Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century by Masha Gessen (PDF)

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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.

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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, MashaPERFECT RIGOR: A Genius and the Mathematical Breakthrough of the CenturyThe 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)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. MATHThe “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 About the Author MASHA GESSEN has written for Slate, the New Republic, Vanity Fair, the New York Times, and other publications. The author of three previous books, she lives in Brookline, Massachusetts. Excerpt. © Reprinted by permission. All rights reserved. PROLOGUEA Problem for a Million DollarsNumbers cast a magic spell over all of us, but mathematicians are especially skilled at imbuing figures with meaning. In the year 2000, a group of the world’s leading mathematicians gathered in Paris for a meeting that they believed would be momentous. They would use this occasion to take stock of their field. They would discuss the sheer beauty of mathematics —a value that would be understood and appreciated by everyone present. They would take the time to reward one another with praise and, most critical, to dream. They would together try to envision the ele gance, the substance, the importance of future mathematical accomplishments.The Millennium Meeting had been convened by the Clay Mathematics Institute, a non profit organization founded by Boston- area businessman Landon Clay and his wife, Lavinia, for the purposes of popularizing mathematical ideas and encouraging their professional exploration. In the two years of its existence, the institute had set up a beautiful office in a building just outside Harvard Square in Cambridge, Massachusetts, and had handed out a few research awards. Now it had an ambitious plan for the future of mathematics, “to record the problems of the twentieth century that resisted challenge most successfully and that we would most like to see resolved,” as Andrew Wiles, the British number theorist who had famously conquered Fermat’s Last Theorem, put it. “We don’t know how they’ll be solved or when: it may be five years or it may be a hundred years. But we believe that somehow by solving these problems we will open up whole new vistas of mathematical discoveries and landscapes.”As though setting up a mathematical fairy tale, the Clay Institute named seven problems —a magic number in many folk traditions —and assigned the fantastical value of one million dollars for each one’s solution. The reigning kings of mathematics gave lectures summarizing the problems. Michael Francis Atiyah, one of the previous century’s most in ?u en tial mathematicians, began by outlining the Poincaré Conjecture, formulated by Henri Poincaré in 1904. The problem was a classic of mathematical topology. “It’s been worked on by many famous mathematicians, and it’s still unsolved,” stated Atiyah. “There have been many false proofs. Many people have tried and have made mistakes. Sometimes they discovered the mistakes themselves, sometimes their friends discovered the mistakes.” The audience, which no doubt contained at least a couple of people who had made mistakes while tackling the Poincaré, laughed.Atiyah suggested that the solution to the problem might come from physics. “This is a kind of clue —hint —by the teacher who cannot solve the problem to the student who is trying to solve it,” he joked. Several members of the audience were indeed working on problems that they hoped might move mathematics closer to a victory over the Poincaré. But no one thought a solution was near.True, some mathematicians conceal their preoccupations when they’re working on famous problems —as Wiles had done while he was working on Fermat’s Last —but generally they stay abreast of one another’s research. And though putative proofs of the Poincaré Conjecture had appeared more or less annually, the last major breakthrough dated back almost twenty years, to 1982, when the American Richard Hamilton laid out a blueprint for solving the problem. He had found, however, that his own plan for the solution —what mathematicians call a program —was too difficult to follow, and no one else had offered a credible alternative. The Poincaré Conjecture, like Clay’s other Millennium Problems, might never be solved.Solving any one of these problems would be nothing short of a heroic feat. Each had claimed dec ades of research time, and many a mathematician had gone to the grave having failed to solve the problem with which he or she had struggled for years. “The Clay Mathematics Institute really wants to send a clear message, which is that mathematics is mainly valuable because of these immensely difficult problems, which are like the Mount Everest or the Mount Himalaya of mathematics,” said the French mathematician Alain Connes, another twentieth-century giant. “And if we reach the peak, first of all, it will be extremely difficult —we might even pay the price of our lives or something like that. But what is true is that when we reach the peak, the view from there will be fantastic.”As unlikely as it was that anyone would solve a Millennium Problem in the foreseeable future, the Clay Institute nonetheless laid out a clear plan for giving each award. The rules stipulated that the solution to the problem would have to be presented in a refereed journal, which was, of course, standard practice. After publication, a two-year waiting period would begin, allowing the world mathematics community to examine the solution and arrive at a consensus on its veracity and authorship. Then a committee would be appointed to make a final recommendation on the award. Only after it had done so would the institute hand over the million dollars. Wiles estimated that it would take at least five years to arrive at the first solution —assuming that any of the problems was ac tually solved —so the procedure did not seem at all cumbersome.Just two years later, in November 2002, a Russian mathematician posted his proof of the Poincaré Conjecture on the Inter net. He was not the first person to claim he’d solved the Poincaré —he was not even the only Russian to post a putative proof of the conjecture on the Inter net that year—but his proof turned out to be right.And then things did not go according to plan —not the Clay Institute’s plan or any other plan that might have struck a mathematician as reasonable. Grigory Perelman, the Russian, did not publish his work in a refereed journal. He did not agree to vet or even to review the explications of his proof written by others. He refused numerous job offers from the world’s best universities. He refused to accept the Fields Medal, mathematics’ highest honor, which would have been awarded to him in 2006. And then he essentially withdrew from not only the world’s mathematical conversation but also most of his fellow humans’ conversation.Perelman’s peculiar behavior attracted the sort of attention to the Poincaré Conjecture and its proof that perhaps no other story of mathematics ever had. The unprecedented magnitude of the award that apparently awaited him helped heat up interest too, as did a sudden plagiarism controversy in which a pair of Chinese mathematicians claimed they deserved the credit for proving the Poincaré. The more people talked about Perelman, the more he seemed to recede from view; eventually, even people who had once known him well said that he had “disappeared,” although he continued to live in the St. Petersburg apartment that had been his home for many years. He did occasionally pick up the phone there —but only to make it clear that he wanted the world to consider him gone.When I set out to write this book, I wanted to find answers to three questions: Why was Perelman able to solve the conjecture; that is, what was it about his mind that set him apart from all the mathematicians who had come before? Why did he then abandon mathematics and, to a large extent, the world? Would he refuse to accept the Clay prize money, which he deserved and most certainly could use, and if so, why?This book was not written the way biographies usually are. I did not have extended interviews with Perelman. In fact, I had no conversations with him at all. By the time I started working on this proj ect, he had cut off communication with all journalists and most people. That made my job more difficult —I had to imagine a person I had literally never met —but also more interesting: it was an investigation. Fortunately, most people who had been close to him and to the Poincaré Conjecture story agreed to talk to me. In fact, at times I thought it was easier than writing a book about a cooperating subject, because I had no allegiance to Perelman’s own narrative and his vision of himself —except to try to figure out what it was. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Pure mathematicians have the reputation of being otherworldly and divorced from practical matters. Grisha or Grigory Perelman, the Russian mathematician who at the turn of this century solved one of the great unsolved problems in mathematics, the Poincare Conjecture, is sadly or perhaps appropriately an almost perfect specimen of this belief. For Perelman, even the rudiments of any kind of monetary, professional or material rewards resulting from his theorem were not just unnecessary but downright abhorrent. He has turned down professorships at the best universities in the world, declined the Fields Medal, and will probably not accept the 1 million dollar prize awarded by the Clay Mathematics Institute for the solution of the some of the most daunting mathematical problems of all time. He has cut himself off from the world after seeing the publicity that his work received and has become a recluse, living with his mother in St. Petersburg. For Perelman, mathematics should purely and strictly be done for its own sake, and could never be tainted with any kind of worldly stigma. Perelman is truly a mathematical hermit, or what a professor of mine would call using mathematical jargon, a “hermitian operator”.Masha Gessen tells us the story of this remarkable individual, but even more importantly tells us the story of the Russian mathematical system that produced this genius. The inside details of Russian mathematics were cut off from the world until the fall of the Soviet Union. Russian mathematics was nurtured by a small group of extraordinary mathematicians including Andrey Kolmogorov, the greatest Russian mathematician of the twentieth century. Kolmogorov and others who followed him believed in taking latent, outstanding talent in the form of young children and single-mindedly transforming them into great problem solvers and thinkers. Interestingly in the early Soviet Union under Stalin’s brutal rule, mathematics flourished where other sciences languished partly because Stalin and others simply could not understand abstract mathematical concepts and thus did not think they posed any danger to communist ideology. Soviet mathematics also got a boost when its great value was recognized during the Great Patriotic War in building aircraft and later in work on the atomic bomb. Mathematicians and physicists thus became unusually valued assets to the Soviet system.Kolmogorov and a select band of others took advantage of the state’s appreciation of math and created small, elite schools for students to train them for the mathematical olympiads. Foremost among the teachers was a man named Sergei Rukshin who Gessen talks about at length. Rukshin believed in completely enveloping his students in his world. In his schools the students entered a different universe, forged by intense thought and mathematical camaraderie. They were largely shielded from outside influences and coddled. The exceptions were women and Jews. Gessen tells us about the rampant anti-Semitism in the Soviet Union which lasted until its end and prevented many bright Jewish students from showcasing their talents. Perelman was one of the very few Jews who made it, and only because he achieved a perfect score in the International Mathematical Olympiad.Perelman’s extreme qualities were partly a result of this system, which had kept him from knowing about politics and the vagaries of human existence and insulated him from a capricious world where compromise is necessary. For him, everything had to be logical and utterly honest. There was no room for things such as diplomacy, white lies, nationalism and manipulation to achieve one’s personal ends. If a mathematical theorem was proven to be true, then any further acknowledgment of its existence in the form of monetary or practical benefits was almost vulgar. This was manifested in his peculiar behavior in the United States. For instance, when he visited the US in the 90s as a postdoctoral researcher he had already made a name for himself. Princeton offered the twenty nine year old an assistant professorship, a rare and privileged opportunity. However Perelman would settle for nothing less than a full professorship and was repulsed even by the request that he officially interview for the position (which would have been simply a formality) and submit his CV. Rudimentary formalities which would be normal for almost everyone were abhorrent for Perelman.After being disillusioned with what he saw as an excessively materialistic academic food chain in the US, Perelman returned to Russia. For five years after that he virtually cut himself off from his colleagues. But it was then that he worked on the Poincare Conjecture and created his lasting achievement. Sadly, his time spent intensely working alone in Russia seemed to have made him even more sensitive to real and perceived slights. However, he did publicly put up his proofs on the internet in 2002 and then visited the US. For a brief period he even seemed to enjoy the reception he received in the country, with mathematicians everywhere vying to secure his services for their universities. He was unusually patient in giving several talks and patiently explaining his proof to mathematicians. Yet it was clear he was indulging in this exercise only for the sake of clarifying the mathematical concepts, and not to be socially acceptable.However, after this brief period of normalcy, a series of events made Perelman reject the world of human beings and even that of his beloved mathematics. He was appalled by the publicity he received in newspapers like the New York Times which could not understand his work. He found the rat race to recruit him, with universities climbing over each other and making him fantastic offers of salary and opportunity, utterly repulsive. After rejecting all these offers and even accusing some of his colleagues of being traitors who gave him undue publicity, he withdrew to Russia and definitively severed himself from the world. The final straw may have been two events; the awarding of the Fields Medal which, since his work was still being verified, could not explicitly state that he had proven the Poincare conjecture, and the publication of a paper by Chinese mathematicians which in hindsight clearly seems to have been written for stealing the limelight and the honors from Perelman. For Perelman, all this (including the sharing of the Fields with three other mathematicians) was a grave insult and unbecoming of the pursuit of pure mathematics.Since then Perelman has been almost completely inaccessible. He does not answer emails, letters and phone calls. In an unprecedented move, the president of the International Mathematical Congress which awards the Fields Medals personally went to St. Petersburg to talk him out of declining the prize. Perelman was polite, but the conversation was to no avail. Neither is there any indication that he would accept the 1 million dollar Clay prize. Gessen himself could never interview him, and because of this the essence of Perelman remains vague and we don’t really get to know him in the book. Since Gessen is trying to somewhat psychoanalyze her subject and depends on second-hand information to draw her own conclusions, her narrative sometimes lacks coherence and meanders off. As some other reviewers have noted, the discussion of the actual math is sparse and disappointing, but this book is not really about the math but about the man and his social milieu. The content remains intriguing and novel.Of course, Perelman’s behavior is bizarre and impenetrable only to us mere mortals. For Perelman it forms a subset of what has in his mind always been a perfectly internally consistent and logical set of postulates and conclusions. Mathematics has to be done for its own sake. Academic appointments, prizes, publicity and professional rivalries should have no place in the acknowledgement of a beautiful mathematical proof. While things like applying for interviews and negotiating job offers may seem to us to be perfectly reasonable components of the real world and may even seem to be necessary evils, for Perelman they are simply evils interfering with a system of pure thought and should be completely rejected. He is the epitome of the Platonic ideal; where pure ideas are concerned, any human association could only be a deeply unsettling imposition.

⭐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 Grigori seethes through her prose. Over and over, she takes the noblest, most selfless, and most understandable acts of Grigori and twists them into a pop-psychological narrative of his 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) 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 an athlete rejects a multimillion dollar salary offer 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 Grigori was thus absolutely correct in turning down this insulting job offer.Similarly, the author all too typically criticizes Grigori for his insistence on ascribing proper credit to others and for his reluctance to work with others who are dishonest. Her reasoning seems to be that because many, if not most, people lie and cheat, Grigori’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 Grigori who misunderstands society – he understands it perfectly well – it’s the author who doesn’t understand Grigori.Likewise, the author seems to think Grigori’s turning down the Field’s medal was aberrant and irrational. But Perelman, like some other mathematicians, doesn’t believe in such prizes (just recently Peter Scholze turned down another award from a mathematical prize, for example).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. Why should he participate in that farce? Why continue to spend his life helping spiteful ingrates? Given how he was treated, his retreat was entirely rational – but instead of criticizing the jealousy and pettiness of Perelman’s 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 demonstrates that they understand social interactions very well. Indeed, she herself notes that mathematicians were among the leaders in reforming and liberalizing harsh practices of the former Soviet Union. Yet she never claims the bureaucrats who did their level best to 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.

⭐For people interested in Dr. Perelman, this is one of the fewest published. It is an indirect research through impressions from people who met Perelman, but it would be dissapointing if someone seeks a complex description by the own personage. The last interpretations about the behaviour of Perelman by Mashga Gessen are very keen of being critized and dissapointingly dubious. Generally speaking, it is a useful book to understand the background where Perelman appears but more authorative and respectful books are warranted in terms of biography. Dr. Perelman would be probably one of the our most important genious and honest figures.

⭐This is a very illuminative and likable biography of a living mathematical genius who did not wish to be biographed at all. Yet Ms. Gessen manages to great a vivid and respectful portrait not only of Perelman himself but also of the circumstances where he grew up in the Soviet Union. That society itself with its many paradoxes has provided the impetus for many a mathematical innovation that might have been unimaginable under less repressive circumstances.

⭐Masha Gessen lives in Russia. So did Grisha Perelman. Perelman, as you probably know, turned down offers to work in the US, even as tenured professor, and also turned down opportunities to work in Israel. He felt most at home in Russia.Despite this, while discussing his career, Ms. Gessen has used the book as a plank to complain about discrimination against Jews in Russia! This theme is the main feature of story, until of course Perelman spends some time in the US, when she suddenly sympathizes with others, who had to put up with his eccentric habits of personal hygiene!This would have been a better book if the author had kept out the Jewish Angle which is completely inappropriate in a case where the hero decided that the US of A and even Israel itself were fit to be turned down in favor of returning to Russia. Not every story about Jews can be modified to justify the need for a homeland.Just the other day I discussed the book with Tatiana Dubovchenko who was Perelman’s classmate in some courses. She was amazed at the tone of the book. As a student in the university and as a Russian married to a Cuban, she is quite certain that the whole math scene was dominated by Jews, far in excess of the two percent claimed by Gessen.It would also have been a better book if a little more of the power of his solution had been typed in instead.But the book is important reading as it is one of the few books on Perelman.

⭐Obwohl die Autorin den Helden ihrer Geschichte nie persönlich getroffen hat, schafft sie es dennoch, eine äußerst spannende und lesenswerte Biographie zu schreiben. Das Buch gibt Einblicke in die “Mathematik als Leistungssport” der späten UDSSR. Für jeden Mathematikfan unbedingt zu empfehlen.

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⭐The book tells a consistent story, filled with historical, mathematical, and psychological insights and anecdotes. A smooth reading from the start to the end, without taking sides, but readers develop a feeling for the central personality.

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