Perelman SRT

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1 00:00:10,994 --> 00:00:23,899 On July 1, 2010 the media broadcasted that the Russian mathematician Grigori Perelman had finally refused the million dollar prize. 2 00:00:23,999 --> 00:00:29,501 The news was bewildering. He had earned the money fairly, 3 00:00:29,601 --> 00:00:37,404 giving a correct proof of the problem that had remained unsolved for a century. 4 00:00:37,504 --> 00:00:45,208 No one in the history of mathematics had ever refused such a large cash prize. 5 00:00:45,424 --> 00:00:54,433 (John Morgan) By no other way could Perelman have attracted more attention to himself, mathematics and the Poincare conjecture. 6 00:00:54,955 --> 00:01:01,588 The media quickly spreads the image of a strange mathematician from St. Petersburg. 7 00:01:01,688 --> 00:01:09,222 One look at this man is enough to see that he is poor, so why does he not need money and fame? 8 00:01:09,322 --> 00:01:16,285 Where is the logic? All attempts to find it out from Perelman himself have been futile. 9 00:01:16,471 --> 00:01:24,865 (Perelman's voice) What I wanted to say I have already said. Goodbye. 10 00:01:25,228 --> 00:01:35,304 (Jim Carlson) The story is so unusual because Perelman is a very unusual person. It brings a romantic element to the story. 11 00:01:35,404 --> 00:01:38,961 People will be retelling it for many years. 12 00:01:39,354 --> 00:01:45,754 Having solved one of the mysteries of the millennium, Perelman becomes a mystery himself. 13 00:01:45,854 --> 00:01:50,047

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Perelman SRT

Transcript of Perelman SRT

Page 1: Perelman SRT

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On July 1, 2010 the media broadcasted that the Russian

mathematician Grigori Perelman had finally refused

the million dollar prize.

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The news was bewildering. He had earned the money fairly,

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giving a correct proof of the problem that

had remained unsolved for a century.

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No one in the history of mathematics had ever

refused such a large cash prize.

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(John Morgan) By no other way could Perelman have attracted more

attention to himself, mathematics and the Poincare conjecture.

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00:00:54,955 --> 00:01:01,588

The media quickly spreads the image of

a strange mathematician from St. Petersburg.

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One look at this man is enough to see that he is poor,

so why does he not need money and fame?

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Where is the logic? All attempts to find it out

from Perelman himself have been futile.

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(Perelman's voice) What I wanted to say I have already said. Goodbye.

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(Jim Carlson) The story is so unusual because Perelman is a

very unusual person. It brings a romantic element to the story.

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People will be retelling it for many years.

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Having solved one of the mysteries of the millennium,

Perelman becomes a mystery himself.

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He has kept silent for many years. And his silence is loud.

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Maybe with all this excitement over the prize we

have missed the most important question at hand.

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Who is this man and what happened with him

in mathematics and in his life?

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The world consists of consumers, it's normal.

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For millions the interest in mathematics ended with school.

Numbers were invented to count money.

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What will we get from great mathematical discoveries?

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(Fedor Bogomolov) You know what they used

to say. Number theory, what is it?

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It turned out that everything we use now – cell phones,

computers and so on – they all use number theory.

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It is all based on some discoveries from the 19th century

and some more modern.

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(Sergei Kislyakov) Do you know that when you put a credit card

into an ATM you use very serious mathematical theorems?

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The data is encrypted. And these theorems

were not discovered for this purpose.

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But suddenly the serene camp of consumers is confused.

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The situation with Perelman ignites

a boom of interest in mathematics.

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People want to know what they will get from the solved problem

and why the Poincare conjecture was assessed with so much money.

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Henri Poincare was the President of the French Academy of Sciences.

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He was noble, correct in disputes, indifferent to fame,

and strictly honored ethical behavior in science.

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He used to say that the geometry of the new century

needs intuition and inspiration.

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Poincare first wrote down his conjecture in 1904. For one

hundred years it was a puzzle left to his colleagues as a legacy.

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In response to the recent interest due to Perelman, people have

tried explaining it in many different ways to the common man.

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But it is not easy to explain

the Poincare's conjecture in simple terms.

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Such explanations have used cups, doughnuts,

soup bubbles and oranges.

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(Oleg Viro) During this fuss there was so much nonsense about it.

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(Nikolai Mnev) All those attempts to explain the Poincare

conjecture – complete nonsense. Not a word of truth.

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(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.

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He begins to describe these properties.

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But it is not easy to explain mathematics

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because it is like a foreign language.

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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.

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So we can amuse ourselves by transforming cups into doughnuts

and by shrinking the Earth into a point,

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but the Poincare conjecture and the mysteries of space

won't become clearer to us.

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Mathematicians live in a different cosmos.

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They know that whoever solves the Poincare conjecture will

come closer to the most important problem

of mathematics and physics:

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what is the shape of the universe?

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There is no other way to describe the world.

It is either a natural language or mathematics.

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Without Grisha it could have remained unsolved

for another century.

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However, the situation is that not even all mathematicians

can understand his thoughts.

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Russia had an amazing mathematical school that created Perelman.

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If we hadn't had this school we would not have had Perelman.

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It was generations of mathematicians

that interacted with him and taught him.

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Grisha Perelman was born in 1966 into a country with a great

mathematical school,

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the country of Lobachevsky, Kovalevsky,

Kolmogorov,and Chebyshev.

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His parents considered it a matter of honor to instill a love

of mathematics into their children Grisha

and his younger sister, Lena.

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(Sergei Rukshin) The first time I heard about Grisha was

from professor Nathanson.

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He said that his former student had a kid who was interested

in mathematics. And why wouldn't I look at him.

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The mother was convinced that mathematics

was perfect for her son.

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The boy was unusual in character – he was

persistent and impeccably honest.

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We are in the subway and Grisha is sweating profusely.

He is wearing a fur hat with tied flaps.

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“Grisha, it is hot, untie the hat.”

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“No,” said Grisha, “I promised my mom I wouldn't, so I won't.”

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Grisha certainly was impeccably honest.

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Mathematics gave him everything he wanted: solitude,

complexity, hard–and–fast rules.

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Not being able to solve a problem was devastating for him.

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Only victories were allowed. It was an axiom for him.

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But this axiom will shatter when life puts into one equation

a great problem, ambitions and a million dollars.

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And this story won't be about mathematics.

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It began when he boarded the plane flying overseas.

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In September 1992 Grigori Perelman comes to New York for his

internship in the Courant Institute of Mathematical Sciences.

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Then he will go to Berkeley.

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He had a great start to science: elite school, a diploma

with distinction from the St.Petersburg State University,

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graduate school and a job in the state's best mathematical organization.

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But in the early 90s the Soviet Union collapses.

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Russia is facing a period of political change and economic turmoil.

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Science was the last thing on the people’s mind.

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(Ludvig Faddeev) In the late 80s, we probably had the best

institute in the world.

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Amongst the 110 members,

70 had Ph.D degrees in some field of mathematics.

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If you had a question you could

always find somebody who could answer it.

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Of the 70 doctorates, 40 of them left.

Can you imagine such loss?

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The lack of intellectual work is dangerous

for a young mathematician.

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So Mikhail Gromov tries to help and invites Grisha to the US.

Perelman's works are well known there. Such is his talent.

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They admired his ability to solve problems that nobody else could.

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While he worked here, he solved three or four problems

that had remained unsolved for 20-30 years.

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Grigori is 26 years old. And he doesn't know that this escape

from the problems will change his life dramatically.

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But everything is fine now. A modest apartment, austerity everywhere,

Manhattan doesn't attract him.

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I couldn't find out if he visited the art museums.

It is, supposedly, not expensive in America.

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Or if America left any impression on him.

He went there to do science and was doing it.

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(Bruce Kleiner) He looked thoughtful, rational,

and never depended on other people's opinion.

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Perelman doesn't get on well with people, but the young

professor Gang Tian from China is an exception.

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Every week they rent a car and drive to Princeton

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or Stony Brook to attend the lectures of the best professors.

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At one of these lectures he meets

the famous geometer Richard Hamilton.

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Although, their encounter was ordinary, just a brief

conversation after the lecture about the Ricci flow

and the continuity of space.

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Hamilton behaved sincerely, interested in the truth of

mathematics. He told Grisha everything he knew on this subject.

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He also told the most important:

he was close to solving the Poincare conjecture.

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Perelman, of course, knew about the conjecture.

But was he interested in it?

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Maybe this encounter with Hamilton was crucial.

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Three years have passed. His internship in America is going well

and several prestigious universities offer him a position.

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He thinks about staying, learns English

and gets a driver's license.

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But on one day Perelman reads a new article by Hamilton

and realizes that Hamilton is unable to proceed

in solving the problem.

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Grisha writes to him saying: “I think I know how to go further.”

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No reply from Hamilton – it is a signal

that Grisha can work on the problem alone.

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He buys a ticket home.

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He had a clear idea – he needed seven years of

peace and quiet in order to work.

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In America he could not have it, he must have a job there.

Besides he had some savings that he could live on.

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So he went back to Russia.

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He returns to St. Petersburg. The father has left

the family and now lives in Israel.

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His sister studies in the same university

but soon will also move to Israel.

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He is alone with his mother.

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They live in different apartments in the same neighborhood.

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But now this loneliness is his salvation.

His main objective is the problem he is facing.

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He has never dealt with a more challenging one. He is obsessed

with the idea to overcome something that nobody else can.

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He knows that he is capable of this.

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Grisha is very strong in mathematics.

Stronger than anybody else. He is super strong.

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Mathematics is not well suited for child prodigies.

The ability to solve problems increases with age.

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Grisha was 12 years old when he came here – the mathematics

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club at Leningrad's Young Pioneer Palace.

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The competition with the other boys here

became his first major challenge.

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Over the span of four years covering the 5th, 6th, 7th and 8th

grades the number one student in the city was another boy,

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Grisha's future classmate Alik Levin.

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What Grisha did in one hour, Alik did in 15 minutes.

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In order to stimulate a teenager's ambition and to reveal

his hidden abilities, a catalyst is required.

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And that catalyst was failure.

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Grisha's stimulus was failing two or three times

during the 8th grade.

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He failed at the city's Olympiad – he only placed second.

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He also failed at the All-Union Olympiad,

where he also placed second.

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This provoked him, and half a year later he became

the number one in the city and in the country.

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Thus, at the age of 15 he had forgotten how to lose.

There would be many victories in the future.

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Acceptance to the best Leningrad's university – a victory.

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Acquiring the reputation of a strong problem solver – a victory.

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Achieving full marks at the International

Mathematical Olympiad in Budapest – a victory.

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His teachers didn't know what was impossible for him in mathematics.

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These abilities are exactly what he needed to work

on the Poincare conjecture for 8-9 years.

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It's not easy to concentrate on a hard problem for a long time.

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At the end of July in the year 2000 the Clay Mathematics

Institute announces the Millennium Prize Problems.

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There are seven problems that have remained unsolved for many years.

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The American philanthropist Landon Clay offers

a million dollars for solving each.

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The idea was to reward the best mathematicians.

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(Anatoly Vershik) I do not approve of this idea of the

Clay Institute. It reminds me of show business.

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Life has shown that something always happens with this prize.

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The Poincare conjecture is on the list, but Perelman doesn't care.

For the last 5 years this problem is everything he thinks about.

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He rarely goes to work.

His only indulgences are walking and classical music concerts.

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And the fact that it is now a prize problem doesn't change

anything. He feels that the solution is feasible.

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This is much more rewarding than any prize.

The most important thing is the solution.

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I can give you an example of how one gets mathematical ideas.

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Sometimes, when you're discussing something,

you will suddenly recall an anecdote.

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The fact that you can recall it at the right moment

has nothing to do with memory.

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It is the same in mathematics.

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(Yuri Tschinkel) It is an incredible emotional stress.

Poincare wrote about it.

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In his book, “Science and Method”, he writes about boarding

a tram, and how insightful thoughts struck him at that time.

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November 11, 2002. Perelman opens the website arXiv.org.

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His proof is finished – "The Entropy Formula for

the Ricci Flow and its Geometric Applications."

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It's 40 pages in English. He signs his name,

“Grisha Perelman,” and then submits it.

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And the mathematical world blows up.

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(Gang Tian) I had not heard from him for many years.

Since 1995, when he went back to Russia.

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It was a big surprise to receive an email from him.

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I already knew Perelman and immediately realized

that this deserved our attention.

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I can say that I knew about it on the next day.

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In fact it was Richard Hamilton who told me.

We had a Christmas party in December 2002.

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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.

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And it was clear that the author was serious.

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During the same year Perelman submits the other

two parts of his work.

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His colleagues are confused. First of all,

the proof was extremely brief.

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Secondly, posting a work on the internet

doesn't have any official status.

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It is if the author was saying

“Here is my solution. I'm not interested in anything else.”

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The fact that he posted the article on the internet might

have meant that the author went crazy.

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But you could see that the reasoning in the article

was logical and sound.

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This wasn't a crank.

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There are many cranks who claim that they have solved

the Poincare conjecture. But in this case it wasn't a crank.

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(Jeff Cheeger) From my experience with Grisha I can tell that

he tends to underestimate himself. Not only in mathematics,

but also in life.

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Someone else in this situation would have widely announced

this achievement and published everything in detail.

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But Grisha was different.

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The first reaction is to meet Grisha,

and to ask him a lot of questions.

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I wrote and invited him to the States, to give a number of lectures

about his work. He replied immediately. Immediately.

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In 2003 Perelman flies again to the US. The best universities

invite him to hold lectures.

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The best mathematicians are eager to attend them.

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But journalists are not allowed.

Perelman can't stand cameras and recorders.

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He was sharp with those who tried to record his lectures.

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I remember at one lecture in Stony Brook

one of the students put a recorder on the table.

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When Perelman saw it, he asked: “What's that?”

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The student explained that he wanted to record the lecture.

Perelman said: “No, no, no!”

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Many people gathered here for the lecture. Supposedly, he was

claiming that he had proved the Poincare conjecture.

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But he did not even mention it. Because he chose those

topics which he found the most important.

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And the conjecture was just a small application of his theory.

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00:21:03,035 --> 00:21:07,417

It happened just like that. The audience was silent.

183

00:21:07,517 --> 00:21:15,843

It was not just the Poincare conjecture, but something more.

He was opening new doors in geometry.

184

00:21:15,943 --> 00:21:22,429

And the conjecture was just a small case

which he had proved along the way.

185

00:21:22,529 --> 00:21:27,877

It was as if he had shaken Poincare's hand and simply moved on.

186

00:21:28,930 --> 00:21:34,083

When Perelman solved this problem,

he was perhaps the only one who understood it.

187

00:21:34,183 --> 00:21:38,359

Now, after a few years, there are several people who understand it.

188

00:21:39,190 --> 00:21:45,759

Perelman does not like be the center of attention.

Among his colleagues, however, he is comfortable.

189

00:21:45,859 --> 00:21:50,855

Even then, they only talk about mathematics.

Everything else is not for him.

190

00:21:52,647 --> 00:22:00,413

I remember how we used to spend time together:

he would come to my office, we would talk for several hours,

191

00:22:00,513 --> 00:22:04,247

and then we would go for a walk. He enjoyed walking.

Page 16: Perelman SRT

192

00:22:05,243 --> 00:22:11,046

I invited him for lunch. The next day was Sunday,

and he was staying with his mother in Brooklyn.

193

00:22:11,146 --> 00:22:16,332

He asked, “Who will be there?”

I said, “My wife, my son and daughter, and myself.”

194

00:22:16,432 --> 00:22:19,580

Then he responded by saying: “No, no. I can't come.”

195

00:22:19,680 --> 00:22:25,547

I think if Hamilton and Gromov had been there,

he would have said: “OK, I will think about it.”

196

00:22:25,900 --> 00:22:31,416

However, Perelman never spoke with Hamilton before his departure.

197

00:22:31,516 --> 00:22:36,594

Hamilton attended the lectures, but did not approach Grisha.

198

00:22:36,694 --> 00:22:42,298

What was the reason for this? Envy?

Resentment? Disbelief? Who knows.

199

00:22:43,863 --> 00:22:49,269

Again, Perelman is invited to stay in America,

but he returns to St. Petersburg.

200

00:22:49,369 --> 00:22:57,194

For Perelman, the conjecture is no longer a conjecture,

but for the other mathematicians the work has just begun.

201

00:22:57,294 --> 00:23:01,705

The discovery requires a serious examination. It can take years.

202

00:23:02,084 --> 00:23:08,502

This problem has a long history of incorrect proofs.

There were dozens of such proofs.

203

00:23:08,602 --> 00:23:14,716

And that's why everyone was suspicious.

It was easy to make a mistake in the proof.

204

00:23:14,979 --> 00:23:23,278

Every day, we get submissions from people who claim that they

Page 17: Perelman SRT

have solved one of the problems

205

00:23:23,378 --> 00:23:30,865

or all of the problems plus the Fermat problem.

Their proofs always contain mistakes.

206

00:23:30,965 --> 00:23:39,176

But Perelman was known as a great mathematician,

and people wanted to understand what he did.

207

00:23:39,348 --> 00:23:43,662

You can't hope to understand in two days what someone

took seven years to come up with. Right?

208

00:23:48,654 --> 00:23:58,751

The world's best mathematicians begin to check the proof.

The bulk of the work is carried out by two teams.

209

00:23:58,851 --> 00:24:03,511

One team consists of Bruce Kleiner and John Lott.

210

00:24:03,611 --> 00:24:12,058

The other one has John Morgan, who worked on

the conjecture for many years, and Gang Tian.

211

00:24:12,769 --> 00:24:20,621

These mathematicians deciphered, verified and commented

on Perelman's proof. It was exhausting work.

212

00:24:20,721 --> 00:24:30,538

Not every mathematician had sufficient knowledge of the different

fields of mathematics required to understand his proof.

213

00:24:30,741 --> 00:24:36,646

Perelman did not invent the method of solving the problem.

214

00:24:36,746 --> 00:24:41,511

William Thurston began working on this in 1975.

215

00:24:41,611 --> 00:24:49,796

Then Richard Hamilton invented a tool

which could potentially solve the problem.

216

00:24:50,573 --> 00:24:57,890

In his proof, Perelman draws on many different fields

of mathematics: the Ricci-Hamilton flow,

217

Page 18: Perelman SRT

00:24:57,990 --> 00:25:02,868

Thurston's geometrization conjecture, the Aleksandrov geometry.

218

00:25:02,968 --> 00:25:12,808

The immense breadth of knowledge – which he acquired in

the Soviet schooling system – is what allows him this freedom.

219

00:25:13,036 --> 00:25:17,607

He bypassed the point at which Hamilton got stuck.

This alone was amazing enough.

220

00:25:17,785 --> 00:25:28,407

Hamilton said that if he was aware of the theorems

that Perelman knew, he would have done more.

221

00:25:35,246 --> 00:25:41,490

This institute at Fontannaya Street was

where Grigori Perelman worked for 15 years.

222

00:25:41,590 --> 00:25:48,976

It was here that he interacted with the best geometers

in the country: Aleksandrov, Zalgaller, Burag.

223

00:25:49,076 --> 00:25:57,377

Here he solved problems; argued with his superiors;

switched laboratories; and reluctantly wrote hateful reports.

224

00:25:57,686 --> 00:26:01,101

Like this one.

225

00:26:01,103 --> 00:26:06,763

Here is his report. No publications.

226

00:26:07,719 --> 00:26:14,347

In December 2005, Perelman suddenly resigns.

227

00:26:18,758 --> 00:26:23,398

Right here, he hands me his resignation paper.

228

00:26:23,498 --> 00:26:34,888

I say, “Grisha, have you thought about this? Let's leave

this paper here, so that you can take it back later.”

229

00:26:34,988 --> 00:26:40,367

“No, I have thought hard about this,” said Grisha.

230

00:26:40,467 --> 00:26:44,685

Page 19: Perelman SRT

Then I asked, “Does your mother know?”

231

00:26:44,785 --> 00:26:52,487

“No, my mother doesn't know. Why does she need to know?

My sister knows.”

232

00:26:52,502 --> 00:26:58,632

As I understand it, he is leaving not just the institute, but also mathematics.

233

00:26:59,228 --> 00:27:05,474

It is difficult to understand, but Perelman insists on it:

for him, mathematics is over.

234

00:27:05,574 --> 00:27:12,341

He quickly stops talking about mathematics.

His circle of friends rapidly shrinks to nothing.

235

00:27:12,441 --> 00:27:19,507

But what is this? Is it simply a whim of a genius, or

is it rather the desperation of a tired man?

236

00:27:19,742 --> 00:27:27,440

If it is true, and Grisha never lies, then he

has left mathematics and will never come back.

237

00:27:28,985 --> 00:27:36,405

But is his brain still capable of doing mathematics?

Maybe it has dried out, like a sponge in the Sahara Desert.

238

00:27:36,581 --> 00:27:49,777

An achievement like that might not happen again.

There are examples of mathematicians who have not contributed

anything after achieving great things.

239

00:27:49,877 --> 00:27:51,942

Because they burned out.

240

00:27:53,374 --> 00:28:02,094

Meanwhile, 2006, the year of his 40th birthday, has come.

And life gives him both a huge present, and a huge nightmare

241

00:28:02,194 --> 00:28:04,123

– worldwide recognition.

242

00:28:04,223 --> 00:28:11,399

Science Magazine chooses the proof of the Poincare

conjecture as its Breakthrough of the Year.

Page 20: Perelman SRT

243

00:28:11,499 --> 00:28:17,519

Perelman is ranked 9th among the top 100 geniuses alive

by the Daily Telegraph.

244

00:28:17,762 --> 00:28:21,814

But the sensation of the year is an article in the New Yorker.

245

00:28:21,914 --> 00:28:29,820

Its authors, two journalists by the name of Sylvia Nasar

and David Gruber, expose a scandal in the mathematical community,

246

00:28:29,920 --> 00:28:37,230

some mathematicians want to strip Perelman of his prize.

The article reveals names and facts. It causes lawsuits.

247

00:28:37,616 --> 00:28:50,799

Sylvia Nasar is a serious opponent. She is the author of

“A Beautiful Mind”, a biography about

the famous mathematician John Nash.

248

00:29:03,499 --> 00:29:10,277

When Hollywood adapted the book into a movie,

Nash became a celebrity, and not just in Princeton.

249

00:29:10,788 --> 00:29:18,244

The hero of the article is Perelman. The villains are Chinese

mathematician Shing-Tung Yau and his students.

250

00:29:18,344 --> 00:29:24,877

The authors investigate and reveal that professor Yau also

worked on the Poincare conjecture,

251

00:29:24,977 --> 00:29:35,418

and is now trying to convince the mathematical community

that Perelman discovered nothing new, but merely presented

a different angle on the subject.

252

00:29:35,944 --> 00:29:48,753

According to Yau, the breakdown of the contributions toward

the discovery was as follows: 50% Hamilton, 25% Perelman,

and 30% the Chinese mathematicians.

253

00:29:48,853 --> 00:29:57,890

This adds up to 105%. Interesting arithmetic.

But Yau gives himself the main credit for the final solution.

254

00:29:59,559 --> 00:30:03,079

Perelman is offended. The world of mathematics is rotten.

Page 21: Perelman SRT

255

00:30:03,179 --> 00:30:07,021

Ethics has deserted it.

You can buy, sell, and steal everything.

256

00:30:07,366 --> 00:30:15,151

He said that the world of mathematics is becoming corrupt,

much like the rest of society.

257

00:30:15,251 --> 00:30:25,005

Perelman believed in some sense that mathematicians were

better and more righteous than the rest of the world.

258

00:30:25,888 --> 00:30:35,581

At the same time the International Mathematical Union announces

that it has awarded Perelman a Fields Medal.

259

00:30:35,681 --> 00:30:38,762

But he doesn't need this gold medal.

260

00:30:40,636 --> 00:30:51,947

Grisha nursed a grudge not only against the international,

but also against the Russian mathematical community

261

00:30:52,047 --> 00:30:59,520

because none of those people tried to restore the truth.

And he was right.

262

00:31:03,166 --> 00:31:09,599

In August 2006 at the award ceremony in Madrid

there are 3000 mathematicians present.

263

00:31:09,699 --> 00:31:15,903

They still hope to see Perelman.

The King of Spain is going to hand out the medals.

264

00:31:31,880 --> 00:31:36,804

But there is confusion – while the king came, Perelman didn't.

265

00:31:38,891 --> 00:31:47,306

Grisha doesn't try to change people. He just stops

interacting with those groups of people he doesn't like.

266

00:31:47,457 --> 00:31:58,199

Perelman scrupulously obeys ethical rules. His teachers

insisted that mathematics is not only the Queen of the Sciences,

but also the most moral science.

Page 22: Perelman SRT

267

00:31:58,299 --> 00:32:06,893

His teacher Aleksandrov used to say, at the end of his life,

“I'm not interested in geometry, I'm interested in morality.”

268

00:32:08,085 --> 00:32:16,981

Mathematicians have a very clear criterion

of what is right and wrong.

269

00:32:17,081 --> 00:32:23,914

It is often subjective but it still is very important.

270

00:32:24,014 --> 00:32:33,040

People can't falsify the truth.

If they do, they stop being professionals.

271

00:32:35,627 --> 00:32:43,714

Perelman's grievances accumulate within him.

He becomes more reclusive.

272

00:32:44,565 --> 00:32:49,978

Kleiner and Lott sent him one of the first versions

of their manuscript with a note:

273

00:32:50,078 --> 00:32:57,252

“Would you like to take a look at it? Maybe we've missed

something. Maybe the explanation is too complicated.”

274

00:32:57,352 --> 00:33:00,939

He replied, “No. I don't want to read your manuscript.”

275

00:33:01,039 --> 00:33:07,041

We sent him our book. Maybe we didn't have the right address,

but the package returned unopened.

276

00:33:07,673 --> 00:33:14,681

He is very persistent. And it is a remarkable quality.

Without it he could not have solved the problem.

277

00:33:14,781 --> 00:33:19,967

You have to be very persistent to concentrate

on one thing for seven years.

278

00:33:20,067 --> 00:33:27,917

But when he was finished, he no longer had anything to apply

his persistence to. And it simply became stubbornness.

279

00:33:29,258 --> 00:33:39,093

Page 23: Perelman SRT

In 2006, after four years of review, the experts present

their final conclusion – the proof is correct.

280

00:33:39,193 --> 00:33:43,629

Its author is Grigori Perelman and nobody else.

281

00:33:46,590 --> 00:33:53,685

This means that Perelman deserves a Millennium Prize.

282

00:34:01,988 --> 00:34:11,834

After Alfred Nobel excluded mathematics as an award category

out of spite, mathematicians agreed that counting dollar bills

was not for them.

283

00:34:11,934 --> 00:34:20,648

Thus the Fields Medal is as prestigious as the Nobel Prize.

But its cash reward is not large – only 15000 Canadian dollars.

284

00:34:24,694 --> 00:34:34,866

(Stanislav Smirnov) The benefit of these prizes and medals

is that it increases the people's interest in sciences.

285

00:34:35,391 --> 00:34:43,681

Over the years, awards become more generous. Several years ago,

Norway began awarding outstanding mathematicians the Abel Prize.

286

00:34:43,781 --> 00:34:49,465

It is also almost a million dollars.

The brilliant Mikhail Gromov is one of its winner.

287

00:34:50,546 --> 00:34:53,709

Mathematicians don't care about money and prizes.

288

00:34:53,809 --> 00:34:58,386

It is, of course, nice to receive money,

I don't say that it is not nice.

289

00:34:58,486 --> 00:35:00,438

But it doesn't change anything.

290

00:35:00,538 --> 00:35:08,347

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.

291

00:35:14,019 --> 00:35:22,539

Here in the Clay Institute at Cambridge,

this elegant piece of glass is still kept.

Page 24: Perelman SRT

292

00:35:23,544 --> 00:35:27,756

It is the Millennium Prize which has made so much noise.

293

00:35:28,328 --> 00:35:31,664

This formula is the Poincare conjecture.

294

00:35:31,764 --> 00:35:39,720

Mathematicians, like poets, try to express complex

situations with a few carefully chosen words.

295

00:35:40,374 --> 00:35:47,918

The news that Perelman is going to get a million dollars

spreads quickly. It causes a mass hysteria.

296

00:35:48,018 --> 00:35:50,075

He is not prepared for this.

297

00:35:50,175 --> 00:35:57,719

They lie in wait for him around his building.

Call his home. They compose songs, poems, jokes about him.

298

00:35:57,819 --> 00:36:02,163

Quickly publish his biographies and write fake interviews.

299

00:36:02,608 --> 00:36:06,443

What's the difference, they need a sensation.

300

00:36:06,543 --> 00:36:16,590

But then behind all these rumours and noise nobody pays

attention to his rare answers to intrusive journalists:

301

00:36:16,952 --> 00:36:21,129

“I have nothing to tell you.”

302

00:36:21,769 --> 00:36:26,282

And he is right. What they are discussing is pointless.

303

00:36:26,382 --> 00:36:35,919

The Clay Institute has not announced its decision about

awarding the prize. Instead it delays for another 4 years.

304

00:36:36,019 --> 00:36:48,281

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:

305

Page 25: Perelman SRT

00:36:50,775 --> 00:37:01,110

William Thurston, the author of the geometrization conjecture,

which has the Poincare conjecture as a special case;

306

00:37:01,210 --> 00:37:08,407

Stephen Smale, who proved the Poincare conjecture

for the five-dimensional space;

307

00:37:08,507 --> 00:37:13,305

Bruce Kleiner, John Morgan and his co-author Gang Tian;

308

00:37:13,405 --> 00:37:18,389

and Misha Gromov, one of the best geometers of our time.

309

00:37:20,591 --> 00:37:25,400

The decision has been made. But it doesn't make Perelman happy.

310

00:37:25,500 --> 00:37:37,202

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.

311

00:37:37,302 --> 00:37:40,988

It is more than he needed to prove the theorem.

312

00:37:41,088 --> 00:37:47,261

They are waiting for his answer again.

But now he is not ready with the answer.

313

00:37:47,412 --> 00:37:52,270

(Perelman's voice) I have not decided yet.

The Clay Institute will know it first.

314

00:37:52,655 --> 00:38:03,061

It is interesting that Grigori was really thinking about

accepting the prize. He really thought about it this year.

315

00:38:03,161 --> 00:38:12,831

If before it was clear that he would refuse the Fields Medal,

this time there was at least some hesitation.

316

00:38:12,931 --> 00:38:18,918

And his mother confirmed it on the phone,

that Grisha was thinking.

317

00:38:20,713 --> 00:38:29,825

What was he thinking about for almost 100 days – nobody knows.

Perhaps the main cause of his doubts is Hamilton.

Page 26: Perelman SRT

318

00:38:30,952 --> 00:38:37,682

When we were discussing it in our community,

we also decided that Perelman and Hamilton,

319

00:38:37,782 --> 00:38:39,895

they both deserve the award.

320

00:38:40,077 --> 00:38:48,404

Thus, after 15 years, Perelman wants to repay the debt

to Hamilton for that brief conversation in America

321

00:38:48,504 --> 00:38:52,385

about the Ricci flow and the Poincare conjecture.

322

00:38:53,216 --> 00:38:59,262

Perelman always said that the contribution of Hamilton

is none less significant than his.

323

00:38:59,362 --> 00:39:04,378

I think that without Hamilton it would

have been difficult to do anything.

324

00:39:05,123 --> 00:39:12,118

Hamilton is surprised, he doesn't remember that conversation.

Besides, it's impossible to split the prize.

325

00:39:12,218 --> 00:39:17,396

It is strange that Perelman himself rejects

an ethical rule of mathematics.

326

00:39:19,235 --> 00:39:26,894

In all mathematical results of this level, you always

rely on the previous results.

327

00:39:26,994 --> 00:39:35,221

But according to an unspoken rule the prize goes

to the one who crosses the finish line.

328

00:39:35,794 --> 00:39:40,875

Besides, the decision of the committee can't be changed.

329

00:39:40,975 --> 00:39:53,246

On July 1, 2010, Perelman breaks his silence and utters the

reason of his refusal – disagreement with

the mathematical community.

330

Page 27: Perelman SRT

00:39:53,346 --> 00:39:58,332

“I don't like their decisions, I find them unjust.”

331

00:40:01,688 --> 00:40:07,157

In June 2010 the first Millennium Prize ceremony is held in Paris.

332

00:40:07,257 --> 00:40:17,523

Standing on the stage with the prize in his hands Landon Clay

merely states that there is one problem fewer in mathematics.

333

00:40:20,709 --> 00:40:26,114

Everyone in this room knows – Perelman will not come

and will not accept the money.

334

00:40:27,911 --> 00:40:32,096

Perelman is a national hero. A national hero.

335

00:40:32,196 --> 00:40:35,701

People talk about it, and here is one.

336

00:40:36,173 --> 00:40:41,132

They tried to buy him and failed. Without a chance.

337

00:40:45,004 --> 00:40:52,560

This story began 20 years ago. Perelman is in his 40's now.

He's got a different life.

338

00:40:52,660 --> 00:41:03,016

Nobody knows what he does and where he gets money to live.

But everyone knows – it is impossible to change him.

339

00:41:08,985 --> 00:41:14,779

First of all, he impoverished his own mother.

She didn't deserve that.

340

00:41:14,879 --> 00:41:24,448

She is an elderly woman who raised two amazing children during

what were not the easiest years of our country.

341

00:41:24,548 --> 00:41:33,502

The life is very difficult for Perelman now.

And he has been living in this condition for several years.

342

00:41:33,602 --> 00:41:38,431

I think he is living on the edge of a nervous breakdown.

343

00:41:39,035 --> 00:41:46,120

Page 28: Perelman SRT

He is a great mathematician. He doesn't teach anybody,

doesn't interact. He is wasting his talent.

344

00:41:46,220 --> 00:41:52,227

A lot of energy was used on him. Many people taught him,

he interacted with them.

345

00:41:52,327 --> 00:41:56,718

And now he's gone and not giving it back.

It is not ethical.

346

00:41:58,509 --> 00:42:06,174

He has chosen freedom for himself and destroyed his career,

his friendships, and the lives of his family.

347

00:42:06,274 --> 00:42:08,304

What has he left? Only music.

348

00:42:09,187 --> 00:42:17,425

Our recent conversations were only about the Mariinsky Theatre,

classical music and the other things that interest him.

349

00:42:18,853 --> 00:42:27,035

Perelman's million is gone. But he doesn't care whether

it was a million dollars or a fistful of coins.

350

00:42:27,135 --> 00:42:34,160

He lives in the world where the mysteries

of the universe are unraveled not for money.

351

00:42:34,260 --> 00:42:38,392

To take this money meant to betray your principles.

352

00:42:38,492 --> 00:42:49,652

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.

353

00:42:54,573 --> 00:42:59,149

Now people talk about mathematician

Grigori Perelman in the past tense.

354

00:42:59,602 --> 00:43:07,698

When he was in geometry, he was

the best geometer in the world, when he functioned.

355

00:43:09,043 --> 00:43:12,284

What will his name say to future generations?

Page 29: Perelman SRT

356

00:43:12,717 --> 00:43:22,087

Now he is just a great mathematician of the 20th century.

So he has moved to another category.

357

00:43:24,597 --> 00:43:30,131

[Chief editor: Lloyd Unverferth. Editors: Amor Fati, K. Z. Khor,

Suren Ganesh, Andrew O'Desky. Translation: Roman Kunin.]