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Perfect Rigour: A Genius and the Mathematical Breakthrough of a Century
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 2000, 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 was awarded the prize this year - and declined the money. 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 astonishing abilities. In telling his story, Masha Gessen has constructed a gripping and tragic tale that sheds rare light on the unique burden of genius.
259 pages, Kindle Edition
First published January 1, 2009
104 people are currently reading
2611 people want to read
About the author
Masha Gessen
30 books1,309 followersMasha Gessen (born 1967) is an American-Russian journalist, translator, and nonfiction author. They identify as non-binary and use they/them pronouns.
Born into an Ashkenazi Jewish family in Russia, in 1981 they moved with their family to the United States to escape anti-Semitism. They returned in 1991 to Moscow, where they worked as a journalist, and covered Russian military activities during the Chechen Wars. In 2013, they were publicly threatened by prominent Russian politicians for their political activism and were forced to leave Russia for the United States.
They write in both Russian and English, and has contributed to The New Republic, New Statesman, Granta and Slate. Gessen is a staff writer at The New Yorker, covering international politics, Russia, LGBT rights, and gender issues.
Born into an Ashkenazi Jewish family in Russia, in 1981 they moved with their family to the United States to escape anti-Semitism. They returned in 1991 to Moscow, where they worked as a journalist, and covered Russian military activities during the Chechen Wars. In 2013, they were publicly threatened by prominent Russian politicians for their political activism and were forced to leave Russia for the United States.
They write in both Russian and English, and has contributed to The New Republic, New Statesman, Granta and Slate. Gessen is a staff writer at The New Yorker, covering international politics, Russia, LGBT rights, and gender issues.
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Displaying 1 - 30 of 174 reviews
July 22, 2021
I read this book after reading Prasad Kothari's article on Perelman & possible application of Ricci Flow in data science. There are lot of applications which have come up after Kothari's article hence I started reading this book. Great book. Its is great to know how Perelman grew up, his genius etc. I am glad to live this era and read about these legends.
November 2, 2015
From an Amazon user:
By rbnn (Berkeley, CA United States)
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.
By rbnn (Berkeley, CA United States)
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.
February 15, 2019
Grigorij Perel’man, per chi non lo avesse mai sentito nominare, è un matematico russo (ebreo) che nei primi anni duemila ha dato un enorme contributo alla scienza dimostrando la congettura di Poincaré, considerata uno dei maggiori problemi matematici irrisolti del millennio. Si è conquistato, per i suoi contributi, la medaglia Fields (il “nobel per la matematica”) e un premio di un milione di dollari istituito da una fondazione privata. Ebbene, ha rifiutato entrambi e si è ritirato a vita privata, lasciando il suo incarico all’università di San Pietroburgo, tagliando i ponti con tutte le persone legate in qualche modo a lui - tranne la madre - e rifiutando ogni contatto con il mondo esterno.
Questo libro tenta una sua biografia; tenta, perché l’autrice non ha mai avuto contatti diretti con lui, ma cerca di ricostruirne la vita, l’attività in ambito matematico e soprattutto il temperamento solo basandosi su interviste a persone che hanno incrociato il suo non comune destino.
Quello che ne esce è una carrellata di personaggi singolari appartenenti al mondo matematico accademico (e non) russo e internazionale, e soprattutto un quadro vivido e interessante - e istruttivo - delle dinamiche all’interno di un ambiente solitamente difficile da immaginare per chi non ne fa parte.
Il libro contiene tra l’altro anche una pesante denuncia dell’antisemitismo dominante - anche se mai ufficialmente dichiarato - nell’era sovietica, qualcosa che per una fortuita combinazione di circostanze non è riuscita a fermare la potenza dell’estro matematico di Perel’man.
Direi nel complesso, quindi, un tentativo riuscito e di sicuro interesse, sotto molti punti di vista.
Anche la storia della congettura di Poincaré, di come “Griša” sia riuscito a dimostrarla e del modo singolare con cui abbia divulgato i suoi risultati, seppure eviti (e per fortuna!) dettagli troppo tecnici, è raccontata bene, in modo appassionante, con ottime capacità narrative.
Non mi è tanto piaciuto il tentativo di appioppare a Perel’man la diagnosi di sindrome di Asperger, non mi pare né serio né rispettoso nei suoi confronti dal momento che una diagnosi di questo tipo richiederebbe quantomeno che la persona in questione sia sottoposta a specifici test i cui risultati siano poi valutati da un esperto.
Tuttavia mi sento di perdonare l’autrice perché alla fine si chiude il libro volendogli un po’ di bene a Griša, e se rimane difficile comprendere le sue motivazioni, si riesce almeno a provare rispetto e stima per la sua purezza e il suo rigore (a fronte di tante bassezze e ipocrisie che nell’ambiente matematico sono presenti in egual misura rispetto a qualsiasi altro ambiente).
Un ultimo appunto: qua e là ho avuto la netta impressione che la traduzione fosse migliorabile.
Questo libro tenta una sua biografia; tenta, perché l’autrice non ha mai avuto contatti diretti con lui, ma cerca di ricostruirne la vita, l’attività in ambito matematico e soprattutto il temperamento solo basandosi su interviste a persone che hanno incrociato il suo non comune destino.
Quello che ne esce è una carrellata di personaggi singolari appartenenti al mondo matematico accademico (e non) russo e internazionale, e soprattutto un quadro vivido e interessante - e istruttivo - delle dinamiche all’interno di un ambiente solitamente difficile da immaginare per chi non ne fa parte.
Il libro contiene tra l’altro anche una pesante denuncia dell’antisemitismo dominante - anche se mai ufficialmente dichiarato - nell’era sovietica, qualcosa che per una fortuita combinazione di circostanze non è riuscita a fermare la potenza dell’estro matematico di Perel’man.
Direi nel complesso, quindi, un tentativo riuscito e di sicuro interesse, sotto molti punti di vista.
Anche la storia della congettura di Poincaré, di come “Griša” sia riuscito a dimostrarla e del modo singolare con cui abbia divulgato i suoi risultati, seppure eviti (e per fortuna!) dettagli troppo tecnici, è raccontata bene, in modo appassionante, con ottime capacità narrative.
Non mi è tanto piaciuto il tentativo di appioppare a Perel’man la diagnosi di sindrome di Asperger, non mi pare né serio né rispettoso nei suoi confronti dal momento che una diagnosi di questo tipo richiederebbe quantomeno che la persona in questione sia sottoposta a specifici test i cui risultati siano poi valutati da un esperto.
Tuttavia mi sento di perdonare l’autrice perché alla fine si chiude il libro volendogli un po’ di bene a Griša, e se rimane difficile comprendere le sue motivazioni, si riesce almeno a provare rispetto e stima per la sua purezza e il suo rigore (a fronte di tante bassezze e ipocrisie che nell’ambiente matematico sono presenti in egual misura rispetto a qualsiasi altro ambiente).
Un ultimo appunto: qua e là ho avuto la netta impressione che la traduzione fosse migliorabile.
won-t-even-start-it
November 1, 2019A maybe-to-read. Maybe-maybe?
Pro:
+G. Perelman is an intriguing person. It might be interesting to read about him, provided the said material is trustworthy, adequate, non-judgmental and well-informed. And that's precisely where the contras come forward:
Contra:
-There is about zero information about G. Perelman in the public domain other than the very bare bones. He holds no court. Gives no interviews. So, the big Q: where did the author get the info and how reliable is it all? It must all be 2nd or 3d hand, at best. Or even imaginary.
-Just how capable of understanding math of a level this advanced is the author? I am not aware of her math talent. So, Q is, what is this book about if the author's not qualified to understand the mathematical minutiae of what he did? About what he eats for breakfast or who he quarreled with as a kid or something equally mundane?
-If the reliable info is scarce, how did the book come about? How much of it fantasy or watered down basic facts?
Should I read it? - The million-dollar question.
So, flipping through it proves that it's not really worth too much for me:
- Too little math. (It must be invisible, there's a lot of talk about it but no math, where's it in all its unearthly beauty?)
- Too much politics (I imagine that's Masha's trademark?). Pathetic. I'm sorry.
- Skewed history perception.
- Math is somehow supposed to be a political tool, which, in all seriousness, is just not right, since the 2 are different dimensions.
- A lot more politics than could be considered healthy. Outright Russia-bashing. For example:
Q:
That Russia produced some of the twentieth century greatest mathematicians is, plainly, a miracle. (c) Actually, how about no? You take education where Mathematics, Physics, Chem and a lot of other stuff are not watered down into some Science. You don't go into the pragmaticism. You develop advanced schools for talented kids in every city and town (yep, Soviet school). Add to that the benefits from the Russian Empire leftover minds and you've got it!
- All kinds of twisty twists. Some random people's mutual relations (?), like some random guy who fell out of favour with some Soviet leaders at some point? How's that relevant? What's he got to do with G. Perelman and his ideas and innovations and discoveries? Lots of what feels like conjecture (who does really remember in 20xx, who was thinking what about whom in the year that G. Perelman went to some or other mathematically gifted school? How reliable or relevant such memories can be? I would totally be damned to remember some or other fellow classmates from MY school, no matter who they or I became.) Ughhh….
DNF so far.
No rating, since this one's really wishy-washy.
I should remember not to invest too much of my time into this one, if I ever return to it. Or, as an alternative, read it heavily tranquilized so as not to become too irritated with the journalist-y twisty style of the book.
Pro:
+G. Perelman is an intriguing person. It might be interesting to read about him, provided the said material is trustworthy, adequate, non-judgmental and well-informed. And that's precisely where the contras come forward:
Contra:
-There is about zero information about G. Perelman in the public domain other than the very bare bones. He holds no court. Gives no interviews. So, the big Q: where did the author get the info and how reliable is it all? It must all be 2nd or 3d hand, at best. Or even imaginary.
-Just how capable of understanding math of a level this advanced is the author? I am not aware of her math talent. So, Q is, what is this book about if the author's not qualified to understand the mathematical minutiae of what he did? About what he eats for breakfast or who he quarreled with as a kid or something equally mundane?
-If the reliable info is scarce, how did the book come about? How much of it fantasy or watered down basic facts?
Should I read it? - The million-dollar question.
So, flipping through it proves that it's not really worth too much for me:
- Too little math. (It must be invisible, there's a lot of talk about it but no math, where's it in all its unearthly beauty?)
- Too much politics (I imagine that's Masha's trademark?). Pathetic. I'm sorry.
- Skewed history perception.
- Math is somehow supposed to be a political tool, which, in all seriousness, is just not right, since the 2 are different dimensions.
- A lot more politics than could be considered healthy. Outright Russia-bashing. For example:
Q:
That Russia produced some of the twentieth century greatest mathematicians is, plainly, a miracle. (c) Actually, how about no? You take education where Mathematics, Physics, Chem and a lot of other stuff are not watered down into some Science. You don't go into the pragmaticism. You develop advanced schools for talented kids in every city and town (yep, Soviet school). Add to that the benefits from the Russian Empire leftover minds and you've got it!
- All kinds of twisty twists. Some random people's mutual relations (?), like some random guy who fell out of favour with some Soviet leaders at some point? How's that relevant? What's he got to do with G. Perelman and his ideas and innovations and discoveries? Lots of what feels like conjecture (who does really remember in 20xx, who was thinking what about whom in the year that G. Perelman went to some or other mathematically gifted school? How reliable or relevant such memories can be? I would totally be damned to remember some or other fellow classmates from MY school, no matter who they or I became.) Ughhh….
DNF so far.
No rating, since this one's really wishy-washy.
I should remember not to invest too much of my time into this one, if I ever return to it. Or, as an alternative, read it heavily tranquilized so as not to become too irritated with the journalist-y twisty style of the book.
November 5, 2009
Ehhhh, I was expecting a good deal more than that. The New Yorker article from 2006 was better reading overall ("Manifold Destiny", http://www.newyorker.com/archive/2006...).
-----
Ahhh, Perelman, you ultimate enigma. Upon this book's arrival, I will lock myself in the bathroom with a liter of homebrewed absinthe, a 24-pack of TaB, and my weight in Dover Mathematical Publishing. I will read it, probably several times. I will come away as confounded as I arrived, and likely several pounds lighter. I will refer to this as my "detoxification diet" and continue to laugh at people who eat natural foods. Gregori Perelman subsists on first-order differential equations and broken dreams, refracted through a prism and spread thinly on black bread. And vodka, vodka distilled in arbitrary closed 3-manifolds which Ricci-tighten and relax through all the phases of 3-sphere homeomorphy, like topological lava lamps. He credits his insights to this strict regimen, along with counting to infinity twice each morning.
-----
Ahhh, Perelman, you ultimate enigma. Upon this book's arrival, I will lock myself in the bathroom with a liter of homebrewed absinthe, a 24-pack of TaB, and my weight in Dover Mathematical Publishing. I will read it, probably several times. I will come away as confounded as I arrived, and likely several pounds lighter. I will refer to this as my "detoxification diet" and continue to laugh at people who eat natural foods. Gregori Perelman subsists on first-order differential equations and broken dreams, refracted through a prism and spread thinly on black bread. And vodka, vodka distilled in arbitrary closed 3-manifolds which Ricci-tighten and relax through all the phases of 3-sphere homeomorphy, like topological lava lamps. He credits his insights to this strict regimen, along with counting to infinity twice each morning.
February 23, 2019
Grigorij Jakovlevič Perel'man ovvero la personificazione di Bartleby.
November 11, 2018
La storia di Perel’man e della congettura di Poincaré sembre essere stata partorita da uno sceneggiatore di Hollywood. Un problema matematico insoluto per quasi un secolo e capace di portare pericolosamente vicini alla follia più di uno dei pur bravissimi scienziati che hanno dedicato le loro energie a risolverlo. Un ricercatore isolato, eccentrico, bravissimo che, raggiunto questo Sacro Graal, rifugge da tutti gli onori che ne conseguono, arrivando a rifiutare il più prestigioso premio a cui un matematico possa ambire, la medaglia Fields, e un premio speciale da un milione di dollari.
segue su
http://maddmaths.simai.eu/divulgazion...
segue su
http://maddmaths.simai.eu/divulgazion...
February 13, 2020
This is the story of Grigori (Grisha) Perelman, the Russian mathematician who famously published a solution to the Poincaré conjecture at the beginning of the century, but rejected all the adulation that came with it and has apparently left mathematics. There's also a lot about the history of the mathematics community in the Soviet Union in the 20th century. I also learned that Anti-Semitism is still much more prevalent, and overt, in Russia than I had realized.
My favorite line: "To those who were seeing him for the first time, Perelman looked striking but entirely within the weirdness bounds of mathematicians."
My favorite line: "To those who were seeing him for the first time, Perelman looked striking but entirely within the weirdness bounds of mathematicians."
Read
December 22, 2017Có những quyển sách mà cầm lên rồi là không muốn đặt xuống, đây là 1 quyển sách như vậy.
Cuốn sách kể về Grigory Perelman, 1 nhà toán học Nga đã giải quyết giả thuyết Poincaré, 1 trong 7 bài toán thiên niên kỷ, 1 danh sách do viện toán học Clay lập ra (có thể so sánh nó với danh sách 23 bài toán của Hilbert, 1 trong những động lực phát triển cho nền toán học thế kỷ 20). Perelman là 1 con người kỳ lạ, đã từ chối gần như toàn bộ các giải thưởng và tiền thưởng trong cuộc đời mà ngừoi ta dành cho anh, kể từ 1 biến cố nào đó (mà chắc không ai biết ngoài anh) những năm 1996.
Perelman là 1 con người xuất chúng, phi thường. Một người mà khi mới 23 tuổi đã được nhiều nhà toán học lớn nhận xét: nhà hình học giỏi nhất thế giới (wow). Tôi cho rằng, 1 người giỏi chẳng có chút nào liên quan tới việc người đó kiêu ngạo hay không cả, và những người giỏi nhất nếu không tự biết mình giỏi nhất thì họ có khả năng nhận thức hơi kém. Perelman biết là mình giỏi, anh là người mà khi bị yêu cầu thêm thông tin, ví như CV để xem xét có cất nhắc vào vị trí giáo sư chính thức ở Princeton, đã nói rằng: "các ông đã nghe bài thuyết trình của tôi thì cần gì phải có thông tin gì thêm?".
Perelman có 1 bộ nguyên tắc của bản thân và rất trung thành với nó. Tuy Perelman thể hiện năng khiếu tuyệt vời trong toán học, nhưng tôi cho rằng, Perelman chẳng hiểu (và cố tình không hiểu) những thứ khác. Tất nhiên, về độ phức tạp, 1 chứ 7 bài toán thiên niên kỷ cũng chẳng thể nào so sánh được với cuộc sống về độ phức tạp cả, như lời John Von Neumann đã nói: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
Cuốn sách kể nhiều về thời thơ ấu của Perelman, những ngày trong câu lạc bộ toán, rồi những ngày trong đội tuyển, những thứ tôi từng trải qua 1 thứ có vỏ bọc hơi giống, nhưng phần hồn thì khác hẳn. Có lẽ vì đã quen đọc những giai thoại toán học nên cuốn sách rất hợp và khá dễ tiếp cận với tôi. Cách kể chuyện cũng khá là lôi cuốn, dù cho giai đoạn trưởng thành và những năm tháng gần đây khá sơ sài, mà phần nào vì sự khép kín của Perelman (hầu như chỉ tiếp xúc với mẹ và thi thoảng với người thầy hồi bé). Cuốn sách đã nêu ra phần nào những bối cảnh xoay quanh Perelman, để người đọc tự có câu trả lời cho những hành vi kỳ dị của anh ta; những lý do này, có phần khác biệt ít nhièu so với những lý do mà tôi từng đọc qua báo chí. Nhân tiện, báo chí trong này miêu tả thật như kền kền vậy :))
Cuốn sách kể về Grigory Perelman, 1 nhà toán học Nga đã giải quyết giả thuyết Poincaré, 1 trong 7 bài toán thiên niên kỷ, 1 danh sách do viện toán học Clay lập ra (có thể so sánh nó với danh sách 23 bài toán của Hilbert, 1 trong những động lực phát triển cho nền toán học thế kỷ 20). Perelman là 1 con người kỳ lạ, đã từ chối gần như toàn bộ các giải thưởng và tiền thưởng trong cuộc đời mà ngừoi ta dành cho anh, kể từ 1 biến cố nào đó (mà chắc không ai biết ngoài anh) những năm 1996.
Perelman là 1 con người xuất chúng, phi thường. Một người mà khi mới 23 tuổi đã được nhiều nhà toán học lớn nhận xét: nhà hình học giỏi nhất thế giới (wow). Tôi cho rằng, 1 người giỏi chẳng có chút nào liên quan tới việc người đó kiêu ngạo hay không cả, và những người giỏi nhất nếu không tự biết mình giỏi nhất thì họ có khả năng nhận thức hơi kém. Perelman biết là mình giỏi, anh là người mà khi bị yêu cầu thêm thông tin, ví như CV để xem xét có cất nhắc vào vị trí giáo sư chính thức ở Princeton, đã nói rằng: "các ông đã nghe bài thuyết trình của tôi thì cần gì phải có thông tin gì thêm?".
Perelman có 1 bộ nguyên tắc của bản thân và rất trung thành với nó. Tuy Perelman thể hiện năng khiếu tuyệt vời trong toán học, nhưng tôi cho rằng, Perelman chẳng hiểu (và cố tình không hiểu) những thứ khác. Tất nhiên, về độ phức tạp, 1 chứ 7 bài toán thiên niên kỷ cũng chẳng thể nào so sánh được với cuộc sống về độ phức tạp cả, như lời John Von Neumann đã nói: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
Cuốn sách kể nhiều về thời thơ ấu của Perelman, những ngày trong câu lạc bộ toán, rồi những ngày trong đội tuyển, những thứ tôi từng trải qua 1 thứ có vỏ bọc hơi giống, nhưng phần hồn thì khác hẳn. Có lẽ vì đã quen đọc những giai thoại toán học nên cuốn sách rất hợp và khá dễ tiếp cận với tôi. Cách kể chuyện cũng khá là lôi cuốn, dù cho giai đoạn trưởng thành và những năm tháng gần đây khá sơ sài, mà phần nào vì sự khép kín của Perelman (hầu như chỉ tiếp xúc với mẹ và thi thoảng với người thầy hồi bé). Cuốn sách đã nêu ra phần nào những bối cảnh xoay quanh Perelman, để người đọc tự có câu trả lời cho những hành vi kỳ dị của anh ta; những lý do này, có phần khác biệt ít nhièu so với những lý do mà tôi từng đọc qua báo chí. Nhân tiện, báo chí trong này miêu tả thật như kền kền vậy :))
August 5, 2021
Wonderful book. I heard about it in Prasad Kothari's lecture on Ramanujan Machine, Ricci flow & topology in AI (Where he gave example about AI, Topology and Ricci Flow. How perelman's work can be used in networks and applications of ricci flow. He also explained CNNs for analyzing Calabi Yau further - volume minimum of Sasaki-Einstein base manifolds and explained importance of Dr Yau's math work). great math geniuses. Somehow Prasad has been able to capture Dr. Yau & Dr Grigori Perelman both at the same time while talking about data and ai.
January 8, 2019
Not so much a biography: instead a study of recent Russian anti-Semitism, the viciousness of Soviet academia, and but also the wonderful alternative subculture that lived uneasily within it. This subculture hid inside the superhuman apolitical dreamland, mathematics.* It could only exist because of the sacrifices of famous and decent men, Kolmogorov and Aleksandrov. Their selective maths schools seem to have been the only nice places to be in the entire empire, for any intellectual with a taste for actual discourse, or for the truth.
(Reasons it can't be so much a biography: the subject refused to talk to her, does things that are very hard to explain, and doesn't go out much.)
The teacher Ryzhik's story about the evil entrance exam he sat is so, so sad:
Gessen is well-placed to write this - she was a maths nerd in Soviet Russia around the same time. As far as I can tell (which isn't very far) her grasp of the maths (one chapter for the crown jewel) is fit for purpose. But Gessen is out to bust Perelman's reputation for hyper-individualism; so she focusses on the devoted teachers and functionaries that pulled strings to get an abrasive Jew into the heart of Soviet academia, and his incredible luck in starting graduate study just as Glasnost happened.
She wants to highlight the poverty of his character - his antisocial withdrawal, his complete and intentional ignorance of politics, his naivete, his savantism. It doesn't work. Yes, he's rigid; maybe he is composed of a curiosity, a competitiveness, an ethics, and nothing else (no vanity, humour, romance, charisma, empathy, theory of mind, tolerance, compromise, doubt).
So what? Why does everyone need to be rounded? Does she sneer at athletes, the other people with lives this seemingly contorted and simple? David Foster Wallace managed to get over himself, on this note:
Gessen is, to be frank, quite cruel: she never passes up an opportunity to mention appearances - that that athletic boy of 1970 is "now an overweight and balding computer scientist", that the house of a man caring for his wife with late-stage dementia is "a messy place, lived in awkwardly" and he himself "similarly unkempt"; that Perelman didn't change his underwear or clip his nails as a teen. This is the shallow side of the New Yorker style on show - or else the malign side of Russian honesty. Either way fuck it. (Though Perelman would probably approve.)
The great mystery, which Gessen understandably can't touch, is why after 36 years of focus he suddenly stopped doing the only thing he'd ever done. How could he? How can that much momentum be shed? What does such a man do next?
Subtract a star if you don't care about maths or if you can't abide people being mean to nerds (as both the old apparatchiks and Gessen were).
---
* One of the oddest things about Perelman, because it maybe explains him turning down a million quid and the highest honours the world can bestow, is that he'd disagree with that sentence: maths, the least animal and least irrational thing we have, is too political for him. There was a little bit of nasty jostling at the time of the announcement - but nothing compared to any other science, let alone any government. Maybe the bubble everyone set up for him was bad for him, because it robbed him of perspective and so made the mild case of fuckery seem like a complete invalidation of mathematical culture. But maybe a rigorous rule-based mind would always explode eventually even given a scale to measure instances of bias.
(Reasons it can't be so much a biography: the subject refused to talk to her, does things that are very hard to explain, and doesn't go out much.)
The teacher Ryzhik's story about the evil entrance exam he sat is so, so sad:
“Coffins” were questions specially designed for the Jewish applicants... rejection was administered in a peculiarly sadistic way... if [Jews] succeeded in answering correctly the two or three questions on the ticket, then, alone in the room with the examiners, they would be casually issued an extra question... a problem not merely complex but unsolvable. The examiners would then nail the cover of the coffin shut: the Jewish applicant had failed the exam...
"They did not even manage to find a problem I couldn't solve; I sat for three hours after the exam was over, I solved them all, and still they failed me. I was just a boy. I went home and cried."
Gessen is well-placed to write this - she was a maths nerd in Soviet Russia around the same time. As far as I can tell (which isn't very far) her grasp of the maths (one chapter for the crown jewel) is fit for purpose. But Gessen is out to bust Perelman's reputation for hyper-individualism; so she focusses on the devoted teachers and functionaries that pulled strings to get an abrasive Jew into the heart of Soviet academia, and his incredible luck in starting graduate study just as Glasnost happened.
She wants to highlight the poverty of his character - his antisocial withdrawal, his complete and intentional ignorance of politics, his naivete, his savantism. It doesn't work. Yes, he's rigid; maybe he is composed of a curiosity, a competitiveness, an ethics, and nothing else (no vanity, humour, romance, charisma, empathy, theory of mind, tolerance, compromise, doubt).
So what? Why does everyone need to be rounded? Does she sneer at athletes, the other people with lives this seemingly contorted and simple? David Foster Wallace managed to get over himself, on this note:
The restrictions on [pro tennis player's] life have been, in my opinion, grotesque; and in certain ways Joyce himself is a grotesque. But the radical compression of his attention and sense of himself have allowed him to become a transcendent practitioner of an art – something few of us get to be. They've allowed him to visit and test parts of his psychic reserves most of us do not even know for sure we have (courage, playing with violent nausea, not choking, et cetera).
Joyce is, in other words, a complete man, though in a grotesquely limited way.
Gessen is, to be frank, quite cruel: she never passes up an opportunity to mention appearances - that that athletic boy of 1970 is "now an overweight and balding computer scientist", that the house of a man caring for his wife with late-stage dementia is "a messy place, lived in awkwardly" and he himself "similarly unkempt"; that Perelman didn't change his underwear or clip his nails as a teen. This is the shallow side of the New Yorker style on show - or else the malign side of Russian honesty. Either way fuck it. (Though Perelman would probably approve.)
[Perelman] sounded his voice only if a solution required his intervention; looked forward to Sundays, sighing happily and saying that he could "finally solve some problems in peace"; and, if asked, patiently explained any math issue to any of his classmates though apparently utterly unable to conceive of anyone not comprehending such a simple thing. His classmates repaid him with kindness: they recalled his civility and his mathematics, and none ever mentioned to me that he walked around with his shoelaces undone...
The great mystery, which Gessen understandably can't touch, is why after 36 years of focus he suddenly stopped doing the only thing he'd ever done. How could he? How can that much momentum be shed? What does such a man do next?
Subtract a star if you don't care about maths or if you can't abide people being mean to nerds (as both the old apparatchiks and Gessen were).
---
* One of the oddest things about Perelman, because it maybe explains him turning down a million quid and the highest honours the world can bestow, is that he'd disagree with that sentence: maths, the least animal and least irrational thing we have, is too political for him. There was a little bit of nasty jostling at the time of the announcement - but nothing compared to any other science, let alone any government. Maybe the bubble everyone set up for him was bad for him, because it robbed him of perspective and so made the mild case of fuckery seem like a complete invalidation of mathematical culture. But maybe a rigorous rule-based mind would always explode eventually even given a scale to measure instances of bias.
January 28, 2010
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.
Perelman is probably the greatest living mathematician and his singular achievement has been to solve the Poincaré Conjecture, one of the most difficult problems in modern math. Perelman, however, was 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. 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 (Boston) to award a million dollar prize to anyone who solved the Poincaré Conjecture, or one of six other math conundrums.
This book is written by a mathematician with a keen eye for what makes Perelman so intriguing. 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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Mikhail Gromov's take on Perelman's refusal to deal with the ICM committee and to accept the Field's Medal, which would be awarded on behalf of the international math community by the king of Spain, is described wonderfully by Gessen on pp 195-196:
"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.
--
April 27, 2015
Perelman là một nhà toán học, một con người dị thường. Là nhà toán học, chứng minh được giả thuyết Poincare-một trong bảy vấn đề thiên niên kỷ do viện Clay đặt ra-nhưng Perelman từ chối nhận huy chương Fields danh giá và sau đó là giải thưởng triệu đô từ viện Clay. Dưới góc độ một con người, Perelman chỉ sống trong hệ quy chiếu của riêng mình, gần như chấm dứt mọi hoạt động giao tiếp với xã hội bên ngoài, kể cả với cộng đồng toán học. Đối với những người ngoài cuộc, đặc biệt là ở Việt Nam, thì đây chắc chắn là chuyện điên rồ, không thể giải thích được, đặc biệt khi các giải thưởng về Toán học được biết đến rộng rãi hơn sau hiệu ứng "Ngô Bảo Châu". Một chuyện thế này thông thường sẽ chỉ nhận gây được một nụ cười theo kiểu mà ai-cũng-biết-rồi-đấy. Nhưng nếu bạn là người tò mò? Bạn luôn thắc mắc những thiên tài ấy tư duy thế nào? Chúc mừng bạn đã có lựa chọn đúng.
Perfect Rigor-Thiên tài kỳ dị và đột phá toán học của thế kỷ là một cuốn "tiểu thuyết"-dõi theo quá trình của Perelman từ khi còn là một bào thai trong bụng mẹ cho tới khi trưởng thành và giành được vinh quang trong toán học-chính là một cố gắng để giải đáp những thắc mắc ấy. Masha Gessen không hề được tiếp xúc với Perelman một phút nào, nhưng thành công của bà là đã tiếp cận được với Ruskhin, thầy dạy chuyên toán của ông, và một số người thân cận với Perelman khác. Điều này làm cho cuốn sách có hơi hướng tiểu thuyết, nhưng những ai đã từng, hoặc đang sống cùng những người làm khoa học thì sẽ thấy rất gần gũi, đáng tin cậy. Masha Gessen cũng rất thông minh khi lược bỏ hầu hết những vấn đề kỹ thuật liên quan đến giả thuyết Poincare, những thứ khi xuất hiện chắc chắn sẽ giết chết cuốn sách của bà, thay vào đó là các câu chuyện bên lề, như hình mẫu chuyên toán của Kolmogorov, những vấn đề của Toán học và các nhà toán học Do Thái trong liên bang Xô Viết, những trò lố của Shing Tung Yau và đồng bọn, hay cả một bất ngờ là Kolmogorov đã tát thầy mình vì không bỏ phiếu bầu vào Viện hàn lâm cho "bạn trai" .... Nhưng quan trọng hơn cả là cách dẫn dắt và sắp xếp mạch lạc của bà cho thấy sự hình thành cách tư duy về toán học và cuộc sống của Perelman từ khi còn là một học sinh chuyên toán tài năng cho tới khi là một nhà toán học trưởng thành, điều đó giúp chúng ta có thể hiểu hơn về cách hành xử và thái độ của ông.
Bản dịch tiếng Việt là một bản dịch rất tốt, nhưng có hai điều đáng tiếc: thứ nhất là phải lược bỏ một ít thông tin nhạy cảm (liên quan đến hình thái xã hội hiện tại) và thứ hai là .... giấy in sách, chất lượng kém hơn loại thường dùng trong tủ sách Khoa học khám phá. Đây không phải là lần đầu nhà xuất bản Trẻ "ưu ái" cho mục Toán như thế (trước đó là cuốn Ngôn ngữ của đối xứng). Có lẽ họ không hề biết rằng đó là hai trong số ba cuốn sách có giá trị nhất trong tủ sách.
Perfect Rigor-Thiên tài kỳ dị và đột phá toán học của thế kỷ là một cuốn "tiểu thuyết"-dõi theo quá trình của Perelman từ khi còn là một bào thai trong bụng mẹ cho tới khi trưởng thành và giành được vinh quang trong toán học-chính là một cố gắng để giải đáp những thắc mắc ấy. Masha Gessen không hề được tiếp xúc với Perelman một phút nào, nhưng thành công của bà là đã tiếp cận được với Ruskhin, thầy dạy chuyên toán của ông, và một số người thân cận với Perelman khác. Điều này làm cho cuốn sách có hơi hướng tiểu thuyết, nhưng những ai đã từng, hoặc đang sống cùng những người làm khoa học thì sẽ thấy rất gần gũi, đáng tin cậy. Masha Gessen cũng rất thông minh khi lược bỏ hầu hết những vấn đề kỹ thuật liên quan đến giả thuyết Poincare, những thứ khi xuất hiện chắc chắn sẽ giết chết cuốn sách của bà, thay vào đó là các câu chuyện bên lề, như hình mẫu chuyên toán của Kolmogorov, những vấn đề của Toán học và các nhà toán học Do Thái trong liên bang Xô Viết, những trò lố của Shing Tung Yau và đồng bọn, hay cả một bất ngờ là Kolmogorov đã tát thầy mình vì không bỏ phiếu bầu vào Viện hàn lâm cho "bạn trai" .... Nhưng quan trọng hơn cả là cách dẫn dắt và sắp xếp mạch lạc của bà cho thấy sự hình thành cách tư duy về toán học và cuộc sống của Perelman từ khi còn là một học sinh chuyên toán tài năng cho tới khi là một nhà toán học trưởng thành, điều đó giúp chúng ta có thể hiểu hơn về cách hành xử và thái độ của ông.
Bản dịch tiếng Việt là một bản dịch rất tốt, nhưng có hai điều đáng tiếc: thứ nhất là phải lược bỏ một ít thông tin nhạy cảm (liên quan đến hình thái xã hội hiện tại) và thứ hai là .... giấy in sách, chất lượng kém hơn loại thường dùng trong tủ sách Khoa học khám phá. Đây không phải là lần đầu nhà xuất bản Trẻ "ưu ái" cho mục Toán như thế (trước đó là cuốn Ngôn ngữ của đối xứng). Có lẽ họ không hề biết rằng đó là hai trong số ba cuốn sách có giá trị nhất trong tủ sách.
January 22, 2011
An admirable attempt at writing about a mathematician who is more myth than man. Gessen also provides a fascinating inside look at the Russian system of training young mathematicians for competitions. Way different from the donuts and pseudo-cheerleading that accompanied my math club competitions. Still, I feel a better book could have -- and should have -- been written about Perelman. Maybe he'll open up some day and allow that to happen.
January 3, 2012
Masha Gessen's book is a biography of a person who is quite alive - as far as we know. But it is written as one would write a biography for a subject who is dead, because the subject of the book, Grigory "Grisha" Perelman, has withdrawn himself from the world, mathematics and otherwise. This is then more of a story of how and why Perelman, the most accomplished mathematician of this new century, managed this withdrawal. It is a strange and at times infuriating story, but one told by a uniquely qualified individual in Ms. Gessen. I highly recommend this articulate and informative book: if you thought you knew the story of Grisha Perelman, you are probably wrong.
Perelman after all is the man who has been acknowledged by the mathematics community as the man who proved the Poincare and Thurston conjectures and thus solved a century-old problem to which not a few professional mathematicians the world over dedicated their lives. But, as momentous an achievement as this is, Perelman is even more well-known for his rejections. Rejections of tenured faculty positions at the best universities in America, despite aggressive offers. Rejection of the Fields Medal, the highest prize the mathematics world has to offer. And, although only speculated in the book, the rejection last month of the first $1 million prize from the Clay Institute for the solution of one of its Millennium Problems. Gessen does what she has to do to get the answers and construct the story: she gets access to everyone who has taught, competed with, and collaborated with Perelman throughout his life.
The story traces Perelman from before he was born: his mother was a mathematician herself, who was rejected for her pregnancy and her Jewishness. It was into her son Grisha that she poured her dreams of greatness. The story then winds its way through Perelman's Olympiad career, where he won first place at the International Math Olympiad in 1982, then University at the Mathmech in Leningrad, then graduate study at the Steklov Institute in Leningrad. Through this journey, we see how Perelman developed into the brilliant being he has become, as well as how he separated himself from the rest of the world.
What Gessen accomplishes here is the weaving of a thread through the people in Perelman's life who worked to shield him from all of the distractions of the world so he could pursue the work that would make him - and them - famous. The distractions that could derail such a “pure” prodigy as Perelman were many and intense: being part of a community, maintaining the body as well as the mind [Perelman’s simple eating habits, long fingernails and curious smell are well-known], paperwork, admissions, etc. Girls seem to barely exist in his world – and Perelman is not tagged as homosexual.
The major distraction from which Perelman was shielded was the brutal anti-Semitism of the Soviet regime. [When I read about this, I always wonder why so many of my fellow Jews got sucked into giving their lives over to these frauds.] Perelman was a Jew [a “zhid”] and therefore subject to the extreme quotas governing intellectual life in the bad old days of the Soviet Union. Perelman, however, was shielded from this abuse through the hard work of the influential professors who saw in Perelman someone who would do great things for mathematics. Perelman’s accomplishments are literally a testament to these professors who did yeoman’s work in getting Perelman into the right Institutes that would further his career.
And it is shielding, the constant protection from the horrors of the world, that seem to shape Perelman into the being that would brook no distractions, ever. He had zero interests outside of not only mathematics, but outside of the very problem on which he was working. And once he was finished working and teaching, he had zero interest in communicating with anybody about it. Perelman’s career arc was such that his work in Alexandrov spaces won him recognition enough to be invited to postdoc in the US from 1991-1995 in various places [NYU, Stony Brook, Berkeley]. Then, suddenly, insulted that he did not instantly get an offer for a tenured faculty position, he returned to now St Petersburg and the Steklov Institute, where he literally disappeared for seven years. He would only return to his grand triumph, the posting of his proof of the conjectures in three papers on arXiv.org in 2002.
Gessen spends a chapter on an attempt to describe Perelman’s achievement. Gessen, no stranger to Russian mathematics herself, does I think a decent job in laying out the problem and explaining why it evaded solution for so long. I liked her explanation of topology’s origins with Euler and the seven bridges of Koenigsberg, and how location rather than distance is what makes topology a special sort of geometry. That said, I think she fell into the trap into which what many mass-market mathematics authors fall, and that is the fear of the equation. English is not the best language for any branch of mathematics [if it were, then lawyers and mathematicians would be interchangeable], and more effort needs to be done than simply fobbing fancy terms at the reader [“Ricci flow”, “diffeomorphism”] after a certain level of difficulty has passed. This is likely not Gessen’s fault, but that of worrisome editors and publishers understandably worried about the impact of such discussions on sales. Those hoping for a slightly more detailed discussion of Perelman’s achievement should consult Donal O’Shea’s nice explanation of the Conjecture and the players involved, including Perelman. [Interestingly, O’Shea has zero interest in Perelman’s foibles; this is what makes Gessen’s book so good.]
The world around Perelman grew increasingly incomprehensible to him and he became more withdrawn, sullen, and vicious. Gessen at this points spends a lot of time speculating on the role Asperger’s has had not only on Perelman, but on mathematicians, and Russian mathematicians in particular. In what could have been a debacle for the book, I think Gessen turns this discussion into a strength through her detailed discussions with the world’s leading experts in the field. One sees through what we have learned about Perelman that he makes for a classic case of Asperger’s, although Gessen reminds us that all this is mere speculation, as she – and we – have never even met Perelman. But this speculation, rather than drag the book into a Fox-Newsian assumption of reality from speculated “facts”, helps Gessen paint a portrait of a subject that refuses to sit.
To be honest, I thought that such a portrait would get me to sympathize with Perelman’s plight. And what a plight. His rejections ironically made him much more of a celebrity than had he simply accepted the rewards he so richly deserved. Russian parazzi followed him around the clock and broke into the apartment he shared with his mother, snapping photos of his unmade bed. Nevertheless, I was horrified at Perelman’s behavior toward his fellow colleagues, most of whom were simply trying to help him, despite the fact that his master stroke more or less instantly altered or destroyed their careers. Gessen lays out evidence that Perelman’s behavior is more complex than that of a “Rain Man’ and many times, he knew perfectly well what he was doing. At the end, Gessen brilliantly makes the analogy that, like the rubber band on the three-dimensional manifold he uniquely understood, Perelman’s social universe shrunk to a point. He now lives, unemployed, with his mother in their St Petersburg apartment.
All in all, this was a thoroughly enjoyable read from which I learned far more than what one can gather in existing New Yorker articles. I recommend in the strongest manner for those interested in this enigmatic genius and the work he did.
Perelman after all is the man who has been acknowledged by the mathematics community as the man who proved the Poincare and Thurston conjectures and thus solved a century-old problem to which not a few professional mathematicians the world over dedicated their lives. But, as momentous an achievement as this is, Perelman is even more well-known for his rejections. Rejections of tenured faculty positions at the best universities in America, despite aggressive offers. Rejection of the Fields Medal, the highest prize the mathematics world has to offer. And, although only speculated in the book, the rejection last month of the first $1 million prize from the Clay Institute for the solution of one of its Millennium Problems. Gessen does what she has to do to get the answers and construct the story: she gets access to everyone who has taught, competed with, and collaborated with Perelman throughout his life.
The story traces Perelman from before he was born: his mother was a mathematician herself, who was rejected for her pregnancy and her Jewishness. It was into her son Grisha that she poured her dreams of greatness. The story then winds its way through Perelman's Olympiad career, where he won first place at the International Math Olympiad in 1982, then University at the Mathmech in Leningrad, then graduate study at the Steklov Institute in Leningrad. Through this journey, we see how Perelman developed into the brilliant being he has become, as well as how he separated himself from the rest of the world.
What Gessen accomplishes here is the weaving of a thread through the people in Perelman's life who worked to shield him from all of the distractions of the world so he could pursue the work that would make him - and them - famous. The distractions that could derail such a “pure” prodigy as Perelman were many and intense: being part of a community, maintaining the body as well as the mind [Perelman’s simple eating habits, long fingernails and curious smell are well-known], paperwork, admissions, etc. Girls seem to barely exist in his world – and Perelman is not tagged as homosexual.
The major distraction from which Perelman was shielded was the brutal anti-Semitism of the Soviet regime. [When I read about this, I always wonder why so many of my fellow Jews got sucked into giving their lives over to these frauds.] Perelman was a Jew [a “zhid”] and therefore subject to the extreme quotas governing intellectual life in the bad old days of the Soviet Union. Perelman, however, was shielded from this abuse through the hard work of the influential professors who saw in Perelman someone who would do great things for mathematics. Perelman’s accomplishments are literally a testament to these professors who did yeoman’s work in getting Perelman into the right Institutes that would further his career.
And it is shielding, the constant protection from the horrors of the world, that seem to shape Perelman into the being that would brook no distractions, ever. He had zero interests outside of not only mathematics, but outside of the very problem on which he was working. And once he was finished working and teaching, he had zero interest in communicating with anybody about it. Perelman’s career arc was such that his work in Alexandrov spaces won him recognition enough to be invited to postdoc in the US from 1991-1995 in various places [NYU, Stony Brook, Berkeley]. Then, suddenly, insulted that he did not instantly get an offer for a tenured faculty position, he returned to now St Petersburg and the Steklov Institute, where he literally disappeared for seven years. He would only return to his grand triumph, the posting of his proof of the conjectures in three papers on arXiv.org in 2002.
Gessen spends a chapter on an attempt to describe Perelman’s achievement. Gessen, no stranger to Russian mathematics herself, does I think a decent job in laying out the problem and explaining why it evaded solution for so long. I liked her explanation of topology’s origins with Euler and the seven bridges of Koenigsberg, and how location rather than distance is what makes topology a special sort of geometry. That said, I think she fell into the trap into which what many mass-market mathematics authors fall, and that is the fear of the equation. English is not the best language for any branch of mathematics [if it were, then lawyers and mathematicians would be interchangeable], and more effort needs to be done than simply fobbing fancy terms at the reader [“Ricci flow”, “diffeomorphism”] after a certain level of difficulty has passed. This is likely not Gessen’s fault, but that of worrisome editors and publishers understandably worried about the impact of such discussions on sales. Those hoping for a slightly more detailed discussion of Perelman’s achievement should consult Donal O’Shea’s nice explanation of the Conjecture and the players involved, including Perelman. [Interestingly, O’Shea has zero interest in Perelman’s foibles; this is what makes Gessen’s book so good.]
The world around Perelman grew increasingly incomprehensible to him and he became more withdrawn, sullen, and vicious. Gessen at this points spends a lot of time speculating on the role Asperger’s has had not only on Perelman, but on mathematicians, and Russian mathematicians in particular. In what could have been a debacle for the book, I think Gessen turns this discussion into a strength through her detailed discussions with the world’s leading experts in the field. One sees through what we have learned about Perelman that he makes for a classic case of Asperger’s, although Gessen reminds us that all this is mere speculation, as she – and we – have never even met Perelman. But this speculation, rather than drag the book into a Fox-Newsian assumption of reality from speculated “facts”, helps Gessen paint a portrait of a subject that refuses to sit.
To be honest, I thought that such a portrait would get me to sympathize with Perelman’s plight. And what a plight. His rejections ironically made him much more of a celebrity than had he simply accepted the rewards he so richly deserved. Russian parazzi followed him around the clock and broke into the apartment he shared with his mother, snapping photos of his unmade bed. Nevertheless, I was horrified at Perelman’s behavior toward his fellow colleagues, most of whom were simply trying to help him, despite the fact that his master stroke more or less instantly altered or destroyed their careers. Gessen lays out evidence that Perelman’s behavior is more complex than that of a “Rain Man’ and many times, he knew perfectly well what he was doing. At the end, Gessen brilliantly makes the analogy that, like the rubber band on the three-dimensional manifold he uniquely understood, Perelman’s social universe shrunk to a point. He now lives, unemployed, with his mother in their St Petersburg apartment.
All in all, this was a thoroughly enjoyable read from which I learned far more than what one can gather in existing New Yorker articles. I recommend in the strongest manner for those interested in this enigmatic genius and the work he did.
August 21, 2019
The book is certainly terrific.
January 5, 2019
Η προσωπικότητα του συγκεκριμένου μαθηματικού δεν έχει να προσφέρει κάποια έμπνευση στον αναγνώστη. Στο βιβλίο γίνεται εκτενής αναφορά σε πολλούς ρώσους μαθηματικούς, για λέσχες μαθηματικών στη ρωσία. Περίμενα περισσότερα στοιχεία για την προσωπικότητα του πέρελμαν
July 8, 2011
I thought this was a very interesting book to read. As a mathematician I certainly saw the faculty at my university abuzz over the solution of the Poincare Conjecturé. Then some odd circumstances happened and the author of the proof started to decline awards and accolades. This probably drew even more attention to him as he was trying to get away from world. It is somewhat of an unfortunate story in some respects, because it appears he has decided to leave the mathematical field altogether. Who could tell what else he could solve if he was just left to his own devices?
The book does suffer from no firsthand accounts, but every reader should expect that going in. It was written after Mr. Perelman stopped talking to the media, so Gessen was unable to ever interview her subject. This must have been quite a challenging biography. Instead she had to go and speak with colleagues and friends to attempt to craft Perelman’s story. One of the most interesting parts of this story wasn’t in the discussion of Perelman’s solution, but the historical background of mathematics being done in the Soviet Union. During the Cold War the Soviet Union appears to have been a strange place, even in which to conduct mathematical research. I felt this book gave a rather penetrating account of the hardships these instructors and students endured as they tried to work in a field they were very passionate about.
After Mr. Perelman provided his solution to the Poincaré Conjecture he did come to the U.S. to give some talks on the topic. According to Gessen he had odd habits, but as someone who has worked in the world of math and higher education, this is certainly not unusual to me. Even I have some very strange and what people would consider relatively strict habits. The only point that sort of bothered me in the book is her attempt to seemingly diagnose his weirdness. I am not sure if she was fully trying to do this, or just giving information to others about the nature of something like Aspergers, but I got the impression she was trying to explain him through a disorder.
In any event, I did find it an incredibly fascinating read and I would highly recommend anyone read this. You certainly don’t have to be a mathematician to read it as the biography is quite well crafted. I walk away feeling as if Gessen achieved her goal of writing a biography without ever having to speak to the individual.
P.S. And as a side note... I have to wonder if the graphic designer who made the cover was aware that the integral sign is an S. So I when I look at this book all I can see is "Persect Rigor".
The book does suffer from no firsthand accounts, but every reader should expect that going in. It was written after Mr. Perelman stopped talking to the media, so Gessen was unable to ever interview her subject. This must have been quite a challenging biography. Instead she had to go and speak with colleagues and friends to attempt to craft Perelman’s story. One of the most interesting parts of this story wasn’t in the discussion of Perelman’s solution, but the historical background of mathematics being done in the Soviet Union. During the Cold War the Soviet Union appears to have been a strange place, even in which to conduct mathematical research. I felt this book gave a rather penetrating account of the hardships these instructors and students endured as they tried to work in a field they were very passionate about.
After Mr. Perelman provided his solution to the Poincaré Conjecture he did come to the U.S. to give some talks on the topic. According to Gessen he had odd habits, but as someone who has worked in the world of math and higher education, this is certainly not unusual to me. Even I have some very strange and what people would consider relatively strict habits. The only point that sort of bothered me in the book is her attempt to seemingly diagnose his weirdness. I am not sure if she was fully trying to do this, or just giving information to others about the nature of something like Aspergers, but I got the impression she was trying to explain him through a disorder.
In any event, I did find it an incredibly fascinating read and I would highly recommend anyone read this. You certainly don’t have to be a mathematician to read it as the biography is quite well crafted. I walk away feeling as if Gessen achieved her goal of writing a biography without ever having to speak to the individual.
P.S. And as a side note... I have to wonder if the graphic designer who made the cover was aware that the integral sign is an S. So I when I look at this book all I can see is "Persect Rigor".
January 16, 2023
There are eccentric people in science, and Grisha Perelman is certainly among the most eccentric mathematicians ever lived.
Author Masha Gessen accomplishes many daunting tasks in this book. Perelman never interviewed for the same, and the accounts gathered are from his minimal social/math circle. Author paints a cogent view of Grisha's journey, explains Poincare Conjecture, Topography and the road to Perelman's solution of a century old problem in a way that's permeable to layman.
Despite many postulates by the community as to why Perelman declined Field's medal/Clay Prize and his departure from Math; we may never know his complete story. Many of his supposed dissatisfactions do make sense : the superfluousness in academia at all levels (which is so common that no one even questions/rather is often celebrated); motives people have in society vs coherent worldview within math; credit pilfering of science discoveries ; pride of Ricci-Flow community in accepting his solution etc. Every now and then there are reports of plagiarism, but it happens at even the very highest level, by the people at top of their field (Cao-Yu in this case). They are humans afterall.
It was a wonder Grisha was shielded from much of the bureaucracy growing up in Soviet Russia; a lot of the credit goes to his mentors and teachers. Giving up million dollars and all the fame feels extreme, but Grisha might be one of the purest people in Science.
The book also sheds light on the culture of Soviet Russia in mid 1950s, and the evolution of its dominance in Math and Physics; interestingly driven by Andrey Kolmogorov (The K in popular K-S Goodness of Fit Test).
Overall a great read and excellent journalism by the author.
Author Masha Gessen accomplishes many daunting tasks in this book. Perelman never interviewed for the same, and the accounts gathered are from his minimal social/math circle. Author paints a cogent view of Grisha's journey, explains Poincare Conjecture, Topography and the road to Perelman's solution of a century old problem in a way that's permeable to layman.
Despite many postulates by the community as to why Perelman declined Field's medal/Clay Prize and his departure from Math; we may never know his complete story. Many of his supposed dissatisfactions do make sense : the superfluousness in academia at all levels (which is so common that no one even questions/rather is often celebrated); motives people have in society vs coherent worldview within math; credit pilfering of science discoveries ; pride of Ricci-Flow community in accepting his solution etc. Every now and then there are reports of plagiarism, but it happens at even the very highest level, by the people at top of their field (Cao-Yu in this case). They are humans afterall.
It was a wonder Grisha was shielded from much of the bureaucracy growing up in Soviet Russia; a lot of the credit goes to his mentors and teachers. Giving up million dollars and all the fame feels extreme, but Grisha might be one of the purest people in Science.
The book also sheds light on the culture of Soviet Russia in mid 1950s, and the evolution of its dominance in Math and Physics; interestingly driven by Andrey Kolmogorov (The K in popular K-S Goodness of Fit Test).
Overall a great read and excellent journalism by the author.
December 25, 2014
I found this book fascinating on several levels because it touches on several areas of interest to me. First, the modern field of mathematics and the remaining great proofs to be solved. Second, the state of the USSR as it stumbled toward its demise in the 1980's as Reagan upped the ante on military strength and broke the back of the Soviet economy. Finally, the nature of human genius. How astounding it is that an infinitesimal fraction of humans have mental powers so far above the scale of the rest of us.
The subject here, Grigory Perelman, is one of the Asperger Syndrome genius category, His achievement described by Ms. Gessen's book is providing the proof of a conjecture made 100 years earlier by a previous genius who was not smart enough to provide his own proof.
For a period of 8 years no one knew what Grigory was doing. Then, suddenly 3 very short papers come forth which seem to contain the proof.
These 3 papers are so short, in fact, that it is by no means obvious that they do contain the proof. Actually, two Japanese mathematicians have the gall to publish a paper claiming that it is they who have solved the proof.
Whether the proof may have any practical value is unknown for now, but the book conveys the sense of how staggeringly difficult this work is.
He was awarded a $1 million prize for his achievement in 2010 and refused the money because he explained he didn't want people staring at him.
Once again nobody knows what Perelman is working on, if anything.
The subject here, Grigory Perelman, is one of the Asperger Syndrome genius category, His achievement described by Ms. Gessen's book is providing the proof of a conjecture made 100 years earlier by a previous genius who was not smart enough to provide his own proof.
For a period of 8 years no one knew what Grigory was doing. Then, suddenly 3 very short papers come forth which seem to contain the proof.
These 3 papers are so short, in fact, that it is by no means obvious that they do contain the proof. Actually, two Japanese mathematicians have the gall to publish a paper claiming that it is they who have solved the proof.
Whether the proof may have any practical value is unknown for now, but the book conveys the sense of how staggeringly difficult this work is.
He was awarded a $1 million prize for his achievement in 2010 and refused the money because he explained he didn't want people staring at him.
Once again nobody knows what Perelman is working on, if anything.
December 14, 2016
What really struck me is that book is not really about Gregory Perelman. This is a book about time and place that creates a certain type of personality, a certain outlook on things, a certain character. If he might have had Asperger's, as Gessen points out, so might half the country. This is a case of plain, pure disgust with all sorts of politicking, maneuvering and manipulating.
In a way, it's the start of a book about the "lost generation" that had to survive, do ten times better than anyone in their grade, get through entrance exams by miracle only, be head and shoulders above their peers in colleges, only to finally emigrate and survive again in USA, Germany, Israel, Australia and everywhere in between - and those were the best and the brightest. I really would like Gessen to write this book.
In a way, it's the start of a book about the "lost generation" that had to survive, do ten times better than anyone in their grade, get through entrance exams by miracle only, be head and shoulders above their peers in colleges, only to finally emigrate and survive again in USA, Germany, Israel, Australia and everywhere in between - and those were the best and the brightest. I really would like Gessen to write this book.
February 22, 2010
I wish I could rate this 3 1/2 stars. I really enjoyed the parts of this book that dealt with the Russian math subculture. The pieces about Perelman were good but because Perelman is by nature so withdrawn and neither he nor the people closest to him (like his mother) were willing to speak to the author, it felt a little light on actual content. For example, a few casual emails that Perelman sent are reprinted and analyzed simply because they are one of the very few pieces of information in Perelman's own words. Overall I did definitely enjoy the book.
August 29, 2018
The further I read the further I empathized with Perelman's withdrawl from public eye. The author makes a lot of big assumptions of Perelman's feelings/beliefs/knowledge (not backed up by any interviews she did) in order to turn him into a spectacle.
June 8, 2020
I bought this book eleven years ago. For reasons I cannot explain, intrigued maybe by another two books I am currently reading (The equation which was never solved by Mario Livio and The Poincaré Conjecture by Donal O'Shea) I thought the time was right to deepen into the life of Perelman.
While surprised about his behaviour, we should learn a lot about this story. Because Perelman, a jew with an immense talent in solving mathematical problems, appears to be a man of principles, maybe brought to the extreme, but we should not play Groucho Marx here. Perelman never did. As a 'matemagician', he understood it from his very childhood perfectly and exploited until he decided to escape from this world. Neither Mathematics, nor the person who contribute to them, can be sold, money ruin everything. The whole parafernalia which may surroind Mathematics (Clay prize, Fields Medal) is (was in his eyes) all but superflous, unnecessary, not to be proud of. I understand Grigori very well.
Then, of course, the modern society put a prize on everything. Grigori simply escaped from his destiny, the one waiting with hands wide open to embrace him. If he were to continue enclosed in the modern box of materialism he would have sold himself for moneny and solving problems is not about money. The merit cannot have a monetary compensation.
Tragic in itself, maybe modern Mathematics (written with captital M) lost in a way a great mind, cause the mathematical world, the world per se, never again got to know anything about Grigori (apart from all the rejections as of contact, his retirement from society and a testimonial publication claiming to have demonstrated the existence of god).
It felt kind of sad to read that around 2006 two chinese geometrists tried to claim they have solved what Perelman had done, correctly and in full (chapeau!!!) years before, a conjecture which one of the greatest mathematicians in the history (Poincaré) wrote when the XX century was just its childhood. It is just dirty, it is disgusting. Those very people should be excluded from making Mathematics or given the right to publish for the rest of their lifes. All in all, they just did it to claim a million dollar the real author did and would never claim. No words.
Mr. Perelman has all my respect, as a mathematician and as a person for his integrity, despite his extreme attitude or exaggerated reaction. Money (and fame) ruin everything, I said. What a contradiction to be ruined by money... In the end not all souls can be taken away by the hand of the devil, despite its reach, size and length. At least not the one of Grigori Perelman. It is a kind of relief to know one can still find such kind of people in this world.
While surprised about his behaviour, we should learn a lot about this story. Because Perelman, a jew with an immense talent in solving mathematical problems, appears to be a man of principles, maybe brought to the extreme, but we should not play Groucho Marx here. Perelman never did. As a 'matemagician', he understood it from his very childhood perfectly and exploited until he decided to escape from this world. Neither Mathematics, nor the person who contribute to them, can be sold, money ruin everything. The whole parafernalia which may surroind Mathematics (Clay prize, Fields Medal) is (was in his eyes) all but superflous, unnecessary, not to be proud of. I understand Grigori very well.
Then, of course, the modern society put a prize on everything. Grigori simply escaped from his destiny, the one waiting with hands wide open to embrace him. If he were to continue enclosed in the modern box of materialism he would have sold himself for moneny and solving problems is not about money. The merit cannot have a monetary compensation.
Tragic in itself, maybe modern Mathematics (written with captital M) lost in a way a great mind, cause the mathematical world, the world per se, never again got to know anything about Grigori (apart from all the rejections as of contact, his retirement from society and a testimonial publication claiming to have demonstrated the existence of god).
It felt kind of sad to read that around 2006 two chinese geometrists tried to claim they have solved what Perelman had done, correctly and in full (chapeau!!!) years before, a conjecture which one of the greatest mathematicians in the history (Poincaré) wrote when the XX century was just its childhood. It is just dirty, it is disgusting. Those very people should be excluded from making Mathematics or given the right to publish for the rest of their lifes. All in all, they just did it to claim a million dollar the real author did and would never claim. No words.
Mr. Perelman has all my respect, as a mathematician and as a person for his integrity, despite his extreme attitude or exaggerated reaction. Money (and fame) ruin everything, I said. What a contradiction to be ruined by money... In the end not all souls can be taken away by the hand of the devil, despite its reach, size and length. At least not the one of Grigori Perelman. It is a kind of relief to know one can still find such kind of people in this world.
January 13, 2019
Come si può scrivere un libro che racconti una scoperta matematica che ha impegnato la comunità per più di un secolo e la cui dimostrazione è così complicata da avere richiesto un anno e mezzo non per produrla, ma banalmente per verificarne la correttezza? Come si può scrivere una biografia su una persona che vive da recluso e si rifiuta di incontrare o anche solo parlare con nessuno? Non ci sono molte possibilità. Masha Gessen, in
Perfect Rigor
(appena tradotto per i tipi di Carbonio Editore) ha scelto una strada peculiare. Pur avendo una formazione matematica di base, ha infatti scelto di mettere in secondo piano l'aspetto scientifico vero e proprio, relegato in poche pagine verso il termine dell'opera, per porre l'accento sull'ambiente accademico matematico e sulla discriminazione degli studenti ebrei nell'Unione Sovietica. Grigorij "Griša" Perel'man è in un certo senso lo specchio attraverso il quale si snodano vicende molto più generali.
Il titolo del libro deriva da una frase del grande matematico francese Henri Poincaré nel suo libro di filosofia della scienza La scienza e l'ipotesi: "Se l'oggetto di studio rimane confinato all'immaginazione, da dove proviene il perfetto rigore che nessuno penserebbe mai di porre in dubbio?" Poincaré si sta riferendo a una secolare diatriba: se cioè tutta la matematica, con le sue cristalline dimostrazioni formali, non sia semplicemente un modo per dire A = A oppure c'è qualcosa in più, e gli oggetti matematici non sono solo frutto dell'immaginazione dei matematici oppure hanno una connessione con il mondo reale. In un certo senso, la congettura di Poincaré dimostrata da Perel'man rientra in questa seconda categoria: con una cruda approssimazione, possiamo dire che il nostro mondo tridimensionale non può avere una forma "strana" se visto all'interno di uno spazio quadridimensionale, ma è proprio come ce lo aspettiamo intuitivamente. Ma il vero rigore è quello della vita di Perel'man. Gessen tratteggia il matematico come una specie di Forrest Gump, con la differenza che Griša solo estremamente intelligente: la sua ipotesi è che il suo comportamento sociale indichi che sia affetto dalla sindrome di Asperger, che come noto a differenza di altre varianti dell'autismo è spesso associato a un quoziente intellettivo molto alto.
Perel'man è una macchina per risolvere problemi, forse spinto in questo dall'ambizione di sua madre che aveva scelto di non proseguire la carriera matematica per metter su famiglia o magari perché il mondo della matematica ha un suo insieme di regole ben precise che non ammettono eccezioni e sono pertanto relativamente semplici da mettere in pratica: potremmo dire che tali regole hanno una rappresentazione molto compatta che richiede pertanto meno spazio di memoria per gestirle. In tutto questo Perel'man pare non accorgersi affatto dei problemi che la sua condizione di ebreo dal cognome inconfondibile gli pone nell'ambiente sovietico. Formalmente non esisteva alcuna discriminazione, ma all'atto pratico gli ebrei erano tenuti il più possibile lontano dalle università più importanti come quelle di Mosca e Leningrado, nelle quali la politica di ammissione - anche in una facoltà come quella di matematica che non sembrava proprio dare chissà quali problemi di fedeltà alla linea ufficiale comunista - si riassumeva in "potranno essere ammessi solo due studenti ebrei l'anno". La matematica Tanya Khovanova ha raccontato di come esistesse una lista di "problemi speciali", che erano praticamente impossibili da risolvere senza conoscere il trucco che li avrebbe resi banali - pronti per tarpare sul nascere le speranze degli studenti dal cognome sbagliato: se li trovavano di fronte e fallivano miseramente. Perel'man ebbe però la fortuna e la bravura di seguire la scuola di matematica di Sergej Rukšin (anch'egli di origine ebraica, tra l'altro) e vincere le Olimpiadi internazionali di matematica, il che permetteva di essere automaticamente ammesso a un'università di propria scelta, riuscendo così a evitare questo destino.
Gessen calca molto la mano sulle regole che Perel'man si dava per affrontare i problemi di matematica e il mondo intorno a lui. Non è chiaro quanto tali regole esistano veramente nella sua mente: leggendo quanto ha fatto negli anni della sua formazione come matematico, la mia sensazione è che lui abbia semplicemente scelto una strada che poi gli sia sfuggita di mano. Indubbiamente la sua mente è in grado di cogliere in un colpo solo tutti gli aspetti di un problema; ma la scelta di dedicarsi alla geometria sembrerebbe più legata al minor numero di colleghi con cui aveva a che fare, e il progressivo allontanarsi anche da quelli con cui aveva punti di contatto si direbbe legata a un concetto utilitarista, perché nessuno di loro poteva essergli più di aiuto. Resta il mistero del perché Perel'man si sia allontanato dalla matematica: non è comunque il primo, poiché Alexander Grothendieck l'aveva preceduto in un isolamento totale. Tra l'altro anche Grothendieck era di origine russa ed ebraica, il suo campo di studi era la geometria, e aveva vinto la medaglia Fields... magari sono tutte coincidenze. Ma è anche opportuno seguire l'altro tema portato avanti da Gessen, vale a dire la descrizione degli ambienti accademici russo e americano, diversissimi tra loro ma entrambi alieni per chi vuole fare solo matematica e non sottostare a regole forse ancora più bizzarre di quelle che Griša sceglieva per sé. È vero che parecchi matematici hanno perso mesi della loro carriera per rimpolpare le dimostrazioni di Perel'man e assicurarsi della loro correttezza, il tutto senza alcun tornaconto se non l'avanzamento della matematica. Però stiamo sempre parlando di esseri umani, con tutti i loro difetti; l'invidia e il tentativo di prendersi meriti non propri sono sempre possibili. Spesso si pensa che i matematici siano esenti da tali difetti: ci induce in errore la visione dei risultati, anche solo quelli che vediamo a scuola, che sono sempre precisi e senza macchie. Non è così, e il testo ce lo mostra molto chiaramente.
In definitiva, questo libro dà una visione per così dire umanista della matematica, cosa di cui abbiamo tantissimo bisogno; non ci renderà certo esperti della materia, ma d'altra parte non ce ne faremmo molto. Se leggiamo un libro di viaggio non siamo interessati alle tariffe autostradali, no? Sono utili se volessimo fare quel viaggio, ma non ci darebbero alcuna sensazione. Perfect rigor racconta un viaggio, non un teorema. Un appunto sulla traduzione di Olimpia Ellero: è scorrevole, ma in un paio di punti farà sobbalzare chi ha conoscenze di matematica.
Il titolo del libro deriva da una frase del grande matematico francese Henri Poincaré nel suo libro di filosofia della scienza La scienza e l'ipotesi: "Se l'oggetto di studio rimane confinato all'immaginazione, da dove proviene il perfetto rigore che nessuno penserebbe mai di porre in dubbio?" Poincaré si sta riferendo a una secolare diatriba: se cioè tutta la matematica, con le sue cristalline dimostrazioni formali, non sia semplicemente un modo per dire A = A oppure c'è qualcosa in più, e gli oggetti matematici non sono solo frutto dell'immaginazione dei matematici oppure hanno una connessione con il mondo reale. In un certo senso, la congettura di Poincaré dimostrata da Perel'man rientra in questa seconda categoria: con una cruda approssimazione, possiamo dire che il nostro mondo tridimensionale non può avere una forma "strana" se visto all'interno di uno spazio quadridimensionale, ma è proprio come ce lo aspettiamo intuitivamente. Ma il vero rigore è quello della vita di Perel'man. Gessen tratteggia il matematico come una specie di Forrest Gump, con la differenza che Griša solo estremamente intelligente: la sua ipotesi è che il suo comportamento sociale indichi che sia affetto dalla sindrome di Asperger, che come noto a differenza di altre varianti dell'autismo è spesso associato a un quoziente intellettivo molto alto.
Perel'man è una macchina per risolvere problemi, forse spinto in questo dall'ambizione di sua madre che aveva scelto di non proseguire la carriera matematica per metter su famiglia o magari perché il mondo della matematica ha un suo insieme di regole ben precise che non ammettono eccezioni e sono pertanto relativamente semplici da mettere in pratica: potremmo dire che tali regole hanno una rappresentazione molto compatta che richiede pertanto meno spazio di memoria per gestirle. In tutto questo Perel'man pare non accorgersi affatto dei problemi che la sua condizione di ebreo dal cognome inconfondibile gli pone nell'ambiente sovietico. Formalmente non esisteva alcuna discriminazione, ma all'atto pratico gli ebrei erano tenuti il più possibile lontano dalle università più importanti come quelle di Mosca e Leningrado, nelle quali la politica di ammissione - anche in una facoltà come quella di matematica che non sembrava proprio dare chissà quali problemi di fedeltà alla linea ufficiale comunista - si riassumeva in "potranno essere ammessi solo due studenti ebrei l'anno". La matematica Tanya Khovanova ha raccontato di come esistesse una lista di "problemi speciali", che erano praticamente impossibili da risolvere senza conoscere il trucco che li avrebbe resi banali - pronti per tarpare sul nascere le speranze degli studenti dal cognome sbagliato: se li trovavano di fronte e fallivano miseramente. Perel'man ebbe però la fortuna e la bravura di seguire la scuola di matematica di Sergej Rukšin (anch'egli di origine ebraica, tra l'altro) e vincere le Olimpiadi internazionali di matematica, il che permetteva di essere automaticamente ammesso a un'università di propria scelta, riuscendo così a evitare questo destino.
Gessen calca molto la mano sulle regole che Perel'man si dava per affrontare i problemi di matematica e il mondo intorno a lui. Non è chiaro quanto tali regole esistano veramente nella sua mente: leggendo quanto ha fatto negli anni della sua formazione come matematico, la mia sensazione è che lui abbia semplicemente scelto una strada che poi gli sia sfuggita di mano. Indubbiamente la sua mente è in grado di cogliere in un colpo solo tutti gli aspetti di un problema; ma la scelta di dedicarsi alla geometria sembrerebbe più legata al minor numero di colleghi con cui aveva a che fare, e il progressivo allontanarsi anche da quelli con cui aveva punti di contatto si direbbe legata a un concetto utilitarista, perché nessuno di loro poteva essergli più di aiuto. Resta il mistero del perché Perel'man si sia allontanato dalla matematica: non è comunque il primo, poiché Alexander Grothendieck l'aveva preceduto in un isolamento totale. Tra l'altro anche Grothendieck era di origine russa ed ebraica, il suo campo di studi era la geometria, e aveva vinto la medaglia Fields... magari sono tutte coincidenze. Ma è anche opportuno seguire l'altro tema portato avanti da Gessen, vale a dire la descrizione degli ambienti accademici russo e americano, diversissimi tra loro ma entrambi alieni per chi vuole fare solo matematica e non sottostare a regole forse ancora più bizzarre di quelle che Griša sceglieva per sé. È vero che parecchi matematici hanno perso mesi della loro carriera per rimpolpare le dimostrazioni di Perel'man e assicurarsi della loro correttezza, il tutto senza alcun tornaconto se non l'avanzamento della matematica. Però stiamo sempre parlando di esseri umani, con tutti i loro difetti; l'invidia e il tentativo di prendersi meriti non propri sono sempre possibili. Spesso si pensa che i matematici siano esenti da tali difetti: ci induce in errore la visione dei risultati, anche solo quelli che vediamo a scuola, che sono sempre precisi e senza macchie. Non è così, e il testo ce lo mostra molto chiaramente.
In definitiva, questo libro dà una visione per così dire umanista della matematica, cosa di cui abbiamo tantissimo bisogno; non ci renderà certo esperti della materia, ma d'altra parte non ce ne faremmo molto. Se leggiamo un libro di viaggio non siamo interessati alle tariffe autostradali, no? Sono utili se volessimo fare quel viaggio, ma non ci darebbero alcuna sensazione. Perfect rigor racconta un viaggio, non un teorema. Un appunto sulla traduzione di Olimpia Ellero: è scorrevole, ma in un paio di punti farà sobbalzare chi ha conoscenze di matematica.
December 6, 2023
Важное уточнение. Куцыми тремя баллами я оценила не личность/биографию талантливейшего математика Григория Перельмана, а лишь саму книгу (и беспринципную методику получения информации, которую использовал автор, если говорить конкретнее).
Григорий Перельман - человек во всех смыслах удивительный. Его имя стало известно далеко за пределами узкого научного математического круга не только благодаря решению важнейшей задачи, над которой безуспешно билось не одно поколение ученых, но и благодаря неуклонному следованию своим принципам, оказавшимися в прямом смысле бесценными.
В современном мире, да и во все времена, такие люди сильно выбиваются из общей массы, словно воспарив над головами обывателей. Вполне понятен интерес общества к подобным персонам, вот только сами эти необыкновенные люди повышенному вниманию к своей личности совсем не рады.
Приступая к чтению данной книги, у меня имелось весьма определенное представление об авторе, поэтому я была готова ко многому. Однако, я не подозревала, что процент всяческих догадок, личных размышлений (многие из которых - бредовые, а другие - просто мерзкие), а главное - размусоливания и рассматривания частной жизни этого закрытого математика словно под микроскопом, окажется таким высоким.
Именно это пренебрежение искренним желанием Григория Перельмана держаться в тени, максимально ограждая свою жизнь от посторонних, и оставило меня в негодовании. Такое впечатление, будто Маша Гессен захотела просто навариться на этой хайповой теме, не задумываясь о чувствах человека и этичности создания такой работы, поднимая на публику многое из того, что Г. Перельман, совершенно точно, предпочел бы скрыть. Неуважение к личной жизни математика тут налицо, и мне это очень не нравится. По этой причине данную книгу, естественно, не рекомендую.
Григорий Перельман - человек во всех смыслах удивительный. Его имя стало известно далеко за пределами узкого научного математического круга не только благодаря решению важнейшей задачи, над которой безуспешно билось не одно поколение ученых, но и благодаря неуклонному следованию своим принципам, оказавшимися в прямом смысле бесценными.
В современном мире, да и во все времена, такие люди сильно выбиваются из общей массы, словно воспарив над головами обывателей. Вполне понятен интерес общества к подобным персонам, вот только сами эти необыкновенные люди повышенному вниманию к своей личности совсем не рады.
Приступая к чтению данной книги, у меня имелось весьма определенное представление об авторе, поэтому я была готова ко многому. Однако, я не подозревала, что процент всяческих догадок, личных размышлений (многие из которых - бредовые, а другие - просто мерзкие), а главное - размусоливания и рассматривания частной жизни этого закрытого математика словно под микроскопом, окажется таким высоким.
Именно это пренебрежение искренним желанием Григория Перельмана держаться в тени, максимально ограждая свою жизнь от посторонних, и оставило меня в негодовании. Такое впечатление, будто Маша Гессен захотела просто навариться на этой хайповой теме, не задумываясь о чувствах человека и этичности создания такой работы, поднимая на публику многое из того, что Г. Перельман, совершенно точно, предпочел бы скрыть. Неуважение к личной жизни математика тут налицо, и мне это очень не нравится. По этой причине данную книгу, естественно, не рекомендую.
August 15, 2023
Eine Art Biographie oder besser ein Psychogramm über jemanden zu schreiben, den man selbst nicht interviewen konnte, ist sicherlich eine besondere Herausforderung. Aber dieses Buch schafft es meines Erachtens dennoch gut, die Persönlichkeit von Perelman einzufangen. Interessant sind aber v.a. die historischen Betrachtungen der Sowjet-Mathematik, der Mathe-Clubs und -olympiaden, die Beschreibung des Einflusses von Kolmogoroff auf die Mathematik in Russland oder der Zeit des Umbruchs Anfang der 1990er sowie der mathematischen Forschung auf einer Meta-Ebene. Worum es bei der Poincaré Vermutung geht, wird man auch nach der Lektüre dieses Buches nicht verstanden haben, wenn man es nicht schon vorher wusste. Aber das kann ein populärwissenschaftliches Buch wohl auch nicht leisten.
January 28, 2021
Masha Gessen's Perfect Rigor is broadly about how Grigori Perelman solved the Poincare Conjecture. Gessen details his life, the education system in the Soviet Union, and what happened after he posted his proof. This level of math is not so interesting to me, but I did get caught up in the drama. I also found that I learned about the Soviet Union, particularly its anti-semitism--in fact, in recommending this book to one of my peers, she pointed out that this is why her family left the USSR. Perfect Rigor is a fine book, and yet it did feel a bit like one of those books that could have been a feature.
October 19, 2020
For most books about mathematicians, I find non-mathematicians to be insufficient tour guides because they do not understand the world of mathematics. Gessen does better than most, and I am glad they were my tour guide rather than a Western mathematician. The world of Russian mathematics is strange and alien, and Gessen did a great job introducing it to the reader. I learned a lot.
Yet ultimately, I finished the book unsatisfied at not knowing what Perelman might have been thinking. Gessen's exploration of Asperger's was interesting, but did not help differentiate Perelman from the many mathematicians with Asperger's who have not alienated themselves from the mathematical community.
Yet ultimately, I finished the book unsatisfied at not knowing what Perelman might have been thinking. Gessen's exploration of Asperger's was interesting, but did not help differentiate Perelman from the many mathematicians with Asperger's who have not alienated themselves from the mathematical community.
January 20, 2023
I would've liked it much more if it was an autobiography, but that doesn't seem like smth he'd do; I wouldve appreciated to know his thoughts on what he does and why he does it, and not Masha guessing on it. If I realize anything about myself in relation to this, it's that I read these biographies to feel closer to a great mind that was still human, to understand, but the coldness here steals that from me, and I could maybe mention a few facts about him I'll eventually forget, but not much else.
Ofcourse though, it's not their fault. Masha actually seemed to have made a commendable effort trying to find out what they could.
Ofcourse though, it's not their fault. Masha actually seemed to have made a commendable effort trying to find out what they could.
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