshin. But sometime in the last couple of years, Perelman stopped talking to him. As far as I know, the only person with whom he is in permanent contact is his mother, with whom he shares an apartment on the outskirts of St. Petersburg.

Fortunately, while I had no access to Perelman, I talked to virtually all the people who had been important in his life: Rukshin, his classmates, his math-club mates, his high school math teacher, his competition coaches and teammates, his university thesis adviser, his graduate school adviser, his coauthors, and those who surrounded him in his postdoc years in the United States. In some ways, I think, these people were more motivated to speak with me because Perelman himself wasn't doing it--and because they felt his story had been misinterpreted in so many ways in the media.

Q: So not being able to talk to him was an advantage?

A: Funny as that sounds, in some ways, yes. When you write a biography of a cooperating subject--even if it is just a magazine story, never mind a book--you are in constant negotiation with that person's view of himself. And people tend to be terrible judges of themselves. So you are always balancing your own perceptions against the subject's aspirations, and this can actually get painful for all involved. All I had was research material and my own perceptions. In this sense, this was more like writing a novel: I was constructing this character.

Q: What made you think you could do this?

A: Actually, I made two erroneous assumptions. I assumed that the journalists who initially wrote about Perelman, around the time when he turned down the Fields Medal, mathematics' highest honor, were wrong. I assumed he was not as crazy, or as weird, as they made him sound. I figured he was a familiar type of Russian scientist--entirely devoted to his field, not at all attuned to social niceties and bureaucratic customs, and given to behaviors that can easily be misinterpreted, especially by foreign journalists. My second assumption, related to the first, was that my background as a Russian math school kid gave me the tools necessary to describe this type. My background certainly helped--I am Perelman's age, I come from the same kind of family, socially, economically, and educationally, as he does (Russian Jewish engineers with two children living on the outskirts of Leningrad in his case and Moscow in mine)--but it was barely a start. Because Perelman turned out to be much stranger than I assumed.

Q: So he is as crazy as they say?

A: I think crazy generally means that a person has an internally consistent view of the world that is entirely different from the view most people consider normal. I think this is true of Perelman. The interesting thing, of course, was to figure out what this internally consistent view of the world was.

Q: And did you manage to figure it out?

A: I think so. I concluded that this view, and the rigidity with which he holds to it, is actually directly related to the reason he was able to solve the hardest mathematical problem ever solved. He has a mind that is capable of taking in more information, and embracing more-complex systems, than any mind that has come before. His mind is like a universal math compactor. He grasps hugely complex problems and reduces them to their solvable essence. The problem is, he expects the world of humans to be similarly subject to reduction. He expects the world to function in accordance with a set of strictly laid out rules, and he absolutely cannot take in anything that does not conform to those rules. The world of humans is unruly, though, so Perelman has had to cut off successive chunks of it until all that was left was the apartment he shares with his mother.

Q: Is that quality of his mind what the title of the book refers to?

A: Yes, it's that "perfect rigor". But in fact that phrase comes from a quote by Henri Poincare, he of the Poincare Conjecture fame--from his ruminations on the nature of mathematical proof, which I quote in the middle of the book.

Q: So what is the Poincare Conjecture?

A: It is no more, actually. Now that Perelman has proved it, it is a theorem. And it is a classic theorem of topology, one of the most wonderfully weird mathematical disciplines. Topology, to my mind, is something like the perfect mathematical discipline. It leaves nothing to reality: though it deals with shape, you never measure objects in topology--not with a ruler, anyway. Rather, the concepts of topology are the products of their verbal definitions. And much of topology is concerned with things that are essentially the same as other things, even if at particular moments in time they happen to look different. For example, if you have a blob that can be reshaped into a sphere, then the sphere and the blob are essentially similar, or homeomorphic, as topologists say. So Poincare asked, in essence, whether all three-dimensional blobs that were not twisted and had no holes in them were homeomorphic to a three-dimensional sphere. And it took more than a hundred years to prove that yes, they were.

Q: So? What's the use of something so abstract?

A: Mathematicians hate that question. Mathematics is not here to be useful. It is beautiful, and that's enough. But the fact is, such discoveries generally have far-reaching--useful--consequences that are rarely evident at the moment of the breakthrough. The Poincare Theory will almost certainly have profound consequences for our understanding of space--the universe that we inhabit.

Q: And Perelman will be awarded a million dollars for this proof?

A: Probably. And he will probably turn it down. The commercialization of mathematics offends him. He was deeply hurt by the many generous offers he received from U.S. universities after he published his proof. He apparently felt he had made a contribution that was far greater than any amount of money--and rather than express their appreciation in appropriately mathematical ways, by studying his proof and working to understand it (he estimated correctly that it would take specialists about a year and a half to understand the proof), they were trying to take a shortcut and basically pay him off. By the same token, the million dollars will probably offend him.

At the same time, if he chose to accept the money, he would find a way to make that consistent with his system of rules and values. But I really don't think this is likely.

(Photo © Vladimir Shirokov)

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  • No Kindle Support so it is clumsy to haul around
    From Amazon

    I have looked at this book many times to see if it is available for the Kindle. It hasn't so I have not bought it nor will I until there is a Kindle edition.

  • Read the "Perfect Rigor" book!
    From Amazon

    I thoroughly enjoyed the book. It is a crime not to read this book.

  • For the lack of anything else on the subject ...
    From Amazon

    this book will have to do. I enjoyed reading it, particularly because very little else is available on the subject of Grisha Perelman (some current books on topology or Poincaré conjecture include some stuff about Perelman, and that's about it). In that regard, I am thankful to Ms. Gessen for writing this book. However, I found it a bit too subjectively judgmental of him, which took away some of the enjoyment. Still I would recommend it to anyone interested to learn about a living genius and the Soviet educational methods and practices.

  • biography of a genius
    From Amazon

    This is a captivating description of a modern day genius. How do we know when someone is a genius? Well, if he can solve a famous 100 year old problem, he probably is. That is what Perelman did. This book tries to follow the life of this man as closely as possibly without actually coming into contact with its subject (not amenable to interviews). Perelman turns out to be a mathematical genius but evidently at a sacrifice: lacks the social skills which we would call normal. His life of ups and downs has resulted in him currently becoming a recluse. The book has a great description of the anti-Semitism that existed in the Soviet Union up till its collapse. I was not aware of the extent of this. The book also describes the intense math olympiads that ambitious Russian students would undertake. The book attempts to describe the Poincare Conjecture to the best of its ability without resorting to the assumption of a sophisticated mathematics background. Great book for someone interested in mathematics and the millenium problems. Also a good book for someone interested in the psychology of genius.

  • Excellent new bio
    From Amazon

    It cannot be easy to write a biography of someone who will not (or cannot) be interviewed. Certainly, posthumous biographers do it all the time. Yet somehow it is different when the subject is living, taunting the researcher with silence and stone walls. Nonetheless, in her excellent new biography of the notoriously reclusive mathematician Grigory Perelman (see Russian Life, Nov/Dec 2006), Gessen does a remarkable job of unraveling what makes the award-declining genius tick, while providing a fascinating portrait of the competitive and political world of high mathematics. Immersing herself in Perelman's world and talking to seemingly everyone he has ever had contact with, Gessen paints a nearly-complete picture of an Aspergian pedant with principles of Tolstoyan proportions, relentlessly stubborn on everything from footnoting to expense reports to black bread. The only thing lacking here is what no one save the subject can provide: an explanation of the Perelman anomaly (rejecting all fame and fortune in a fame and fortune obsessed world). The closest we can come is the answer Perelman himself gave, that he does not want to compromise his principles or be "treated as a pet." But that merely begs the question. And so, not unlike a tantalizingly unsolvable math puzzle, the anomaly remains. As reviewed in Russian Life Jan/Feb 2010 issue.

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