On July 1, 2010 the media broadcasted that the Russian mathematician Grigori Perelman had finally refused the million dollar prize. The news was bewildering. He had earned the money fairly, giving a correct proof of the problem that had remained unsolved for a century. No one in the history of mathematics had ever refused such a large cash prize. (John Morgan) By no other way could Perelman have attracted more attention to himself, mathematics and the Poincare conjecture. The media quickly spreads the image of a strange mathematician from St. Petersburg. One look at this man is enough to see that he is poor, so why does he not need money and fame? Where is the logic? All attempts to find it out from Perelman himself have been futile. (Perelman's voice) What I wanted to say I have already said. Goodbye. (Jim Carlson) The story is so unusual because Perelman is a very unusual person. It brings a romantic element to the story. People will be retelling it for many years. Having solved one of the mysteries of the millennium, Perelman becomes a mystery himself. He has kept silent for many years. And his silence is loud. Maybe with all this excitement over the prize we have missed the most important question at hand. Who is this man and what happened with him in mathematics and in his life? The world consists of consumers, it's normal. For millions the interest in mathematics ended with school. Numbers were invented to count money. What will we get from great mathematical discoveries? (Fedor Bogomolov) You know what they used to say. Number theory, what is it? It turned out that everything we use now – cell phones, computers and so on – they all use number theory. It is all based on some discoveries from the 19th century and some more modern. (Sergei Kislyakov) Do you know that when you put a credit card into an ATM you use very serious mathematical theorems? The data is encrypted. And these theorems were not discovered for this purpose. But suddenly the serene camp of consumers is confused. The situation with Perelman ignites a boom of interest in mathematics. People want to know what they will get from the solved problem and why the Poincare conjecture was assessed with so much money. Henri Poincare was the President of the French Academy of Sciences. He was noble, correct in disputes, indifferent to fame, and strictly honored ethical behavior in science. He used to say that the geometry of the new century needs intuition and inspiration. Poincare first wrote down his conjecture in 1904. For one hundred years it was a puzzle left to his colleagues as a legacy. In response to the recent interest due to Perelman, people have tried explaining it in many different ways to the common man. But it is not easy to explain the Poincare's conjecture in simple terms. Such explanations have used cups, doughnuts, soup bubbles and oranges. (Oleg Viro) During this fuss there was so much nonsense about it. (Nikolai Mnev) All those attempts to explain the Poincare conjecture – complete nonsense. Not a word of truth. (Mikhail Gromov) Here is his hypothesis as I see it. There is the space we live in and he tries to extract its essential properties. He begins to describe these properties. But it is not easy to explain mathematics because it is like a foreign language. You can't explain in two words what the Chinese language is to someone who doesn't know it. You have to study it for years. So we can amuse ourselves by transforming cups into doughnuts and by shrinking the Earth into a point, but the Poincare conjecture and the mysteries of space won't become clearer to us. Mathematicians live in a different cosmos. They know that whoever solves the Poincare conjecture will come closer to the most important problem of mathematics and physics: what is the shape of the universe? There is no other way to describe the world. It is either a natural language or mathematics. Without Grisha it could have remained unsolved for another century. However, the situation is that not even all mathematicians can understand his thoughts. Russia had an amazing mathematical school that created Perelman. If we hadn't had this school we would not have had Perelman. It was generations of mathematicians that interacted with him and taught him. Grisha Perelman was born in 1966 into a country with a great mathematical school, the country of Lobachevsky, Kovalevsky, Kolmogorov,and Chebyshev. His parents considered it a matter of honor to instill a love of mathematics into their children Grisha and his younger sister, Lena. (Sergei Rukshin) The first time I heard about Grisha was from professor Nathanson. He said that his former student had a kid who was interested in mathematics. And why wouldn't I look at him. The mother was convinced that mathematics was perfect for her son. The boy was unusual in character – he was persistent and impeccably honest. We are in the subway and Grisha is sweating profusely. He is wearing a fur hat with tied flaps. “Grisha, it is hot, untie the hat.” “No,” said Grisha, “I promised my mom I wouldn't, so I won't.” Grisha certainly was impeccably honest. Mathematics gave him everything he wanted: solitude, complexity, hard–and–fast rules. Not being able to solve a problem was devastating for him. Only victories were allowed. It was an axiom for him. But this axiom will shatter when life puts into one equation a great problem, ambitions and a million dollars. And this story won't be about mathematics. It began when he boarded the plane flying overseas. In September 1992 Grigori Perelman comes to New York for his internship in the Courant Institute of Mathematical Sciences. Then he will go to Berkeley. He had a great start to science: elite school, a diploma with distinction from the St.Petersburg State University, graduate school and a job in the state's best mathematical organization. But in the early 90s the Soviet Union collapses. Russia is facing a period of political change and economic turmoil. Science was the last thing on the people’s mind. (Ludvig Faddeev) In the late 80s, we probably had the best institute in the world. Amongst the 110 members, 70 had Ph.D degrees in some field of mathematics. If you had a question you could always find somebody who could answer it. Of the 70 doctorates, 40 of them left. Can you imagine such loss? The lack of intellectual work is dangerous for a young mathematician. So Mikhail Gromov tries to help and invites Grisha to the US. Perelman's works are well known there. Such is his talent. They admired his ability to solve problems that nobody else could. While he worked here, he solved three or four problems that had remained unsolved for 20-30 years. Grigori is 26 years old. And he doesn't know that this escape from the problems will change his life dramatically. But everything is fine now. A modest apartment, austerity everywhere, Manhattan doesn't attract him. I couldn't find out if he visited the art museums. It is, supposedly, not expensive in America. Or if America left any impression on him. He went there to do science and was doing it. (Bruce Kleiner) He looked thoughtful, rational, and never depended on other people's opinion. Perelman doesn't get on well with people, but the young professor Gang Tian from China is an exception. Every week they rent a car and drive to Princeton or Stony Brook to attend the lectures of the best professors. At one of these lectures he meets the famous geometer Richard Hamilton. Although, their encounter was ordinary, just a brief conversation after the lecture about the Ricci flow and the continuity of space. Hamilton behaved sincerely, interested in the truth of mathematics. He told Grisha everything he knew on this subject. He also told the most important: he was close to solving the Poincare conjecture. Perelman, of course, knew about the conjecture. But was he interested in it? Maybe this encounter with Hamilton was crucial. Three years have passed. His internship in America is going well and several prestigious universities offer him a position. He thinks about staying, learns English and gets a driver's license. But on one day Perelman reads a new article by Hamilton and realizes that Hamilton is unable to proceed in solving the problem. Grisha writes to him saying: “I think I know how to go further.” No reply from Hamilton – it is a signal that Grisha can work on the problem alone. He buys a ticket home. He had a clear idea – he needed seven years of peace and quiet in order to work. In America he could not have it, he must have a job there. Besides he had some savings that he could live on. So he went back to Russia. He returns to St. Petersburg. The father has left the family and now lives in Israel. His sister studies in the same university but soon will also move to Israel. He is alone with his mother. They live in different apartments in the same neighborhood. But now this loneliness is his salvation. His main objective is the problem he is facing. He has never dealt with a more challenging one. He is obsessed with the idea to overcome something that nobody else can. He knows that he is capable of this. Grisha is very strong in mathematics. Stronger than anybody else. He is super strong. Mathematics is not well suited for child prodigies. The ability to solve problems increases with age. Grisha was 12 years old when he came here – the mathematics club at Leningrad's Young Pioneer Palace. The competition with the other boys here became his first major challenge. Over the span of four years covering the 5th, 6th, 7th and 8th grades the number one student in the city was another boy, Grisha's future classmate Alik Levin. What Grisha did in one hour, Alik did in 15 minutes. In order to stimulate a teenager's ambition and to reveal his hidden abilities, a catalyst is required. And that catalyst was failure. Grisha's stimulus was failing two or three times during the 8th grade. He failed at the city's Olympiad – he only placed second. He also failed at the All-Union Olympiad, where he also placed second. This provoked him, and half a year later he became the number one in the city and in the country. Thus, at the age of 15 he had forgotten how to lose. There would be many victories in the future. Acceptance to the best Leningrad's university – a victory. Acquiring the reputation of a strong problem solver – a victory. Achieving full marks at the International Mathematical Olympiad in Budapest – a victory. His teachers didn't know what was impossible for him in mathematics. These abilities are exactly what he needed to work on the Poincare conjecture for 8-9 years. It's not easy to concentrate on a hard problem for a long time. At the end of July in the year 2000 the Clay Mathematics Institute announces the Millennium Prize Problems. There are seven problems that have remained unsolved for many years. The American philanthropist Landon Clay offers a million dollars for solving each. The idea was to reward the best mathematicians. (Anatoly Vershik) I do not approve of this idea of the Clay Institute. It reminds me of show business. Life has shown that something always happens with this prize. The Poincare conjecture is on the list, but Perelman doesn't care. For the last 5 years this problem is everything he thinks about. He rarely goes to work. His only indulgences are walking and classical music concerts. And the fact that it is now a prize problem doesn't change anything. He feels that the solution is feasible. This is much more rewarding than any prize. The most important thing is the solution. I can give you an example of how one gets mathematical ideas. Sometimes, when you're discussing something, you will suddenly recall an anecdote. The fact that you can recall it at the right moment has nothing to do with memory. It is the same in mathematics. (Yuri Tschinkel) It is an incredible emotional stress. Poincare wrote about it. In his book, “Science and Method”, he writes about boarding a tram, and how insightful thoughts struck him at that time. November 11, 2002. Perelman opens the website arXiv.org. His proof is finished – "The Entropy Formula for the Ricci Flow and its Geometric Applications." It's 40 pages in English. He signs his name, “Grisha Perelman,” and then submits it. And the mathematical world blows up. (Gang Tian) I had not heard from him for many years. Since 1995, when he went back to Russia. It was a big surprise to receive an email from him. I already knew Perelman and immediately realized that this deserved our attention. I can say that I knew about it on the next day. In fact it was Richard Hamilton who told me. We had a Christmas party in December 2002. He said that there is this guy, a topologist, who put out an article about the Ricci flow, claiming at the end that he proved the Poincare conjecture. And it was clear that the author was serious. During the same year Perelman submits the other two parts of his work. His colleagues are confused. First of all, the proof was extremely brief. Secondly, posting a work on the internet doesn't have any official status. It is if the author was saying “Here is my solution. I'm not interested in anything else.” The fact that he posted the article on the internet might have meant that the author went crazy. But you could see that the reasoning in the article was logical and sound. This wasn't a crank. There are many cranks who claim that they have solved the Poincare conjecture. But in this case it wasn't a crank. (Jeff Cheeger) From my experience with Grisha I can tell that he tends to underestimate himself. Not only in mathematics, but also in life. Someone else in this situation would have widely announced this achievement and published everything in detail. But Grisha was different. The first reaction is to meet Grisha, and to ask him a lot of questions. I wrote and invited him to the States, to give a number of lectures about his work. He replied immediately. Immediately. In 2003 Perelman flies again to the US. The best universities invite him to hold lectures. The best mathematicians are eager to attend them. But journalists are not allowed. Perelman can't stand cameras and recorders. He was sharp with those who tried to record his lectures. I remember at one lecture in Stony Brook one of the students put a recorder on the table. When Perelman saw it, he asked: “What's that?” The student explained that he wanted to record the lecture. Perelman said: “No, no, no!” Many people gathered here for the lecture. Supposedly, he was claiming that he had proved the Poincare conjecture. But he did not even mention it. Because he chose those topics which he found the most important. And the conjecture was just a small application of his theory. It happened just like that. The audience was silent. It was not just the Poincare conjecture, but something more. He was opening new doors in geometry. And the conjecture was just a small case which he had proved along the way. It was as if he had shaken Poincare's hand and simply moved on. When Perelman solved this problem, he was perhaps the only one who understood it. Now, after a few years, there are several people who understand it. Perelman does not like be the center of attention. Among his colleagues, however, he is comfortable. Even then, they only talk about mathematics. Everything else is not for him. I remember how we used to spend time together: he would come to my office, we would talk for several hours, and then we would go for a walk. He enjoyed walking. I invited him for lunch. The next day was Sunday, and he was staying with his mother in Brooklyn. He asked, “Who will be there?” I said, “My wife, my son and daughter, and myself.” Then he responded by saying: “No, no. I can't come.” I think if Hamilton and Gromov had been there, he would have said: “OK, I will think about it.” However, Perelman never spoke with Hamilton before his departure. Hamilton attended the lectures, but did not approach Grisha. What was the reason for this? Envy? Resentment? Disbelief? Who knows. Again, Perelman is invited to stay in America, but he returns to St. Petersburg. For Perelman, the conjecture is no longer a conjecture, but for the other mathematicians the work has just begun. The discovery requires a serious examination. It can take years. This problem has a long history of incorrect proofs. There were dozens of such proofs. And that's why everyone was suspicious. It was easy to make a mistake in the proof. Every day, we get submissions from people who claim that they have solved one of the problems or all of the problems plus the Fermat problem. Their proofs always contain mistakes. But Perelman was known as a great mathematician, and people wanted to understand what he did. You can't hope to understand in two days what someone took seven years to come up with. Right? The world's best mathematicians begin to check the proof. The bulk of the work is carried out by two teams. One team consists of Bruce Kleiner and John Lott. The other one has John Morgan, who worked on the conjecture for many years, and Gang Tian. These mathematicians deciphered, verified and commented on Perelman's proof. It was exhausting work. Not every mathematician had sufficient knowledge of the different fields of mathematics required to understand his proof. Perelman did not invent the method of solving the problem. William Thurston began working on this in 1975. Then Richard Hamilton invented a tool which could potentially solve the problem. In his proof, Perelman draws on many different fields of mathematics: the Ricci-Hamilton flow, Thurston's geometrization conjecture, the Aleksandrov geometry. The immense breadth of knowledge – which he acquired in the Soviet schooling system – is what allows him this freedom. He bypassed the point at which Hamilton got stuck. This alone was amazing enough. Hamilton said that if he was aware of the theorems that Perelman knew, he would have done more. This institute at Fontannaya Street was where Grigori Perelman worked for 15 years. It was here that he interacted with the best geometers in the country: Aleksandrov, Zalgaller, Burag. Here he solved problems; argued with his superiors; switched laboratories; and reluctantly wrote hateful reports. Like this one. Here is his report. No publications. In December 2005, Perelman suddenly resigns. Right here, he hands me his resignation paper. I say, “Grisha, have you thought about this? Let's leave this paper here, so that you can take it back later.” “No, I have thought hard about this,” said Grisha. Then I asked, “Does your mother know?” “No, my mother doesn't know. Why does she need to know? My sister knows.” As I understand it, he is leaving not just the institute, but also mathematics. It is difficult to understand, but Perelman insists on it: for him, mathematics is over. He quickly stops talking about mathematics. His circle of friends rapidly shrinks to nothing. But what is this? Is it simply a whim of a genius, or is it rather the desperation of a tired man? If it is true, and Grisha never lies, then he has left mathematics and will never come back. But is his brain still capable of doing mathematics? Maybe it has dried out, like a sponge in the Sahara Desert. An achievement like that might not happen again. There are examples of mathematicians who have not contributed anything after achieving great things. Because they burned out. Meanwhile, 2006, the year of his 40th birthday, has come. And life gives him both a huge present, and a huge nightmare – worldwide recognition. Science Magazine chooses the proof of the Poincare conjecture as its Breakthrough of the Year. Perelman is ranked 9th among the top 100 geniuses alive by the Daily Telegraph. But the sensation of the year is an article in the New Yorker. Its authors, two journalists by the name of Sylvia Nasar and David Gruber, expose a scandal in the mathematical community, some mathematicians want to strip Perelman of his prize. The article reveals names and facts. It causes lawsuits. Sylvia Nasar is a serious opponent. She is the author of “A Beautiful Mind”, a biography about the famous mathematician John Nash. When Hollywood adapted the book into a movie, Nash became a celebrity, and not just in Princeton. The hero of the article is Perelman. The villains are Chinese mathematician Shing-Tung Yau and his students. The authors investigate and reveal that professor Yau also worked on the Poincare conjecture, and is now trying to convince the mathematical community that Perelman discovered nothing new, but merely presented a different angle on the subject. According to Yau, the breakdown of the contributions toward the discovery was as follows: 50% Hamilton, 25% Perelman, and 30% the Chinese mathematicians. This adds up to 105%. Interesting arithmetic. But Yau gives himself the main credit for the final solution. Perelman is offended. The world of mathematics is rotten. Ethics has deserted it. You can buy, sell, and steal everything. He said that the world of mathematics is becoming corrupt, much like the rest of society. Perelman believed in some sense that mathematicians were better and more righteous than the rest of the world. At the same time the International Mathematical Union announces that it has awarded Perelman a Fields Medal. But he doesn't need this gold medal. Grisha nursed a grudge not only against the international, but also against the Russian mathematical community because none of those people tried to restore the truth. And he was right. In August 2006 at the award ceremony in Madrid there are 3000 mathematicians present. They still hope to see Perelman. The King of Spain is going to hand out the medals. But there is confusion – while the king came, Perelman didn't. Grisha doesn't try to change people. He just stops interacting with those groups of people he doesn't like. Perelman scrupulously obeys ethical rules. His teachers insisted that mathematics is not only the Queen of the Sciences, but also the most moral science. His teacher Aleksandrov used to say, at the end of his life, “I'm not interested in geometry, I'm interested in morality.” Mathematicians have a very clear criterion of what is right and wrong. It is often subjective but it still is very important. People can't falsify the truth. If they do, they stop being professionals. Perelman's grievances accumulate within him. He becomes more reclusive. Kleiner and Lott sent him one of the first versions of their manuscript with a note: “Would you like to take a look at it? Maybe we've missed something. Maybe the explanation is too complicated.” He replied, “No. I don't want to read your manuscript.” We sent him our book. Maybe we didn't have the right address, but the package returned unopened. He is very persistent. And it is a remarkable quality. Without it he could not have solved the problem. You have to be very persistent to concentrate on one thing for seven years. But when he was finished, he no longer had anything to apply his persistence to. And it simply became stubbornness. In 2006, after four years of review, the experts present their final conclusion – the proof is correct. Its author is Grigori Perelman and nobody else. This means that Perelman deserves a Millennium Prize. After Alfred Nobel excluded mathematics as an award category out of spite, mathematicians agreed that counting dollar bills was not for them. Thus the Fields Medal is as prestigious as the Nobel Prize. But its cash reward is not large – only 15000 Canadian dollars. The benefit of these prizes and medals is that it increases the people's interest in sciences. Over the years, awards become more generous. Several years ago, Norway began awarding outstanding mathematicians the Abel Prize. It is also almost a million dollars. The brilliant Mikhail Gromov is one of its winner. Mathematicians don't care about money and prizes. It is, of course, nice to receive money, I don't say that it is not nice. But it doesn't change anything. It is convenient to live when you don't have to think about money. If you break your glasses, you go and buy a new pair. Here in the Clay Institute at Cambridge, this elegant piece of glass is still kept. It is the Millennium Prize which has made so much noise. This formula is the Poincare conjecture. Mathematicians, like poets, try to express complex situations with a few carefully chosen words. The news that Perelman is going to get a Millennium Prize spreads quickly. It causes a mass hysteria. He is not prepared for this. They lie in wait for him around his building. Call his home. They compose songs, poems, jokes about him. Quickly publish his biographies and write fake interviews. What's the difference, they need a sensation. But then behind all these rumours and noise nobody pays attention to his rare answers to intrusive journalists: “I have nothing to tell you.” And he is right. What they are discussing is pointless. The Clay Institute has not announced its decision about awarding the prize. Instead it delays for another 4 years. Only in 2010, in this room, where one can see Harvard University through the windows, the decision to award Perelman is made by a special committee: William Thurston, the author of the geometrization conjecture, which has the Poincare conjecture as a special case; Stephen Smale, who proved the Poincare conjecture for the five-dimensional space; Bruce Kleiner, John Morgan and his co-author Gang Tian; and Misha Gromov, one of the best geometers of our time. The decision has been made. But it doesn't make Perelman happy. Now it is the spring of 2010. You don't have to be a great mathematician to calculate that all the arguments, scandals, and verifications took 8 years. It is more than he needed to prove the theorem. They are waiting for his answer again. But now he is not ready with the answer. (Perelman's voice) I have not decided yet. The Clay Institute will know it first. It is interesting that Grigori was really thinking about accepting the prize. He really thought about it this year. If before it was clear that he would refuse the Fields Medal, this time there was at least some hesitation. And his mother confirmed it on the phone, that Grisha was thinking. What was he thinking about for almost 100 days – nobody knows. Perhaps the main cause of his doubts is Hamilton. When we were discussing it in our community, we also decided that Perelman and Hamilton, they both deserve the award. Thus, after 15 years, Perelman wants to repay the debt to Hamilton for that brief conversation in America about the Ricci flow and the Poincare conjecture. Perelman always said that the contribution of Hamilton is none less significant than his. I think that without Hamilton it would have been difficult to do anything. Hamilton is surprised, he doesn't remember that conversation. Besides, it's impossible to split the prize. It is strange that Perelman himself rejects an ethical rule of mathematics. In all mathematical results of this level, you always rely on the previous results. But according to an unspoken rule the prize goes to the one who crosses the finish line. Besides, the decision of the committee can't be changed. On July 1, 2010, Perelman breaks his silence and utters the reason of his refusal – disagreement with the mathematical community. “I don't like their decisions, I find them unjust.” In June 2010 the first Millennium Prize ceremony is held in Paris. Standing on the stage with the prize in his hands Landon Clay merely states that there is one problem fewer in mathematics. Everyone in this room knows – Perelman will not come and will not accept the money. Perelman is a national hero. A national hero. People talk about it, and here is one. They tried to buy him and failed. Without a chance. This story began 20 years ago. Perelman is in his 40's now. He's got a different life. Nobody knows what he does and where he gets money to live. But everyone knows – it is impossible to change him. First of all, he impoverished his own mother. She didn't deserve that. She is an elderly woman who raised two amazing children during what were not the easiest years of our country. The life is very difficult for Perelman now. And he has been living in this condition for several years. I think he is living on the edge of a nervous breakdown. He is a great mathematician. He doesn't teach anybody, doesn't interact. He is wasting his talent. A lot of energy was used on him. Many people taught him, he interacted with them. And now he's gone and not giving it back. It is not ethical. He has chosen freedom for himself and destroyed his career, his friendships, and the lives of his family. What has he left? Only music. Our recent conversations were only about the Mariinsky Theatre, classical music and the other things that interest him. Perelman's million is gone. But he doesn't care whether it was a million dollars or a fistful of coins. He lives in the world where the mysteries of the universe are unraveled not for money. To take this money meant to betray your principles. He solved the problem which only few people on the planet can understand. It is ridiculous to think that he is interested in our opinion. Now people talk about mathematician Grigori Perelman in the past tense. When he was in geometry, he was the best geometer in the world, when he functioned. What will his name say to future generations? Now he is just a great mathematician of the 20th century. So he has moved to another category. [Chief editor: Lloyd Unverferth. Editors: Amor Fati, K. Z. Khor, Suren Ganesh, Andrew O'Desky. Translation: Roman Kunin.]
This was fantastic.
Ohhh, I remember watching this and then spending two months studying nothing but physics at HS. Then I realised that I was in way over my head. This stuff needs book smarts, which I just. don't. got.
coincidences hein?!... so, today I was driving from work and was thinking about this guy. I juzt get curious about ppl like him I guess. I really thought he was never interviewed and was very reclusive... and here it is some hours later.. go and figure!
thnx a bunch i'll watch it later.
Totally forgot about him. It's sad to hear that he's still a recluse.
Thanks for this link! I love documentaries about mathematicians, and good ones are rare.
Interesting and definitely worth the 45 minutes. However, I just couldn't get over that I was reading subtitles for an interview in English because the original was dubbed in Russian. I guess I'm just not used to foreign documentaries.