Posts Tagged ‘Grigory Perelman’

I discovered ‘Perfect Rigour’ by Masha Gessen during one of my random book browsing sessions at the bookstore recently. It was about the Russian mathematician Grigory Perelman and how he solved the Poincare Conjecture. I had read in the news sometime back that a nearly century-old mathematical problem which was first proposed by the French Mathematician Poincare in 1904 was recently solved by the Russian mathematician Grigory Perelman. It made me look at the news in more detail because this was one of the few times that mathematics was in the news in recent times. The last time something like this happened was when Andrew Wiles proved Fermat’s Last Theorem in 1995. I read a little bit more about Perelman and the Poincare Conjecture. I even got a book on the Poincare Conjecture by mathematician Donal O’Shea, which was written for general readers and kept it on my book pile for reading later. When I browsed Masha Gessen’s book, it looked like the focus here was more on Perelman and less on the Poincare Conjecture and so it didn’t look like a demanding read. So I got tempted and got it and read it in a few days. Here is the review.


Description of the book


I am giving below a description of the book as given in the inside flap.


In 2006, an eccentric Russian mathematician named Grigori Perelman was confirmed to have 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 posted his answer online in 2002. Once it was proved correct in 2006 he was awarded the Fields Medal, the mathematical world’s greatest honour, and he received lucrative job offers from the world’s finest universities. The Clay Institute’s million-dollar prize followed in 2010. He declined them all.


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 maths 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.



What I think


Masha Gessen’s book, in the initial chapters, provides the setting by giving a fascinating overview of Soviet Mathematics during the twentieth century. It talks about the main figures who developed Soviet mathematics and kept it alive and world-class during the days of the Iron Curtain like Luzin, Kolmogorov, the evolution of maths clubs, the Mathematics Olympiads and the discrimination against Jewish students and Jewish mathematicians. Then it introduces Grigory Perelman into the story and describes his evolution from a talented child to an Olympiad winner to one of the world’s best mathematicians. It also shows glimpses of how the mathematical world works – the profound ideas, the personalities, the rivalries, the jealousies, the secretiveness, the backstabbings. It also gives a reasonably detailed background into the mathematical branch called topology and the Poincare Conjecture – that is reasonably detailed for a general reader and a layperson. Gessen doesn’t attempt to give much information about Perelman’s solution, which I am sure is quite technical and beyond the scope of the book. She also talks about the Clay Mathematics Institute’s announcement of the seven millennium problems and how the institute decided to give one million dollars to anyone who solved any of these problems. Gessen also goes into reasonable detail into why Perelman rejected all the awards and recognition that came his way – the Fields Medal, which is the mathematics equivalent of the Nobel prize, the Clay Institute’s prize of one million dollars and job offers from leading American universities, Stanford, MIT, Princeton, Columbia – you name it. From reading the book, it is quite apparent that Gessen has talked to many of the people involved in Perelman’s life – his fellow students, his teachers, his colleagues, his friends. Unfortunately Perelman himself had stopped speaking to the press after the news of his declining the Clay Institute’s prize came out and so the main character’s voice is missing from the book.


One of the things I liked about the book was that it was written in a journalistic style and so it was easy to read. It is easy for a writer of a book on a mathematical or a scientific topic to slip into technical language about the field, but because Masha Gessen is a journalist and not a scientist, her journalistic style makes this book highly accessible to the general reader. Also because Masha Gessen is Russian-born, she is able to interview the right kinds of people and provide inside information about Soviet mathematics and about Grigory Perelman – information which would be inaccessible otherwise.


I had a few issues about the book too. The first one is really minor – I am really nitpicking here 🙂 Gessen is careful to mention in most places in the book that solving the Poincare Conjecture is really the mathematical breakthrough of this century. She seemed to imply that ‘century’ here meant the 21st century. But being the kind of ‘nit-picking’ reader I am, I was waiting for her to slip 🙂 And slip she did 🙂 In page 154 while describing the audience who had come to a seminar in MIT to hear Perelman lecture about his proof in 2003, she says this – “a majority were curious mathematicians who had come to look at the man who might have made the biggest mathematical breakthrough in a century”. Here ‘century’ clearly implies a hundred years and so I get an opportunity to write on what I think about this topic 🙂 In my opinion, I think that distinction – ‘the biggest mathematical breakthrough in a century’ – belongs to Fermat’s Last Theorem, which was proved by Andrew Wiles in 1995. There are two reasons I feel this way. The first is because Fermat’s Last Theorem is easy to understand for a layperson (one needs to just know what the Pythagoras theorem is, which most of us do, to appreciate Fermat’s Last Theorem). The second reason is that Fermat’s Last Theorem defied mathematicians for nearly 360 years. It was proposed in 1637 and was only proved in 1995 (it probably lends support to the point that simple questions are the most difficult to answer). In comparison, the Poincare Conjecture is complex. (The simplified version that Masha Gessen states goes like this – “if a three-dimensional manifold is smooth and simply connected, then is it diffeomorphic to a three-dimensional sphere?” Here ‘three-dimensional’, ‘smooth’, ‘simply connected’ and ‘sphere’ don’t have their regular meanings. They are loaded terms. For example, ‘three-dimensional manifold’ really means the surface of a four-dimensional object which has certain mathematical properties. ‘Manifold’ and ‘diffeomorphic’ are topological terms). Also, the Poincare Conjecture was proposed in 1904 and didn’t survive even a century. But these are all subjective judgements and one can’t say absolutely which theorem / conjecture is really the more important one. The Poincare Conjecture’s solution will help in answering questions on what is the shape of space and the universe that we inhabit and so it definitely is a significant breakthrough. There are two more problems in the Clay Institute’s Millennium problems list which are legendary. One is the Riemann Hypothesis which has defied solution for nearly 150 years (it was proposed in 1859) and which is mentioned in Yoko Ogawa’s beautiful novel ‘The Housekeeper and the Professor’ (just trying to inspire you to read it :)) The second one is the P=NP? problem. It is related to cryptography, prime numbers and computer passwords and online security and if this is proven it will probably sound the death knell for computer and online security. The novel ‘PopCo’ by Scarlett Thomas touches on this 🙂


The other issue I had with Masha Gessen’s book is that the mathematics part, though written for the layperson and general reader, is extremely simplified. So for readers who want to get into it a bit more, it is not really satisfying.


The third issue I had with the book was that in one of the later chapters, Gessen starts describing autism and Asperger’s Syndrome and speculates on whether Perelman could be autistic or could have Asperger’s Syndrome and whether this made him reject all the awards that came his way and whether this is why he has cut off contact with everyone and pursues a solitary life. My own take on this is that wanting to be left alone or wanting to live in solitude or being an introvert doesn’t mean that one is autistic. Or one has Asperger’s Syndrome. Some people are just introverts and like being left alone and love solitude. Author Emily Maguire (author of ‘Taming the Beast’) wrote an article in the Sydney Morning Herald called ‘Solitude is Bliss’ which describes this point of view quite beautifully. British scientist Henry Cavendish who discovered hydrogen was so shy that when a lady admirer came to his home to meet him, he ran away and came back only after she had left. Of course, modern commentators are speculating now that Cavendish probably had Asperger’s Syndrome! There is also a story about Greek philosopher Diogenes, which goes like this (taken from Wikipedia) – “while Diogenes was relaxing in the sunlight in the morning, Alexander, thrilled to meet the famous philosopher, asked if there was any favour he might do for him. Diogenes replied, “Yes, stand out of my sunlight”. Alexander then declared, “If I were not Alexander, then I should wish to be Diogenes.”” Diogenes never cared about money or riches. It doesn’t mean that Diogenes had Asperger’s!


In one place, Perelman’s former teacher and friend Rukshin says this when he explains the reason for Perelman’s refusal to accept awards and his disappointment with the establishment :


      “It took him eight or nine years to solve the Poincare,” Rukshin told me, recalling that conversation. “Now imagine that for eight years you did not know whether your child, who was born ill, would survive. You have spent eight years caring for him day and night. And now he has grown strong. From an ugly duckling, he has tured to a fine swan. And now someone says to you, ‘Why don’t you sell your baby to me? Here is some grant money, for half a year, or perhaps a year, we could publish the work together, we’d make this a joint result.'”


In another place the author describes her own interpretation of the situation as she has understood.


Great mathematical achievement should be rewarded with professional recognition, which can take only one form : the form of studying and understanding the work that teh person has done. Money is no substitute for work. In fact, money is insulting. If you think it is natural for a university to offer money to someone who has solved a huge problem even though no one at this university understands the solution, imagine the following parallel : a publisher approaches a writer, saying, “I have not read any of your books; in fact, no one has gotten to the end of one, but they say you are a genius, so we want to sign you to a contract.” This is a caricature. There was no place for caricatures in Perelman’s script.


All of us, atleast once during our lives, would have thumbed our nose at the establishment. Or would have done something that we didn’t tell anyone about and when what we did brought some ‘glory’ or resulted in something good, we would have shared it with others, which would have made people around us surprised. I have done both a few times. And so when Perelman and his friends give the reasons on why he acted the way he did and why he refused all the rewards and recognition that he got, one can understand his point of view. I feel though, that it would have been good for him, if Perelman had taken up one of those job offers. Not because of the money, but because it would have helped him do what he liked to do, for the rest of his life – do research in mathematics and solve problems. But who knows what went inside the mind of this tortured soul, when he made all those big decisions?


The book also talks about the shameful episode involving Harvard mathematician Shing-Tung Yau who tried to project his two students as the ones who solved the Poincare Conjecture and mentioned this in press conferences and hurried the publication of their paper in a journal without following a proper peer-review process. Yau was also quoted as saying that though Perelman made important contributions, his students were the ones who developed the important part of the proof and hence deserve major credit for the achievement. It turned out that his students had really plagiarised important parts of their paper from the notes prepared by Bruce Kleiner and John Lott who were studying Perelman’s proof. It also came out that Yau has been involved in other controversies in the past. The interesting thing which happened during this controversy was that ‘The New Yorker’ magazine published an article on it called ‘Manifold Destiny : A legendary problem and a battle over who solved it’ by Sylvia Nasar and David Gruber. It showed Yau in poor light. Yau got furious at it that he sent a letter through his attorneys asking ‘The New Yorker’ to apologize for this article. ‘The New Yorker’ stood its ground and Yau blinked. The matter ended there.


‘Perfect Rigour’is an interesting book and I liked it. It makes me want to read more about the Poincare Conjecture and other mathematical topics. I also found the life of Grigory Perelman as described in the book, quite fascinating. I also really liked the way Masha Gessen had written the book in a racy style which appeals to the general reader. If you like reading books on maths and science for the general reader, you will like this.


On a parting note, one of the discoveries for me after I read this book is that Masha Gessen has written and translated other books 🙂 The most interesting of them, for me, is ‘Half a Revolution : Contemporary Fiction by Russian Women’. I want to get that now 🙂

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