Customer Reviews

Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century

5 star:		(38)
4 star:		(29)
3 star:		(7)
2 star:		(4)
1 star:		(2)

 

 

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.

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.

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.

I first read of the Poincare Conjecture and the man who provided its proof, Grigory Perelman, in an article that appeared in the New York Times. More recently, I read a chapter on the Conjecture and Perelman in The Math Book by Clifford Pickover. I was happy to be able to obtain Perfect Rigor, which further explains the background of the Conjecture and the man who proved it.

Poincare was a contemporary of Albert Einstein. He worked in whatever areas pleased him, including both math and physics. Interestingly, Poincare, as Einstein, studied the relation between energy and mass. Poincare's Conjecture is something else again. It was published at the beginning of the twentieth century around the same time as Einstein's Special Relativity, but was not proved until recently. The proofs of relativity theory are readily apparent to me. They are based on observations of the physical world. However, the Conjecture is purely theoretical. Fundamentally, it deals with the topological difference between spheres and other objects such as doughnuts (Mmmm ... doughnuts).

Perfect Rigor describes the life of Grigory Perelman who grew up in the Soviet Union, and eventually, to the surprise of at least the New York Times, provided a proof of the Poincare Conjecture. Perelman then withdrew from the public eye. He has declined to accept the Fields medal for his work, and it is speculated that he may decline a $1 million prize for solving the Conjecture.

How do you explain the eccentric nature of Perelman? Is he crazy? I do not think so. The author explains that he exhibits the symptoms of Asperger's syndrome, a high-level form of autism. This makes sense to me. In the course of my work, I have met two well-known mathematicians who also lack many of the usual social graces. Perelman's behavior is entirely consistent with expectations for Asperger people: self-centered, socially inept, intelligent, and often highly focused on a single subject. Grigory has had to overcome a lot just to deal with people. I hope that he does get it together enough to take the money.

Grigory Perelman was a brilliant young Russian mathematician who disappeared from view in the mid-1990s after some very impressive achievements. In 2002 he stunned the mathematical world by resurfacing with a proof of the Poincare conjecture, one of the outstanding unsolved problems in mathematics. After explaining his results in a series of talks in the United States, he returned to Russia and gradually retreated into more and more extreme isolation.

His spectacular achievements and unusual behavior attracted popular attention, especially after he failed to publish his results, merely posting them on the Internet, and refused the Fields Medal, the great award in professional mathematics. Interest was further piqued by a million dollar prize offered for the Poincare solution, which will likely be offered to Perelman this year.

The story of the problem and solution has inspired at least two good popular books, Poincare's Prize and The Poincare Conjecture. This book concentrates instead on Perelman himself, and the Russian mathematical system in which he grew up, and his professional relationships (he appears to have had few personal relationships outside his mother and sister). The great difficulty in this project, of course, is that Perelman refused to speak with the author and there is sparse secondary material available. The book is based primarily on unhelpful official records and interviews with colleagues and former acquaintances. Few of the interview subjects claimed to understand him well, and all seemed anxious not to offend him. None gives any insight into the period that transformed him from an everyday eccentric brilliant mathematician to the most eccentric and brilliant mathematician in recent memory.

The major negative aspect of the book is the author's indiscriminate mixing of speculation and opinion with verifiable fact. She tries much too hard to make the story both coherent and satisfying, without the necessary information. She also uses it as a platform for her views about the Soviet Union, especially in the 1970s and 80s, and also the mathematical profession. These views are not unreasonable, but they are not well supported in this book. In the absence of both central character and driving motive, these aspects color the story far more than they should. The mathematics of the conjecture and solution are discussed only in the most cursory way, which may relieve many non-mathematical readers, but means another ballast is missing.

On the other hand, without some unconventional reporting, the book could not have been written at all. That would have deprived us of many fascinating details. I can't resist saying the author explores a manifold with wonderful neighborhoods, but errs in thinking she can use local conditions to describe its overall shape. The writing is beautiful and many parts can stand on their own as essay or even poetry. The book is a pleasure to read.

I recommend this book highly, with the warning that it is a bunch of jigsaw puzzle pieces that the author has to force to look like the picture on the cover of the box. I love many of the pieces, but I don't think they were put together right, and I'm not even sure if they're all from the same puzzle.

The story is fascinating. The storyteller's ability has positives and negatives. The author interviews all Perelman's old professors, his friends and coworkers. However, she never interviews the subject or the subject's mother. This makes her objective, but it seems like she gets this image of Perelman and no amount of evidence to the contrary is going to convince her she's wrong. She relates the interviews, but then points out the interviewees have to be wrong about Perelman. It is true that Perelman is very private person, and the author probably does have a more comprehensive picture of the subject than any of the people she interviewed, but it is annoying.

Another problem is both a strength and a weakness. The author is a Russian Jew and is good in math. Thus, her life has many of the same trials as Perelman. However, the analysis of society and the school system comes off as a personal narrative and not a very objective analysis.

The author thinks Perelman has Aspergers. She's probably right. However, she has no proof. She talks to Asperger experts and they refuse to diagnose him. She then relates all the insights this diagnosis gives us. I found that a tad annoying. She also tries to get into Perelman's motivations about why he made certain decisions. She's never met the man and it seems disingenuous. Final problem, she presents math concepts and writes about the Poincaire conjecture. Her explanations are far more confusing than helpful.

In summary, the story is great, but writing at times has problems. I thought the book could be much shorter.

No one is lonelier than the true genius, and rare is the true genius lonelier than the mathematical genius.

Grigory Perelman is a first-rate mathematical genius whose unique mind unraveled the Poincare Conjecture, a topological problem which had stymied top minds for over a century. Masha Gessen, no slouch herself, undertook to understand how he did it and why he will not accept the $1 million prize for doing so. In the process, we learn the tragic limitations of genius: living in a world among those who will never understand you, bound by the only rules you understand----those you set for yourself.

Perelman is the closest humanity has come to producing an Ayn Rand archetype. He doesn't undertake problem-solving for the glory, for the money, or for the fame---he simply follows his intellectual interest, and once a problem is solved to his satisfaction, moves on.

Geshen is perhaps too ready to psychoanalyze Perelman from afar---she didn't succeed in getting an interview with him---and the book unfortunately has a little too much of the therapeutic in it for my taste. Perelman is only a tragic figure by our lights---by his own, he set out to conquer mathematics and succeeded. He is one of the fortunate few who realized a lifelong ambition and moved on to other pursuits.

One need not be mentally defective in order to appreciate that, nor even to classify such as a life well-lived.

As a retired research engineer who has spent his entire life either using mathematics or being taught by mathematicians, I actually can empathize with Grigory Perelman's plight - told so well by mathematician-author Masha Gessen. Although Perelman's affliction is an extreme case, many engineers, I think, may have a least borderline Asperger's Syndrome, the low-level autism that causes poor people skills and single-mindedness. This is a fascinating story; a peak into the Russian school system, as well as into a life so single minded that only mathematics mattered - eventually only one problem mattered. After Perelman had applied his powerful mind to that problem to the point of complete isolation, he solved it. However, it seemed to him that no one really understood the significance of the accomplishment. Instead, those who did not even understand the problem proposed to give him money and rock star fame for solving it. That was not the appreciation by colleagues that he really needed. In fact, by the time he had solved the problem, and it had been recognized, he had alienated most of his colleagues. Some were even saying that he had made a mistake or that they had solved it instead. What he needed were friends, but with his ultra-brilliant mind and Asperger's drill-like concentration on mathematics, he did not know how to be a friend.

So what is this problem? As I understand it, the job is to prove that any completely enclosed surface (without holes) can be conformally mapped into a closed spherical surface. Why is this important? Well it simplifies the boundary conditions for calculations inside the sphere - some say it can be applied to calculation of properties of the universe. But to a mathematician, the significance is that it had never been done before, though the world's best mathematicians had tried for millennia.

I wish Dr. Perelman well, and hope he can somehow find peace in his soul. And I am grateful to the author, for this interesting biography. The writing was mostly well done, although it obviously consisted of different pieced-together interviews, and sometimes seemed a little disorganized.

In 2006 an eccentric Russian mathematician named Grigori Perelman reportedly solved one of the world's greatest and most challenging mathematical problems. The Poincare conjecture is a profoundly difficult and arcane topological problem that had been unsolved for over a century. In 1998, the Clay Institute in Boston famously called it one of seven most important unsolved mathematical problems, promising a million dollars to anyone who could discover a viable solution. In August 2006, Perelman was awarded the Fields Medal, the mathematical equivalent of the Nobel Prize. Perelman declined to accept the award or to appear at the congress. He has since stopped working on mathematics. On March 18 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize Problems award of $1,000,000, for his resolution of the Poincaré conjecture. Perelman declined the award as reported in The New York Times on July 3 2010, asserting that Columbia University Mathematics Professor Richard Hamilton was equally entitled to the award. Perelman has built some of his work on Hamilton's and has always been careful to credit it at every opportunity, exhibiting great generosity of spirit.

Perelman's brilliance as a mathematician and eccentricity and strangeness as a person are well depicted in this rather easy book to read. There are no complex mathematics, the author predominantly relying on descriptive history more than any other technique. This makes the book ideal for general readers with little or no background in mathematics or science. You are unlikely to be intimidated by anything contained herein. More specialized readers may find the lack of even rudimentary mathematical analysis a disappointment that obscures the precise nature of Perelman's achievement. This is a good book that might have been improved by at least some mathematical analysis to help clarify this complex topic. I learned quite a bit about the somewhat bigoted Soviet system of technical education and the history behind the rise of this mathematically gifted genius. I felt slightly frustrated, however, that the nature of Perelman's creative work wasn't examined enough for me to appreciate its rigor and its beauty. But as a history and cultural background this book is superb.

An engrossing and fascinating look at the mind and social milieu of the great Soviet mathematician, Grigory ("Grisha") Perelman. That this exotic (and "Greek") mathematical culture could thrive in the midst of one of the Twentieth Century's most repressive regimes is astonishing in and of itself. That it could produce such extraordinary mathematical minds --driven as much by a love of aesthetic beauty in poetry or music as they were by the austere rigor of mathematical logic-- is a testament to the dedication and drive of the teachers who made it possible. Some of them are introduced to us in this work, but they are not the focus. The milieu they create is important to the author only insofar as it helps her "explain" to us how a great mathematical mind can be "created" and nurtured, even in a system so bleakly oppressive.

"Grisha" Perelman is probably the world's greatest living mathematician --though he has dropped out of the mathematical community in recent years. His singular achievement has been to solve the Poincaré Conjecture, one of the most difficult problems in modern math. Perelman, however, is less than pleased with what he has always regarded as a lack of integrity in the international community of mathematics scholars. In particular, he has felt slighted and undervalued by the failure of his intellectual peers to confirm and validate his work in a timely fashion. Perelman has also felt sullied by the insinuation in the western media (particularly The New York Times) that his work was motivated less by the perfectionist drive of the pure mathematician than by the decision of the Clay Mathematics Institute in Boston to award a million dollar prize to anyone who solved the Poincaré Conjecture, or one of six other math conundrums.

Perelman is a pure mathematician in the time-honored sense that he's not wrestling with a problem in the hope of becoming rich. The glory that he seeks is personal and professional, not popular and material. The accolades must come from ones peers, not from those (like me) outside the mathematical community -- people incapable of truly judging the quality of his achievement.

There's a social/ideological component to this mind-set too, though the author -- rather oddly-- doesn't pick up on it: Perelman is a true representative of the anti-capitalist, anti-cash-nexus ideology of the Soviet Union. Socialist Idealism is part and parcel of Perelman's meritocratic approach to the study of mathematics: One is motivated by higher principles, rather than by the mere scramble for personal wealth.

This book is written by a mathematician with a keen eye for what makes Perelman so intriguing to the ordinary reader. Gessen, herself a product of the Soviet math system, is ideally suited to the task of introducing the rest of us to this phenomenally gifted mind. The book provides just enough math to make the Conjecture an interesting conundrum for the non-math reader; but this is not a book about math. It's about the mind of an undoubtedly Great Mathematician.

I won't spoil the book by revealing Gessen intriguing "clinical" analysis of Perelman's psyche, but I will say that she has convinced at least one reader of the rightness of her diagnosis.

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One of the more interesting and revealing anecdotes in this book describes how one of Perelman's friends and mentors, Mikhail Gromov, viewed Perelman's refusal to deal with the ICM committee and his refusal to accept the Fields Medal, which would be awarded on behalf of the international math community by the king of Spain. Gessen on pp 195-196:


[Gromov:]"Most people are perfectly content to talk to committees. They are satisfied to travel to Beijing and accept a prize from the hands of Chairman Mao. Or the king of Spain, which is the same thing."

Why I pleaded was the king of Spain undeserving of the honor of hanging a medal around Perelman's neck?

"Who the hell are kings?"

Gromov was really cranked up now.

"Kings are the same kind of crap as communists. Why should a king give a mathematician his prize? Who is he? He is nothing. From a mathematician's point of view, he is nothing. Same as Chairman Mao. So one of them seized power like a robber while the other got it from his father. That's no difference." In contrast to these people, Gromov explained, Perelman had actually made a real contribution.

----

What a wonderfully revealing anecdote -- itself an insight into the pure, unsullied "moral" stance of Grigory Perelman, who refused to compromise his principles ... no matter how arcane and indecipherable they may seem to outsiders.

Gessen provides other similar gems in this wonderfully engaging and absorbing intellectual biography. I hope she manages to connect with a wide, popular audience because both the book and its subject matter deserve wide acclaim.