Poincare Conjecture and Grigory Perelman

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Perelman Rejects $1M Millennium Prize
July 2, 2010. Source: The Moscow Times

Grigory Perelman, a reclusive 43-year-old mathematician who lives with his mother in St. Petersburg, said Thursday that he had decided to reject a $1 million cash prize from a U.S. institute.

The “Millennium Prize” was awarded by the Clay Mathematics Institute in Cambridge, Massachusetts, in March for Perelman’s proving of a theorem known as the Poincare conjecture.

Perelman blamed the “unjust” decisions of the “organized mathematician community” for his decision, saying American mathematician Richard Hamilton, ignored by the institute, had contributed to proving the theorem no less than Perelman himself.

Perelman said he notified the institute last week. The institute said in a statement that it would decide what to do with the money this fall.

'Nyet' to $1 million? Math genius, Grigory Perelman, may reject award

Marzo 29, 2010. Source: AP by Malcom Ritter and Irina Titova

ST. PETERSBURG, Russia - Who doesn't want to be a millionaire? Maybe a 43-year-old unemployed bachelor who lives with his elderly mother in Russia - and who won $1 million for solving a problem that has stumped mathematicians for a century.

Grigory Perelman can't decide if he wants the money.

"He said he would need to think about it," said James Carlson, who telephoned Perelman with the news he had won the Millennium Prize awarded by the Clay Mathematics Institute of Cambridge, Mass.

Carlson said he wasn't too surprised by the apparent lack of interest from Perelman, a reclusive genius who has a history of refusing big prizes.

In 2006, Perelman made headlines when he stayed away from the ceremony in Madrid where he was supposed to get a Fields Medal, often called the Nobel prize of mathematics. He remained at home in St. Petersburg instead.

As for the new prize, Perelman (PER-il-mahn) told a local television station he hasn't made a decision on whether to accept the money, and that Carlson's institute will be the first to know when he does.

Sergei Rukshin, Perelman's high school math teacher, told The Associated Press on Monday that Perelman is still unsure whether to accept it.

"I know that this time he is seriously thinking about whether he will accept the prize. He still has some time," Rukshin said. The awards ceremony is in June.

Rukshin said Perelman has been without work for four years and has declined all job offers. He previously worked at the Steklov Mathematics Institute.

"As far as I know, after there was so much media attention ... he did not want to be a public person and to look like an animal in the zoo," Rukshin said.

He said he had encouraged Perelman to accept the prize to provide for himself and his elderly mother.

Technically, the award is a done deal.

"He has been awarded the prize. That's the decision of the committee," Carlson said. "He may or may not accept the money."
Carlson declined to discuss what would happen to the $1 million if Perelman rejects it. Several groups in Russia, including the St. Petersburg Communist Party, have made public appeals to Perelman to give them the cash to fight poverty if he doesn't want it for himself.

Perelman was honored for proving the Poincare conjecture, which deals with shapes that exist in four or more dimensions, rather than the familiar three dimensions. The conjecture proposes a test for determining whether a shape in such space, no matter how distorted, is a three-dimensional sphere.

That was one of seven problems the Clay institute identified in 2000 as being worthy of a $1 million Millennium Prize. It's the first problem on the list to be solved.

The Clay institute was founded in 1998 by Landon T. Clay, a Boston businessman, and his wife, Lavinia D. Clay.

Tamara Yefimova, a deputy director of Perelman's high school who has known the mathematician since he was a student there, said that once he started working on the Poincare conjecture he became totally absorbed in it.

She said Perelman stopped visiting his old school to help students and stopped attending meetings of the city's math society.
As a high school student, Perelman obviously was the most gifted student, Yefimova said. The only reason he didn't get a gold medal upon graduation, she said, was that the unathletic scholar didn't get the top grade in physical education. Perelman went on to earn college and postgraduate degrees in mathematics and mechanical engineering from Leningrad State University and Steklov Mathematics Institute.

"It could have been only him who would solve the Poincare conjecture," Yefimova said.

Indeed, Carlson said, Perelman's solution was "a truly amazing piece of mathematics."

Perelman lives in an aging three-room high-rise apartment with his mother and doesn't like to pick up awards he's won, money or not. What is going on here?

Dean Simonton, a psychology professor at the University of California, Davis, said the field of abstract mathematics can attract people who live in extreme isolation, are aggressively nonconformist and "too often let their personalities interfere with their professional success."

Thomas Greenspon, a Minneapolis psychologist who has long worked with gifted children and adults, speculated that Perelman may be reacting to growing up brilliant.

"It's easy to grow up feeling bad about yourself and maybe even feeling like a freak and sort of reacting accordingly," so social skills can suffer, he said.

Mathematicians will gather in Paris in June to celebrate Perelman's achievement and put on some kind of ceremony whether he's there or not.

Does Carlson care whether Perelman shows up?

"It would be nice," Carlson said. "But on the other hand, I respect his desire for calm and tranquility."

Associated Press Science Writer Malcolm Ritter reported from New York.
 

Russian to turn down million dollar prize for maths

August 17, 2006. Source: Telegraph.co.uk by Harry Mount in New York

An eccentric Russian genius who is thought to have solved one of the world's trickiest maths problems is expected to turn down the mathematics equivalent of a Nobel prize and another award worth a million dollars.

Experts agree that Grigory Perelman, of St Petersburg, cracked the century-old Poincaré Conjecture in 2002. Next Tuesday he is almost certain to win a Fields Medal, the ultimate maths prize, awarded every four years by the executive committee of the International Mathematical Union at Princeton University.

The only problem is that Dr Perelman is not interested in prizes and has already turned down a European maths prize, because he did not think the judges were eminent enough.

This is the last year that Dr Perelman, who turned 40 in June, can claim the Fields prize, open only to mathematicians under 40.

Dr Perelman is equally unexcited by the £530,000 that the Clay Mathematics Institute in Boston is almost certain to give him for solving the problem. In 2000, the institute offered a million dollars to anybody who could solve any one of seven "millennium problems".

"There will still need to be up to two years of checking Dr Perelman's work," said an institute spokesman, "But he probably will get it. If he doesn't want the money, it's going to be difficult."

Dr Perelman was a child prodigy, trained at a St Petersburg school devoted to maths and physics. At 16 he achieved a gold medal with the perfect score at the 1982 International Mathematical Olympiad.

The Poincaré Conjecture was posed by the French mathematician, Jules Henri Poincaré, in 1904. It seeks to understand the shape of the universe by explaining the relationship between shapes, spaces and surfaces.

See also: Fields Medal: Four mathematicians win world's top math prize
 

Meet the cleverest man in the world (who's going to say no to a $1m prize)

August 16, 2006. Source; The Guardian, James Randerson, science correspondent

He is possibly the cleverest person on the planet: an enigmatic and reclusive genius who shocked the academic world with his claim to have solved one of the hardest problems in maths. He is tipped to win a "maths Nobel" for his work on possible shapes of the universe. But rumours are rife that the brilliant Russian mathematician will spurn the greatest accolade his peers can bestow.

Since Grigory "Grisha" Perelman revealed his solution in 2002 to a century-old maths problem, it has been subjected to unparalleled scrutiny by the best academic minds. But no one has been able to find a mistake and there is a growing consensus that he has cracked the problem.

So, next Tuesday he is tipped to win a Fields medal. But even by the standards of troubled maths virtuosos such as John Nash, portrayed in the film A Beautiful Mind, Dr Perelman is described as "unconventional".
He has said he will refuse a $1m prize offered by a private maths research institute in the US that would be his if his claim is proved correct. And upper echelons of the maths world are buzzing with rumours that even if he is offered the gong he will not accept it. The medals are open to mathematicians under 40 years old at the beginning of the prize year. Dr Perelman turned 40 in June so this is the last year that he can win.

He has also refused a major European maths prize, supposedly on the grounds that he did not believe the committee awarding the prize was sufficiently qualified to judge his work.

"I just don't see him turning up in a stretch limo with four over-endowed women and waving his cheque in the air. It's not his style," said Jeremy Gray, a maths historian at the University of Oxford.

"I think he's a very unconventional person. He's against being involved in pageantry and idolatry," said Arthur Jaffe at Harvard University. "But he carries it to extreme which people might describe as a little crazy."

Little is known about Dr Perelman, who refuses to talk to the media. He was born on June 13 1966 and his prodigious talent led to his early enrolment at a St Petersburg school specialising in advanced mathematics and physics. At the age of 16, he won a gold medal with a perfect score at the 1982 International Mathematical Olympiad, a competition for gifted schoolchildren.

After receiving his PhD from the St Petersburg State University, he worked at the Steklov Institute of Mathematics before moving to the US in the late 80s to take posts at various universities. He returned to the Steklov about 10 years ago to work on his proof of the universe's shape.

The maths world was set humming in 2002 by the first instalment of his ground-breaking work on the problem which was set out by the French mathematician, physicist and philosopher Jules Henri Poincaré in 1904. The conjecture, which is difficult for most non-mathematicians even to understand, exercised some of the greatest minds of the 20th century.

It concerns the geometry of multidimensional spaces and is key to the field of topology. Dr Perelman claims to have solved a more general version of the problem called Thurston's geometrisation conjecture, of which the Poincaré conjecture is a special case.

"It's a central problem both in maths and physics because it seeks to understand what the shape of the universe can be," said Marcus Du Sautoy at Oxford University, who will be giving this year's Royal Institution Christmas Lectures. "It is very tricky to pin down. A lot of people have announced false proofs of this thing."

The obsession with the problem, shared by several great mathematicians, has been dubbed Poincaritis.

But Dr Perelman seems to have succeeded where so many failed. "I think for many months or even years now people have been saying they were convinced by the argument," said Nigel Hitchin, professor of mathematics at Oxford University. "I think it's a done deal."

Even the way he announced his proof - which took eight years to complete - was unusual. Rather than publishing in a peer-reviewed journal, he posted three manuscripts in an online archive of maths and physics papers.

"He placed the papers on the web archive and basically said 'that's it'," Prof Hitchin said. "A lot of details needed to be filled in. And there's a bit of squabbling in the background actually about who was first to fill in the details." The most recent of the papers fleshing out his proof runs to a mind-numbing 473 pages.

There is more than just professional acclaim at stake. In 2000, the Clay Institute in Boston, a private maths research organisation, established seven "millennium problems", each with a million-dollar reward for a solution. The Poincaré conjecture is one, but Dr Perelman has said he is not interested in the money. "There are all sorts of jokes going round the community that having a million dollars in St Petersburg is quite dangerous," Prof Hitchin said.

No one is quite sure what will happen if the Russian spurns the medal. "If he were to win it and turn it down it would be slightly insulting," said Prof Du Sautoy. But it seems unlikely that Dr Perelman, who recently relinquished his academic position, will care much about offending his peers. "He has sort of alienated himself from the maths community," Prof Du Sautoy added. "He has become disillusioned with mathematics, which is quite sad. He's not interested in money. The big prize for him is proving his theorem."
 

This hairy hermit could save maths

August 17, 2006. Source: Telegraph.co.uk by Simon Singh

The Russian Grigory Perelman is being called the cleverest and craziest person on the planet. He has come up with the greatest mathematical proof of the 21st century, while sporting the sort of facial hair that makes him look like Rasputin's twin. He has been offered the most prestigious prize in mathematics, but it is unlikely that he will bother to claim it.

The reclusive Perelman is reinforcing the stereotype that mathematical geniuses are strange eccentrics, and he seems to be exactly the sort of person who puts people off maths. At a time when Europe is trying to encourage young people to study maths, why can't our top-notch mathematicians be beautiful, witty extroverts? Why can't they drive around in fast cars and fill the tabloids with gossip about their Hollywood-style orgies?

Realistically, mathematicians are never going to be very glamorous, and moreover it could be that Perelman is exactly what mathematics needs in order to promote itself. Perversely, however, I believe that this hairy Russian hermit could be the poster boy who helps create a new generation of mathematical geniuses. First, it is clear that Perelman is a genius. It is widely accepted among scholars that he has solved the notorious Poincaré conjecture, which had mathematicians baffled for more than a century.

The conjecture is about spheres that live in a higher dimension. Although mathematicians knew how to define a normal three-dimensional sphere, it had been hard to pin down the properties of the fiendishly abstract four-dimensional sphere, until Perelman came along. His proof of the Poincaré conjecture runs to several hundred pages of dense mathematics and is considered a mathematical masterpiece.

In 2000, to add some glitz to number-crunching, the Clay Mathematics Institute in America offered seven Millennium Prizes of $1 million each for the solutions to seven major problems in mathematics, including the Poincaré conjecture. None of the other problems are close to being solved, so Perelman would be the first to claim $1 million, but he has shown no interest in becoming a millionaire and spurned any approaches by the prize organizers.

The majority of the population will find this type of behavior bizarre, and it will serve only to reinforce their antipathy towards mathematics, mathematicians, all numbers bigger than a million and any polygon with more than four sides. Unfortunately, mathematicians are never going to be fun, cuddly folk who appeal to the masses, because what they do is inherently extremely esoteric.

More importantly, however, Perelman might appeal to a small, but critical, audience - namely the tiny fraction of the teenage population who have a talent and enthusiasm for abstract mathematics. They are currently awaiting their exam results and wondering what to do next. Those around them might be saying that studying mathematics could lead to a career as an accountant (which is an important profession) or perhaps to becoming a teacher (an even more important job), but these opportunities are not necessarily going to inspire every mathematically inclined teenager.

In contrast, Perelman shows that studying mathematics can also offer another path. It can lead to a romantic, obsessive lifestyle that is on a par with being a poet or a musician. Perelman spurns money, medals and honours, because the highest reward for him is simply the opportunity to create wonderful mathematics.

Perelman is not unique - the history of maths is full of heroes who exhibit a purity of spirit and utter determination that make mathematics the sexiest discipline on the planet. For example, Sophie Germain had to disguise herself as a man in order to overcome the prejudices of early-19th-century Paris and make discoveries that eluded earlier generations. At roughly the same time, the 20-year-old Evariste Galois knew that he was going to die in a duel and spent his final night writing down all his mathematical ideas. If he was going to die, then he did not want his maths to die with him, and, sure enough, his radical ideas continue to influence modern research.

More recently, Paul Erdõs, the most prolific mathematician of the 20th century, shared many of Perelman's traits. He worked for 19 hours a day, fuelled by coffee and amphetamines. Erdõs would often say: "A mathematician is a machine for turning coffee into theorems." His entire belongings fitted easily into two battered suitcases, and instead of buying a house, he lodged with fellow mathematicians. His motto was: "Another roof, another proof."

Erdõs was not interested in wealth and gave away his money by offering rewards for the solution to various problems. Once, when the outstanding rewards totalled $15,000, a colleague pointed out that Erdõs would be bankrupted if all his problems were solved, to which he replied: "But what would happen to the strongest bank if all the creditors asked for their money back? The bank would surely go broke. And a run on the bank is much more likely than solutions to all my problems."

The last time that mathematics had a hero figure was when Andrew Wiles proved Fermat's last theorem, which required seven years of secret devotion and a similarly formidable proof. Although Wiles has accepted his prizes, totalling several hundred thousand dollars, his real motivation was mere curiosity and the desire to explore the uncharted regions of the mathematical universe. Wiles, Erdõs, Germain, Galois and Perelman all share a desire for knowledge and wonder, as opposed to money and fame.

Next week Perelman will get another chance to show his disdain for baubles and fancy prizes, because it is likely that he will be offered the Fields Medal - the mathematical version of the Nobel Prize. Perelman has already refused to give a lecture at the International Congress of Mathematicians in Madrid, where the medal is to be awarded, which means that he will probably refuse to accept the medal. It will be the ultimate act of defiance, as the Fields Medal can only be awarded to mathematicians aged 40 or less, and Perelman's 40th birthday was earlier this summer.

Simon Singh is a science writer and the author of 'Fermat's Last Theorem'
 

Russian genius exchanges money and glory for seclusion

August 17, 2006. Source: Regnum News

Vanishing act has math pros re-solving riddle

Grisha Perelman, where are you?

August 20, 2006. Source: San Francisco Chronicle. Dennis Overbye, New York Times

Three years ago, a Russian mathematician by the name of Grigory Perelman, a.k.a. Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincare conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world's mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose among them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought.

"It's really a great moment in mathematics," said Bruce Kleiner of Yale, who has spent the past three years helping to explicate Perelman's work. "It could have happened 100 years from now, or never."

In a speech at a conference in Beijing this summer, Shing-Tung Yau of Harvard said the understanding of three-dimensional space brought about by Poincare's conjecture could be one of the major pillars of math in the 21st century.

Quoting Poincare himself, Yau said, "Thought is only a flash in the middle of a long night, but the flash that means everything."

World's top maths genius jobless and living with mother

A maths genius who won fame last week for apparently spurning a million-dollar prize is living with his mother in a humble flat in St Petersburg, co-existing on her £30-a-month pension, because he has been unemployed since December.

August 20, 2006. Source: Telegraph.co.uk by Nadejda Lobastova in St Petersburg and Michael Hirst.

The Sunday Telegraph tracked down the eccentric recluse who stunned the maths world when he solved a century-old puzzle known as the Poincaré Conjecture.

Grigory "Grisha" Perelman's predicament stems from an acrimonious split with a leading Russian mathematical institute, the Steklov, in 2003. When the Institute in St Petersburg failed to re-elect him as a member, Dr Perelman, 40, was left feeling an "absolutely ungifted and untalented person", said a friend. He had a crisis of confidence and cut himself off.

Other friends say he cannot afford to travel to this week's International Mathematical Union's congress in Madrid, where his peers want him to receive the maths equivalent of the Nobel Prize, and that he is too modest to ask anyone to underwrite his trip.

Interviewed in St Petersburg last week, Dr Perelman insisted that he was unworthy of all the attention, and was uninterested in his windfall. "I do not think anything that I say can be of the slightest public interest," he said. "I am not saying that because I value my privacy, or that I am doing anything I want to hide. There are no top-secret projects going on here. I just believe the public has no interest in me."

He continued: "I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing. I realised this a long time ago and nobody is going to change my mind. "Newspapers should be more discerning over who they write about. They should have more taste. As far as I am concerned, I can't offer anything for their readers.

"I don't base that on any negative experiences with the press, although they have been making up nonsense about my father being a famous physicist. It's just plain and simply that I don't care what anybody writes about me at all."

Dr Perelman has some small savings from his time as a lecturer, but is apparently reluctant to supplement them with the $1 million (£531,000) offered by the Clay Mathematics Institute in Cambridge, Massachusetts, for solving one of the world's seven "Millennium Problems".

The Poincaré Conjecture was first posed by the French mathematician, Jules Henri Poincaré, in 1904, and seeks to understand the shape of the universe by linking shapes, spaces and surfaces.

Friends say that evidence of Dr Perelman's innate modesty came when - having finally solved the problem after more than 10 years' work - he simply posted his conclusion on the internet, rather than publishing his explanation in a recognised journal. "If anybody is interested in my way of solving the problem, it's all there - let them go and read about it," said Dr Perelman. "I have published all my calculations. This is what I can offer the public." More

Russian Refuses Math's Highest Honor

August 22, 2006. Source: Washington Post, The Associated Press by Daniel Woolls

MADRID, Spain -- A reclusive Russian won the math world's highest honor Tuesday for solving a problem that has stumped some of the discipline's greatest minds for a century _ but he refused the award.

Grigory Perelman, a 40-year-old native of St. Petersburg, won a Fields Medal _ often described as math's equivalent of the Nobel prize _ for a breakthrough in the study of shapes that experts say might help scientists figure out the shape of the universe.

John Ball, president of the International Mathematical Union, said that he had urged Perelman to accept the medal, but Perelman said he felt isolated from the mathematics community and "does not want to be seen as its figurehead." Ball offered no further details of the conversation.

Besides shunning the award for his work in topology, Perelman also seems uninterested, according to colleagues, in a separate $1 million prize he could win for proving the Poincare conjecture, a theorem about the nature of multidimensional space.

The award, given out every four years, was announced at the mathematical union's International Congress of Mathematicians. Three other mathematicians _ Russian Andrei Okounkov, Frenchman Wendelin Werner and Australian Terence Tao _ won Fields medals in other areas of mathematics.

They received their awards from King Juan Carlos to loud applause from delegates to the conference. But Perelman was not present.

"I regret that Dr. Perelman has declined to accept the medal," Ball said. More

Four mathematicians win world's top math prize

August 23, 2006. Source: Xinhua

Three leading international mathematicians won the world's top math prize -- the Fields Medal -- on Tuesday and received medals from Spanish King Juan Carlos, but another winner, Russia's Grigori Perelman, snubbed the award.

The other three winners are Andrei Okounkov of Russia, Terence Tao of Australia and Wendelein Werner of France.

The Fields Medal was founded in 1936 and named after Canadian mathematician, John Charles Fields.

The International Mathematics Union (IMU) awards the medals every four years during its Congress. The 25th annual International Congress of Mathematicians is being held from Aug. 22 to Aug. 30 in Madrid, attracting some 4,000 scientists from around 120 countries.

The IMU said it had rewarded Okounkov "for his contribution to the work on the interaction of probability theory, representation theory and geometrical algebra."

Tao won the award "for his contributions to the partial derivatives equations: combinatory and with theory of additive numbers."

Werner, who was born in Germany, won the award "for his contribution to the development of Loewner's stochastic evolution, the geometry of Brownian motion in two dimensions and his theory of field formation."

Perelman won for "contributions to geometry and his revolutionary deepening of the analysis and structural geometry of Ricci flows." However, he refused the prize and remained in Russia ignoring the award.
 

When being a genius just doesn't add up

Like Garbo, Grigory Perelman just wants to be left alone. Fair enough, says Katherine Kizilos.

August 26, 2006. Source: The Sydney Morning Herald www.smh.com.au

What would possess the reclusive Russian mathematician Grigory Perelman to reject the Fields Medal, described as the Nobel of mathematics?

Perelman achieved international fame this week by refusing to accept the prize, becoming the first mathematician to do so. His refusal won as much public attention as his groundbreaking mathematical work, possibly because the refusal is easier to describe, although it is not necessarily easier for the media to understand.

Perelman's achievement has been to solve the Poincare Conjecture. According to The New York Times, mathematicians say it may be 100 years before its full implications for math and physics are understood.

The same report described Perelman's work as a "landmark, not just of mathematics but of human thought". The Guardian story was headlined: "Meet the cleverest man in the world.".

All of which makes Perelman's reluctance to stand in the limelight all the more intriguing. Reports about his breakthrough have inevitably also referred to his shyness, his reclusiveness and lack of interest in material success.

There is an unspoken assumption that Perelman, 40, is acting like a freak, that he is defying a natural impulse to beat himself on the chest and declare himself king. Colleagues have described him as a quiet man who lives with his mother on her meagre pension and who likes to wander around the forest near St Petersburg.

It is difficult not to feel sympathy for Perelman who appears to want nothing more than to be left alone and who, like Garbo before him, has become the subject of intense speculation.

Although he had done a series of postdoctoral fellowships in the US in the early 1990s, he turned down offers of work at Stanford and Princeton, taking up a post at the Steklov Institute of Mathematics in St Petersburg.

It may be that Perelman's ambition has been to pursue mathematics and his burden has been the razzamatazz attached to the success he has achieved in this arcane pursuit. The real world, which demands he travels, give speeches and meet the King of Spain, may seem to him a crazy show, quite unconnected to the place where his intellect and imagination has taken him. One report has it that he has become disillusioned with mathematics, which must be a terrible blow. But if it is true, his reclusiveness makes perfect sense.
 

In genius, intentions appear to be simple

August 27, 2006. Source: The New York Times by  George Johnson

Long before John Forbes Nash Jr., the schizophrenic Nobel laureate fictionalized on-screen in "A Beautiful Mind," mathematics has been infused with the legend of the mad genius cut off from the physical world and dwelling in a separate realm of numbers. In ancient times, there was Pythagoras, guru of a cult of geometers, and Archimedes, so distracted by an equation he was scratching in the sand that he was slain by a Roman soldier. Pascal and Newton in the 17th century, Gödel in the 20th - each reinforced the image of the mathematician as ascetic, forgoing a regular life to pursue truths too rarefied for the rest of us to understand.

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré's conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute, in Cambridge, Massachusetts.

Unlike Marlon Brando's turning down an Academy Award or Jean-Paul Sartre a Nobel Prize, Perelman did not appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature's secrets the discoverer is more important than the discovery. More

 

Multifold of Destiny in 'A Complete Proof of the Poincare'

According to Harvard mathematician Shing-Tung Yau, a scathing profile in the New Yorker doesn’t add up.
The article on Yau, which was published in late August, alleges that the mathematician has claimed credit where none is due for solving the Conjecture.

September 28, 2006. Source: The Harvard Crimson by By Leon Neyfakh

Acording to Harvard mathematician Shing-Tung Yau, the first time journalist Sylvia Nasar got in touch with him for a story she was writing for the New Yorker, she told him she was interested in the fusion of math and physics as represented in the age-old Poincare Conjecture. Yau, a Harvard string thle, Perelman had posted a solution to the Poincare online, without even bothering to formally publish in an accredited math journal. The luminaries of the profession, according to the piece, all agreed that Perelman had done it. The International Mathematical Union had even offered him the Fields Medal, a high honor awarded to brilliant mathematicians under the age of 40. Perelman turned down the prize, saying that his proof spoke for itself, and that no further recognition was needed. Yau, meanwhile, according to the article, enlisted a pair of colleagues and, in an attempt to win prestige in the Chinese math community, had them put together a more technically rigorous, and nominally more complete, version of the proof. More