Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century [Hardcover]

Masha Gessen (Author)

Book Description

Publication Date: November 11, 2009

A gripping and tragic tale that sheds rare light on the unique burden of genius

 

In 2006, an eccentric Russian mathematician named Grigori Perelman solved the Poincare Conjecture, an extremely complex topological problem that had eluded the best minds for over a century. A prize of one million dollars was offered to anyone who could unravel it, but Perelman declined the winnings, and in doing so inspired journalist Masha Gessen to tell his story. Drawing on interviews with Perelman’s teachers, classmates, coaches, teammates, and colleagues in Russia and the United States—and informed by her own background as a math whiz raised in Russia—Gessen uncovered a mind of unrivaled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength turned out to be Perelman's undoing and the reason for his withdrawal, first from the world of mathematics and then, increasingly, from the world in general.

--This text refers to the Kindle Edition edition.

Editorial Reviews

Amazon.com Review

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)

---

Review

Gessen, Masha

PERFECT RIGOR: A Genius and the Mathematical Breakthrough of the Century



The story of Russian mathematical prodigy Grigory Perelman, who solved a problem that had stumped everyone for a century—then walked away from his chosen field.

Gessen (Blood Matters: From Inherited Illness to Designer Babies, How the World and I Found Ourselves in the Future of the Gene, 2008, etc.) tells Perelman’s story from the viewpoint of a former student in the educational system of which he was a product. Soviet mathematicians worked in isolation from their Western counterparts during the Stalinist era, but were encouraged because of their value to the state. Perelman, an unusually gifted student, was identified early and his talent nurtured, even though, as a Jew, he faced crippling handicaps under the Soviets. He won the attention of an innovative math coach, Sergei Rukshin. The coach and student bonded early, and Perelman was accepted at a prestigious university and then at a top graduate school. As a star, he was allowed an unusual degree of eccentricity, which in his case included an almost total disregard of other people. Numerous contemporaries attest to his fanatical adherence to a set of ideals that essentially ignored the realities of the Soviet state. Politics, prejudice, making friends and getting ahead in the world—these meant nothing to Perelman. During postdoctoral work in the United States, he refused to cut his hair and nails and turned down job offers because he felt it beneath his dignity to apply for them. Meanwhile, he was homing in on a solution to the Poincaré Conjecture, a topological riddle so puzzling that the Clay Institute in Boston offered a $1 million prize to anyone who could solve it. When, in 2002, Perelman posted a solution on the Internet, he seemed to expect instant recognition. Instead, the world’s mathematicians meticulously checked his proof, which Perelman took it as an insult and turned down a Fields medal, the math equivalent of a Nobel. To this day, there is significant doubt about whether he will accept the Clay prize. Though Gessen was unable to interview her subject, she paints a fascinating picture of the Soviet math establishment and of the mind of one of its most singular products.

An engrossing examination of an enigmatic genius.

 (Agent: Elyse Cheney/Elyse Cheney Literary Associates)

(Kirkus Reviews )

Gessen, Masha. Perfect Rigor: [A Genius] + [The Mathematical Breakthrough of the Century]. Houghton Harcourt. Nov. 2009. c.256p. index. ISBN 978-0-15-101406-4. $26. MATH



The "genius" here is Russian mathematician Grigory Perelman, who announced in 2002 a proof of the Poincaré Conjecture, a complex problem that had resisted the best efforts of the world''s mathematicians for almost a full century. Strangely, since that moment of apparent triumph, Perelman has progressively withdrawn from contact with the mathematics community and with most other humans as well. Russian American journalist and author Gessen (Slate, New Republic; Blood Matters) now tells of Perelman''s very unconventional life and career. Denied access to Perelman himself, she interviewed many people who knew him as a student and (later) as a researcher. Gessen details the special Russian schools for young mathematical prospects that Perelman attended and describes apparently incorrigible Russian anti-Semitism. Most important, the gist of her excellent discussion of the Poincaré Conjecture and its proof should be intelligible even to readers lacking a background in higher mathematics. VERDICT General science buffs curious about how researchers go about creating new mathematics or about the eccentric personalities in this field will be fascinated by Gessen''s book. More advanced readers can also turn to Donal O''Shea''s The Poincaré Conjecture: In Search of the Shape of the Universe.€€?Jack W. Weigel, Ann Arbor, MI

(Library Journal )

See all Editorial Reviews

Product Details

• Hardcover: 256 pages
• Publisher: Houghton Mifflin Harcourt; 2nd Edition edition (November 11, 2009)
• Language: English
• ISBN-10: 015101406X
• ISBN-13: 978-0151014064
• Product Dimensions: 9.7 x 6.1 x 1.1 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (80 customer reviews)
• Amazon Best Sellers Rank: #97,002 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

202 of 217 people found the following review helpful:

5.0 out of 5 stars Nasty and petty book, but great information, November 4, 2009

By 

rbnn (Berkeley, CA United States) - See all my reviews

Amazon Verified Purchase

This review is from: Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century (Hardcover)

This is the first review on Amazon I've written for which I had difficulty determining whether the book merited one or five stars.

Based purely on the information in the book and the story the book tells, it's easily a five-star book.

The author beautifully weaves together fascinating strands of narrative: the bizarre yet powerful culture of mathematics education in the former Soviet Union; the extraordinary brilliance of Grisha Perelman; the deep mathematical questions underlying the problems he solves; and the culture of mathematics generally. (As to this aspect of the book, I might point out, I would have liked to have seen more detail on precisely what problems Grisha solved as a student - e.g. his curriculum, his mathematical Olympiad problems and answers, his final exams - and some photos would have been interesting too.)

So that's the five star part of the book.

The one star part of the book is that it's written, not as a dispassionate account, nor even from the supportive perspective most biographers take towards their subjects, but rather as if the author hates her subject with a passion.

The author's contempt and distaste for Grisha seethes through her prose. Over and over, she takes the noblest, most selfless, and most understandable acts of Grisha and twists them into a pop-psychological narrative of Grisha's supposed mental illness or lack of "understanding" of society. It's a contemptible display, this attempted character assassination of a great man, but at the same time it's so ineptly done that Perelman comes out of it fine, at least for a careful reader.

For example, the author criticizes Perelman (and in harsh personal terms, insinuating he's mentally ill or cannot understand others' point of view) for turning down an assistant professorship at Princeton prior to his solving the Poincare conjecture. But Perleman's rationale is absolutely valid: he had abundantly demonstrated he merited a tenured position, having already proven another major conjecture and demonstrated his supernal talent. Why should he struggle along having to worry about job security on some meager salary, when he deserved to be decently treated? Everyone understands when a good athlete or coach turns down a multimillion dollar salary because he thinks it's not merited; why inveigh against one of the most talented people on the planet when the best that's offered is pay maybe 3% of a top athlete's with no job security? It's a preposterous situation and Grisha was thus absolutely correct in turning down this insulting job offer.

Similarly, the author all too typically criticizes Grisha for his insistence on ascribing proper credit to others and for his reluctance to work with others who are dishonest or corrupt. Her reasoning seems to be that because many, if not most, people lie and cheat, Grisha's insistence on not working with those who do is a sign of a failure to understand society. But it is not that at all: it's a sign of his strong ethical character. If more people took his stance, then corruption and dishonesty would be much less pervasive. It's not Grisha who misunderstands society - he understands it perfectly well; it's the author who doesn't understand Grisha.

Likewise, the author seems to think Grisha's turning down the Field's medal was a sign of some sort of mental illness. But Perelman would have had to share that medal with two other mathematicians, whose work, although impressive, was not in the same class as his own. It would degrade the value of mathematical achievement for Perelman to give his imprimateur to such an obviously unfair award, particularly as a key justification for such awards is to incentivize mathematical achievement.

Indeed, as meticulously documented in the book, what happened to Perelman is one of the great shames of the mathematical community, and even of the entire culture in which it's embedded.

Perelman created a lasting, beautiful, and important contribution to human thought. In response, a group of mathematicians shamelessly tried to steal his work (and, abetted by a credulous press, nearly got away with it); he was shunted over and ignored for major prizes and recognition; mediocrities who have never done anything a millionth as useful spend their time complaining about his clothes or the length of his fingernails. Why should he participate in that farce? Why continue to spend his life helping the development of such a nasty and spiteful, group of ingrates? Given how he was treated, his retreat was entirely rational - but instead of criticizing Perelman's jealous enemies, the author spends most of her time criticizing Perelman.

To some extent, the author attacks not just Perelman but great mathematicians generally. Her theory is that many of them have some sort of mental illness preventing them from understanding ordinary social interactions. To the contrary, the actual data in the book shows them to understand social interactions very well. Indeed, she herself notes that mathematicians were among the leaders in reforming and liberalizing some of the harsh practices of the former Soviet Union. Yet she never claims the bureaucrats who did their level best to imprison or destroy the lives of so many brilliant young Russian scientists were culpable - these, by her theory, one supposes understood social conventions. As long as they dressed well, they were justified, seems to be the subtext of her narrative.

In conclusion, there's a great story underlying the viciousness and pettiness of the narrative: a story of a courageous, ruthlessly honest, deeply creative man who gave to humanity a wonderful gift, and has since been almost universally mocked and rejected. To the extent that this story emerges through the scum of authorial condescension, it's a book well worth reading - but to the extent that condescension occludes this story, it's a contemptible one.

And that's why I did not know whether to give it 5 stars or 1 star. 5 stars for the actual facts; 1 star for its vicious presentation.

But I reluctantly settled on 5 stars because, frankly, the story is interesting and there's nowhere else to get it. This book furthermore would be a very useful jumping off point for someone who wants to write a real biography of the man.

49 of 54 people found the following review helpful:

4.0 out of 5 stars good insights into what makes Perelman tick, October 9, 2009

By 

Nim Sudo - See all my reviews

This review is from: Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century (Hardcover)

(What's this?)

In 2002-3, Grisha Perleman, a reclusive Russian mathematician, posted three preprints on the internet summarizing a proof of the Poincare conjecture, one of the most famous unsolved problems in mathematics. During a lecture tour in the US in 2004 he was offered positions at countless top universities, but he turned all of these offers down and returned to a quiet life in Russia. In 2006 he was awarded the Fields medal, one of the highest honors in mathematics and comparable to a Nobel prize, for his work. However, in a surprising move, he declined to accept the award. He also resigned his position at the Steklov Institute (a Russian mathematics research institute), cut off contact with mathematical colleagues, and as far as anyone knows has left mathematics completely.

Why did he decline the Fields medal and effectively leave mathematics?

The main achievement of this book, in my opinion, is to give a plausible picture of what makes Perelman tick and to make these decisions, which may at first appear bizarre, seem understandable. To try to summarize it in a sentence: real like is filled with small dishonesties, but Perelman has a strict personal moral code which does not tolerate these, so he chose to withdraw from the system instead (and was previously sheltered from ordinary real-world issues). But the book gives a much more convincing picture than my one-sentence attempt at a summary. (It should be mentioned that the author was unable to interview Perelman directly, only some people close to him, which makes the achievement all the more remarkable.)

Along the way we get an interesting portrait of the Soviet mathematical system in which Perelman was raised (although if any former Soviet mathematicians read this book, I would like to know how much of this they agree with).

The book spends little time explaining what the Poincare conjecture is, and does not do so until a relatively late chapter. This chapter is a disaster, full of wrong or nonsensical statements. The author clearly doesn't understand math at this level. There are also little annoyances elsewhere which indicate deficient mathematical fact-checking. (Dear Publisher: When you publish a popular book about math, please have it fact-checked by someone who actually knows math! I'll be happy to send you my cv if you're interested.) Anyway, as mentioned above, the mathematical content is only a small part of the book, so one can ignore these annoyances and focus on the rest of the book, which does an excellent job of explaining the human story.

Let me end by comparing this book to two other popular books on the Poincare conjecture, by O'Shea and Szpiro. O'Shea actually knows what he is talking about regarding the mathematics, and does a very good (if not perfect) job of explaining it. However the non-mathematical parts of his book are dull at times. Szpiro's book does a lousy job of explaining the math, but an excellent job of explaining the human story. However his book discusses a number of people related to the story, e.g. historical characters such as Poincare. Gessen's book is focused on Perelman and does a much better job getting under his skin. So if you already know what the Poincare conjecture is or don't need to know and are only interested in the human story, then this book is highly recommended.

35 of 45 people found the following review helpful:

5.0 out of 5 stars The Perfect Soviet Mathbot, September 23, 2009

By 

oldtaku (San Diego, CA United States) - See all my reviews

This review is from: Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century (Hardcover)

(What's this?)

First, this is not a deep examination of the Poincaré Conjecture, nor is it meant to be. See Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles for a good book on that. This is a biography of the genius who solved it. It also means that if you're math-phobic, never fear. This is a book about human problems.

Perelman is a notorious recluse who almost completely withdrew from the world after he solved the problem. He won't talk to reporters or biographers, or even other mathematicians. This presents something of a dilemma to anyone seeking to do a biography of him, which is perhaps why most books on the problem avoid discussing him too much. The author, however, is uniquely qualified. Like Perelman, Gessen grew up in the last days of the Soviet Union. As a consequence, this book is the result of extensive interviews of people who knew him (and I use the past tense because he's cut off ties with everyone).

Even if Perelman were not involved at all the first third of the book, which describes the Soviet math establishment, is gripping. The USSR despised merit, distrusted scientists and other intellectuals, and Jews like Perelman were considered even worse than intellectuals. But they needed mathematicians for the war effort and to show off the glory of the Soviet system, and unlike genetics they didn't really see how math could be too dangerous. So you ended up with this little isolated math community where even uncloseted homosexuals (even worse than Jews!) could teach. As the book says, if you were a woman you had to be twice as good, and if you were a Jew you had to be four times as good, but once you were in the system it was a protective cocoon.

The portrait of Perelman that emerges is almost a caricature of the brilliant, focused, unsociable scientist, but I don't believe this is Gessen's failing given the sheer number of people who paint a similar portrait. It's quite heartbreaking to see how the system that protected and sheltered him also left him totally unable to cope with the outside world. You might think 'Perfect Soviet Mathbot' was a flippant title for the review, but he almost seems to have been deliberately programmed to solve this problem then self destruct.

The author has written for numerous magazines, but avoids the usual trap of trying to write a book as a long magazine article (the too punchy style gets old fast). It's paced quite well. Every page contains interesting anecdotes and information, and I never felt like she was trying to pad the book - in fact, it seems obvious she had far too much information from her hundreds of hours of interview material and had pared it back substantially. And that's a good thing! It clocks in at about 200 pages, and I never felt a page of it was wasted. I finished this in one night, and I learned a lot. That's a five star book.