Perelman Documentary SRT

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

14
00:01:50,147 --> 00:01:57,209
Maybe with all this excitement over the prize we
have missed the most important question at hand.

15
00:01:57,309 --> 00:02:02,682
Who is this man and what happened with him
in mathematics and in his life?

16
00:02:04,500 --> 00:02:09,000
A man following a different path. A lesson from Perelman.

17
00:02:11,902 --> 00:02:15,187
The world consists of consumers, it's normal.

18
00:02:15,287 --> 00:02:22,719
For millions the interest in mathematics ended with school.
Numbers were invented to count money.

19
00:02:22,819 --> 00:02:26,888
What will we get from great mathematical discoveries?

20
00:02:28,403 --> 00:02:34,304
(Fedor Bogomolov) You know what they used
to say. Number theory, what is it?

21
00:02:34,404 --> 00:02:43,297
It turned out that everything we use now – cell phones,
computers and so on – they all use number theory.

22
00:02:43,397 --> 00:02:49,881
It is all based on some discoveries from the 19th century
and some more modern.

23
00:02:50,119 --> 00:02:59,375
(Sergei Kislyakov) Do you know that when you put a credit card
into an ATM you use very serious mathematical theorems?

24
00:02:59,475 --> 00:03:05,674
The data is encrypted. And these theorems
were not discovered for this purpose.

25
00:03:05,920 --> 00:03:10,244
But suddenly the serene camp of consumers is confused.

26
00:03:10,344 --> 00:03:15,974
The situation with Perelman ignites
a boom of interest in mathematics.

27
00:03:16,074 --> 00:03:26,357
People want to know what they will get from the solved problem
and why the Poincare conjecture was assessed with so much money.

28
00:03:27,522 --> 00:03:32,079
Henri Poincare was the President of the French Academy of Sciences.

29
00:03:32,179 --> 00:03:39,153
He was noble, correct in disputes, indifferent to fame,
and strictly honored ethical behavior in science.

30
00:03:39,253 --> 00:03:44,985
He used to say that the geometry of the new century
needs intuition and inspiration.

31
00:03:45,187 --> 00:03:54,318
Poincare first wrote down his conjecture in 1904. For one
hundred years it was a puzzle left to his colleagues as a legacy.

32
00:03:55,850 --> 00:04:03,538
In response to the recent interest due to Perelman, people have
tried explaining it in many different ways to the common man.

33
00:04:03,638 --> 00:04:08,013
But it is not easy to explain
the Poincare's conjecture in simple terms.

34
00:04:08,113 --> 00:04:12,302
Such explanations have used cups, doughnuts,
soup bubbles and oranges.

35
00:04:12,671 --> 00:04:20,014
(Oleg Viro) During this fuss there was so much nonsense about it.

36
00:04:20,729 --> 00:04:27,232
(Nikolai Mnev) All those attempts to explain the Poincare
conjecture – complete nonsense. Not a word of truth.

37
00:04:27,775 --> 00:04:35,809
(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.

38
00:04:35,909 --> 00:04:38,294
He begins to describe these properties.

39
00:04:38,394 --> 00:04:43,352
But it is not easy to explain mathematics
because it is like a foreign language.

40
00:04:43,452 --> 00:04:50,923
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.

41
00:04:51,324 --> 00:04:57,668
So we can amuse ourselves by transforming cups into doughnuts
and by shrinking the Earth into a point,

42
00:04:57,768 --> 00:05:02,794
but the Poincare conjecture and the mysteries of space
won't become clearer to us.

43
00:05:05,281 --> 00:05:07,680
Mathematicians live in a different cosmos.

44
00:05:07,780 --> 00:05:15,213
They know that whoever solves the Poincare conjecture will
come closer to the most important problem
of mathematics and physics:

45
00:05:15,313 --> 00:05:17,246
what is the shape of the universe?

46
00:05:17,247 --> 00:05:21,269
There is no other way to describe the world.
It is either a natural language or mathematics.

47
00:05:21,369 --> 00:05:24,319
Without Grisha it could have remained unsolved
for another century.

48
00:05:24,949 --> 00:05:32,154
However, the situation is that not even all mathematicians
can understand his thoughts.

49
00:05:33,581 --> 00:05:36,522
Russia had an amazing mathematical school that created Perelman.

50
00:05:36,622 --> 00:05:39,330
If we hadn't had this school we would not have had Perelman.

51
00:05:39,430 --> 00:05:42,980
It was generations of mathematicians
that interacted with him and taught him.

52
00:05:44,627 --> 00:05:50,436
Grisha Perelman was born in 1966 into a country with a great
mathematical school,

53
00:05:50,536 --> 00:05:54,965
the country of Lobachevsky, Kovalevsky,
Kolmogorov,and Chebyshev.

54
00:05:55,065 --> 00:06:04,579
His parents considered it a matter of honor to instill a love
of mathematics into their children Grisha
and his younger sister, Lena.

55
00:06:05,118 --> 00:06:12,931
(Sergei Rukshin) The first time I heard about Grisha was
from professor Nathanson.

56
00:06:13,031 --> 00:06:23,417
He said that his former student had a kid who was interested
in mathematics. And why wouldn't I look at him.

57
00:06:25,113 --> 00:06:30,774
The mother was convinced that mathematics
was perfect for her son.

58
00:06:30,874 --> 00:06:37,494
The boy was unusual in character – he was
persistent and impeccably honest.

59
00:06:39,778 --> 00:06:47,255
We are in the subway and Grisha is sweating profusely.
He is wearing a fur hat with tied flaps.

60
00:06:47,355 --> 00:06:50,249
“Grisha, it is hot, untie the hat.”

61
00:06:50,349 --> 00:06:55,495
“No,” said Grisha, “I promised my mom I wouldn't, so I won't.”

62
00:06:55,595 --> 00:06:58,652
Grisha certainly was impeccably honest.

63
00:06:59,039 --> 00:07:05,377
Mathematics gave him everything he wanted: solitude,
complexity, hard–and–fast rules.

64
00:07:05,477 --> 00:07:09,727
Not being able to solve a problem was devastating for him.

65
00:07:09,827 --> 00:07:13,632
Only victories were allowed. It was an axiom for him.

66
00:07:14,740 --> 00:07:25,461
But this axiom will shatter when life puts into one equation
a great problem, ambitions and a million dollars.

67
00:07:25,561 --> 00:07:29,532
And this story won't be about mathematics.

68
00:07:29,963 --> 00:07:34,340
It began when he boarded the plane flying overseas.

69
00:07:34,440 --> 00:07:45,034
In September 1992 Grigori Perelman comes to New York for his
internship in the Courant Institute of Mathematical Sciences.

70
00:07:45,134 --> 00:07:47,498
Then he will go to Berkeley.

71
00:07:47,598 --> 00:07:57,229
He had a great start to science: elite school, a diploma
with distinction from the St.Petersburg State University,

72
00:07:57,329 --> 00:08:03,460
graduate school and a job in the state's best mathematical organization.

73
00:08:03,741 --> 00:08:08,867
But in the early 90s the Soviet Union collapses.

74
00:08:08,967 --> 00:08:16,165
Russia is facing a period of political change and economic turmoil.

75
00:08:16,265 --> 00:08:21,611
Science was the last thing on the people’s mind.

76
00:08:23,728 --> 00:08:29,150
(Ludvig Faddeev) In the late 80s, we probably had the best
institute in the world.

77
00:08:29,250 --> 00:08:34,185
Amongst the 110 members,
70 had Ph.D degrees in some field of mathematics.

78
00:08:34,285 --> 00:08:39,290
If you had a question you could
always find somebody who could answer it.

79
00:08:39,390 --> 00:08:43,701
Of the 70 doctorates, 40 of them left.
Can you imagine such loss?

80
00:08:45,225 --> 00:08:49,018
The lack of intellectual work is dangerous
for a young mathematician.

81
00:08:49,118 --> 00:08:55,591
So Mikhail Gromov tries to help and invites Grisha to the US.
Perelman's works are well known there. Such is his talent.

82
00:08:56,250 --> 00:08:59,143
They admired his ability to solve problems that nobody else could.

83
00:08:59,243 --> 00:09:03,473
While he worked here, he solved three or four problems
that had remained unsolved for 20-30 years.

84
00:09:03,702 --> 00:09:12,907
Grigori is 26 years old. And he doesn't know that this escape
from the problems will change his life dramatically.

85
00:09:13,007 --> 00:09:20,886
But everything is fine now. A modest apartment, austerity everywhere,
Manhattan doesn't attract him.

86
00:09:21,060 --> 00:09:28,927
I couldn't find out if he visited the art museums.
It is, supposedly, not expensive in America.

87
00:09:29,027 --> 00:09:36,458
Or if America left any impression on him.
He went there to do science and was doing it.

88
00:09:36,749 --> 00:09:43,172
(Bruce Kleiner) He looked thoughtful, rational,
and never depended on other people's opinion.

89
00:09:43,849 --> 00:09:52,849
Perelman doesn't get on well with people, but the young
professor Gang Tian from China is an exception.

90
00:09:52,949 --> 00:10:02,849
Every week they rent a car and drive to Princeton
or Stony Brook to attend the lectures of the best professors.

91
00:10:02,949 --> 00:10:09,249
At one of these lectures he meets
the famous geometer Richard Hamilton.

92
00:10:09,349 --> 00:10:21,052
Although, their encounter was ordinary, just a brief
conversation after the lecture about the Ricci flow
and the continuity of space.

93
00:10:21,297 --> 00:10:31,030
Hamilton behaved sincerely, interested in the truth of
mathematics. He told Grisha everything he knew on this subject.

94
00:10:31,356 --> 00:10:38,976
He also told the most important:
he was close to solving the Poincare conjecture.

95
00:10:39,076 --> 00:10:46,020
Perelman, of course, knew about the conjecture.
But was he interested in it?

96
00:10:46,120 --> 00:10:50,558
Maybe this encounter with Hamilton was crucial.

97
00:10:51,920 --> 00:11:04,753
Three years have passed. His internship in America is going well
and several prestigious universities offer him a position.

98
00:11:04,853 --> 00:11:11,748
He thinks about staying, learns English
and gets a driver's license.

99
00:11:12,478 --> 00:11:22,326
But on one day Perelman reads a new article by Hamilton
and realizes that Hamilton is unable to proceed
in solving the problem.

100
00:11:22,426 --> 00:11:27,584
Grisha writes to him saying: “I think I know how to go further.”

101
00:11:27,684 --> 00:11:34,171
No reply from Hamilton – it is a signal
that Grisha can work on the problem alone.

102
00:11:34,271 --> 00:11:35,913
He buys a ticket home.

103
00:11:36,391 --> 00:11:42,967
He had a clear idea – he needed seven years of
peace and quiet in order to work.

104
00:11:43,067 --> 00:11:51,673
In America he could not have it, he must have a job there.
Besides he had some savings that he could live on.

105
00:11:51,773 --> 00:11:53,803
So he went back to Russia.

106
00:11:55,569 --> 00:12:02,848
He returns to St. Petersburg. The father has left
the family and now lives in Israel.

107
00:12:02,948 --> 00:12:09,606
His sister studies in the same university
but soon will also move to Israel.

108
00:12:09,706 --> 00:12:12,102
He is alone with his mother.

109
00:12:12,202 --> 00:12:17,353
They live in different apartments in the same neighborhood.

110
00:12:17,928 --> 00:12:24,094
But now this loneliness is his salvation.
His main objective is the problem he is facing.

111
00:12:24,194 --> 00:12:32,557
He has never dealt with a more challenging one. He is obsessed
with the idea to overcome something that nobody else can.

112
00:12:32,657 --> 00:12:35,138
He knows that he is capable of this.

113
00:12:35,485 --> 00:12:43,140
Grisha is very strong in mathematics.
Stronger than anybody else. He is super strong.

114
00:12:46,862 --> 00:12:52,792
Mathematics is not well suited for child prodigies.
The ability to solve problems increases with age.

115
00:12:52,892 --> 00:12:58,942
Grisha was 12 years old when he came here – the mathematics
club at Leningrad's Young Pioneer Palace.

116
00:12:59,042 --> 00:13:03,417
The competition with the other boys here
became his first major challenge.

117
00:13:03,701 --> 00:13:16,553
Over the span of four years covering the 5th, 6th, 7th and 8th
grades the number one student in the city was another boy,

118
00:13:16,653 --> 00:13:20,465
Grisha's future classmate Alik Levin.

119
00:13:20,565 --> 00:13:26,012
What Grisha did in one hour, Alik did in 15 minutes.

120
00:13:27,770 --> 00:13:33,457
In order to stimulate a teenager's ambition and to reveal
his hidden abilities, a catalyst is required.

121
00:13:33,557 --> 00:13:35,207
And that catalyst was failure.

122
00:13:37,041 --> 00:13:44,817
Grisha's stimulus was failing two or three times
during the 8th grade.

123
00:13:44,917 --> 00:13:51,435
He failed at the city's Olympiad – he only placed second.

124
00:13:51,535 --> 00:13:59,197
He also failed at the All-Union Olympiad,
where he also placed second.

125
00:13:59,297 --> 00:14:10,163
This provoked him, and half a year later he became
the number one in the city and in the country.

126
00:14:10,492 --> 00:14:17,125
Thus, at the age of 15 he had forgotten how to lose.
There would be many victories in the future.

127
00:14:17,225 --> 00:14:21,317
Acceptance to the best Leningrad's university – a victory.

128
00:14:21,417 --> 00:14:26,003
Acquiring the reputation of a strong problem solver – a victory.

129
00:14:26,103 --> 00:14:32,383
Achieving full marks at the International
Mathematical Olympiad in Budapest – a victory.

130
00:14:32,483 --> 00:14:37,143
His teachers didn't know what was impossible for him in mathematics.

131
00:14:37,783 --> 00:14:43,861
These abilities are exactly what he needed to work
on the Poincare conjecture for 8-9 years.

132
00:14:43,961 --> 00:14:48,081
It's not easy to concentrate on a hard problem for a long time.

133
00:14:48,350 --> 00:14:58,744
At the end of July in the year 2000 the Clay Mathematics
Institute announces the Millennium Prize Problems.

134
00:14:58,844 --> 00:15:05,414
There are seven problems that have remained unsolved for many years.

135
00:15:05,514 --> 00:15:13,456
The American philanthropist Landon Clay offers
a million dollars for solving each.

136
00:15:13,556 --> 00:15:18,068
The idea was to reward the best mathematicians.

137
00:15:18,625 --> 00:15:27,276
(Anatoly Vershik) I do not approve of this idea of the
Clay Institute. It reminds me of show business.

138
00:15:27,376 --> 00:15:32,673
Life has shown that something always happens with this prize.

139
00:15:32,908 --> 00:15:43,228
The Poincare conjecture is on the list, but Perelman doesn't care.
For the last 5 years this problem is everything he thinks about.

140
00:15:43,328 --> 00:15:50,154
He rarely goes to work.
His only indulgences are walking and classical music concerts.

141
00:15:50,254 --> 00:15:58,786
And the fact that it is now a prize problem doesn't change
anything. He feels that the solution is feasible.

142
00:15:58,886 --> 00:16:05,633
This is much more rewarding than any prize.
The most important thing is the solution.

143
00:16:06,654 --> 00:16:09,336
I can give you an example of how one gets mathematical ideas.

144
00:16:09,436 --> 00:16:12,922
Sometimes, when you're discussing something,
you will suddenly recall an anecdote.

145
00:16:13,022 --> 00:16:16,642
The fact that you can recall it at the right moment
has nothing to do with memory.

146
00:16:16,742 --> 00:16:18,040
It is the same in mathematics.

147
00:16:18,204 --> 00:16:25,026
(Yuri Tschinkel) It is an incredible emotional stress.
Poincare wrote about it.

148
00:16:25,126 --> 00:16:36,043
In his book, “Science and Method”, he writes about boarding
a tram, and how insightful thoughts struck him at that time.

149
00:16:37,599 --> 00:16:43,304
November 11, 2002. Perelman opens the website arXiv.org.

150
00:16:43,404 --> 00:16:53,827
His proof is finished – "The Entropy Formula for
the Ricci Flow and its Geometric Applications."

151
00:16:53,927 --> 00:17:03,033
It's 40 pages in English. He signs his name,
“Grisha Perelman,” and then submits it.

152
00:17:03,133 --> 00:17:06,974
And the mathematical world blows up.

153
00:17:07,844 --> 00:17:20,903
(Gang Tian) I had not heard from him for many years.
Since 1995, when he went back to Russia.

154
00:17:21,003 --> 00:17:28,424
It was a big surprise to receive an email from him.

155
00:17:29,125 --> 00:17:34,935
I already knew Perelman and immediately realized
that this deserved our attention.

156
00:17:35,035 --> 00:17:38,335
I can say that I knew about it on the next day.

157
00:17:38,766 --> 00:17:46,701
In fact it was Richard Hamilton who told me.
We had a Christmas party in December 2002.

158
00:17:46,801 --> 00:18:00,432
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.

159
00:18:00,532 --> 00:18:04,641
And it was clear that the author was serious.

160
00:18:08,937 --> 00:18:15,072
During the same year Perelman submits the other
two parts of his work.

161
00:18:15,172 --> 00:18:21,396
His colleagues are confused. First of all,
the proof was extremely brief.

162
00:18:21,496 --> 00:18:27,809
Secondly, posting a work on the internet
doesn't have any official status.

163
00:18:27,909 --> 00:18:36,003
It is if the author was saying
“Here is my solution. I'm not interested in anything else.”

164
00:18:36,222 --> 00:18:47,758
The fact that he posted the article on the internet might
have meant that the author went crazy.

165
00:18:47,858 --> 00:18:56,724
But you could see that the reasoning in the article
was logical and sound.

166
00:18:56,860 --> 00:18:58,105
This wasn't a crank.

167
00:18:58,205 --> 00:19:05,887
There are many cranks who claim that they have solved
the Poincare conjecture. But in this case it wasn't a crank.

168
00:19:05,952 --> 00:19:15,988
(Jeff Cheeger) From my experience with Grisha I can tell that
he tends to underestimate himself. Not only in mathematics,
but also in life.

169
00:19:16,088 --> 00:19:24,326
Someone else in this situation would have widely announced
this achievement and published everything in detail.

170
00:19:24,426 --> 00:19:26,225
But Grisha was different.

171
00:19:28,426 --> 00:19:36,171
The first reaction is to meet Grisha,
and to ask him a lot of questions.

172
00:19:37,013 --> 00:19:51,091
I wrote and invited him to the States, to give a number of lectures
about his work. He replied immediately. Immediately.

173
00:19:52,379 --> 00:20:01,628
In 2003 Perelman flies again to the US. The best universities
invite him to hold lectures.

174
00:20:01,728 --> 00:20:06,773
The best mathematicians are eager to attend them.

175
00:20:07,344 --> 00:20:12,316
But journalists are not allowed.
Perelman can't stand cameras and recorders.

176
00:20:13,430 --> 00:20:18,458
He was sharp with those who tried to record his lectures.

177
00:20:18,558 --> 00:20:26,459
I remember at one lecture in Stony Brook
one of the students put a recorder on the table.

178
00:20:26,559 --> 00:20:30,689
When Perelman saw it, he asked: “What's that?”

179
00:20:30,789 --> 00:20:38,601
The student explained that he wanted to record the lecture.
Perelman said: “No, no, no!”

180
00:20:39,081 --> 00:20:48,455
Many people gathered here for the lecture. Supposedly, he was
claiming that he had proved the Poincare conjecture.

181
00:20:48,555 --> 00:20:56,494
But he did not even mention it. Because he chose those
topics which he found the most important.

182
00:20:56,594 --> 00:21:01,747
And the conjecture was just a small application of his theory.

183
00:21:03,035 --> 00:21:07,417
It happened just like that. The audience was silent.

184
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.

185
00:21:15,943 --> 00:21:22,429
And the conjecture was just a small case
which he had proved along the way.

186
00:21:22,529 --> 00:21:27,877
It was as if he had shaken Poincare's hand and simply moved on.

187
00:21:28,930 --> 00:21:34,083
When Perelman solved this problem,
he was perhaps the only one who understood it.

188
00:21:34,183 --> 00:21:38,359
Now, after a few years, there are several people who understand it.

189
00:21:39,190 --> 00:21:45,759
Perelman does not like be the center of attention.
Among his colleagues, however, he is comfortable.

190
00:21:45,859 --> 00:21:50,855
Even then, they only talk about mathematics.
Everything else is not for him.

191
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,

192
00:22:00,513 --> 00:22:04,247
and then we would go for a walk. He enjoyed walking.

193
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.

194
00:22:11,146 --> 00:22:16,332
He asked, “Who will be there?”
I said, “My wife, my son and daughter, and myself.”

195
00:22:16,432 --> 00:22:19,580
Then he responded by saying: “No, no. I can't come.”

196
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.”

197
00:22:25,900 --> 00:22:31,416
However, Perelman never spoke with Hamilton before his departure.

198
00:22:31,516 --> 00:22:36,594
Hamilton attended the lectures, but did not approach Grisha.

199
00:22:36,694 --> 00:22:42,298
What was the reason for this? Envy?
Resentment? Disbelief? Who knows.

200
00:22:43,863 --> 00:22:49,269
Again, Perelman is invited to stay in America,
but he returns to St. Petersburg.

201
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.

202
00:22:57,294 --> 00:23:01,705
The discovery requires a serious examination. It can take years.

203
00:23:02,084 --> 00:23:08,502
This problem has a long history of incorrect proofs.
There were dozens of such proofs.

204
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.

205
00:23:14,979 --> 00:23:23,125
Every day, we get submissions from people who claim that they
have solved one of the problems

206
00:23:23,225 --> 00:23:30,574
or all of the problems plus the Fermat problem.
Their proofs always contain mistakes.

207
00:23:30,674 --> 00:23:39,176
But Perelman was known as a great mathematician,
and people wanted to understand what he had done.

208
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?

209
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.

210
00:23:58,851 --> 00:24:03,511
One team consists of Bruce Kleiner and John Lott.

211
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.

212
00:24:12,769 --> 00:24:20,621
These mathematicians deciphered, verified and commented
on Perelman's proof. It was exhausting work.

213
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.

214
00:24:30,741 --> 00:24:36,646
Perelman did not invent the method of solving the problem.

215
00:24:36,746 --> 00:24:41,511
William Thurston began working on this in 1975.

216
00:24:41,611 --> 00:24:49,796
Then Richard Hamilton invented a tool
which could potentially solve the problem.

217
00:24:50,573 --> 00:24:57,890
In his proof, Perelman draws on many different fields
of mathematics: the Ricci-Hamilton flow,

218
00:24:57,990 --> 00:25:02,868
Thurston's geometrization conjecture, the Aleksandrov geometry.

219
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.

220
00:25:13,036 --> 00:25:17,607
He bypassed the point at which Hamilton got stuck.
This alone was amazing enough.

221
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.

222
00:25:35,246 --> 00:25:40,434
This institute at Fontannaya Street was
where Grigori Perelman worked for 15 years.

223
00:25:40,534 --> 00:25:44,140
A small room with a window, a table,
a blackboard and chalk.

224
00:25:44,240 --> 00:25:50,377
It was here that he interacted with the best geometers
in the country: Aleksandrov, Zalgaller, Burag.

225
00:25:50,477 --> 00:25:57,377
Here he solved problems; argued with his superiors;
switched laboratories; and reluctantly wrote hateful reports.

226
00:25:57,686 --> 00:26:01,101
Like this one.

227
00:26:01,103 --> 00:26:06,763
Here is his report. No publications.

228
00:26:07,719 --> 00:26:14,347
In December 2005, Perelman suddenly resigns.

229
00:26:18,758 --> 00:26:23,398
Right here, he hands me his resignation paper.

230
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.”

231
00:26:34,988 --> 00:26:40,367
“No, I have thought hard about this,” said Grisha.

232
00:26:40,467 --> 00:26:44,685
Then I asked, “Does your mother know?”

233
00:26:44,785 --> 00:26:52,487
“No, my mother doesn't know. Why does she need to know?
 My sister knows.”

234
00:26:52,502 --> 00:26:58,632
As I understand it, he is leaving not just the institute, but also mathematics.

235
00:26:59,228 --> 00:27:05,474
It is difficult to understand, but Perelman insists on it:
for him, mathematics is over.

236
00:27:05,574 --> 00:27:12,341
He quickly stops talking about mathematics.
His circle of friends rapidly shrinks to nothing.

237
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?

238
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.

239
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.

240
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.

241
00:27:49,877 --> 00:27:51,942
Because they burned out.

242
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

243
00:28:02,194 --> 00:28:04,123
– worldwide recognition.

244
00:28:04,223 --> 00:28:11,399
Science Magazine chooses the proof of the Poincare
conjecture as its Breakthrough of the Year.

245
00:28:11,499 --> 00:28:17,519
Perelman is ranked 9th among the top 100 geniuses alive
by the Daily Telegraph.

246
00:28:17,762 --> 00:28:21,814
But the sensation of the year is an article in the New Yorker.

247
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,

248
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.

249
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.

250
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.

251
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.

252
00:29:18,344 --> 00:29:24,877
The authors investigate and reveal that professor Yau also
worked on the Poincare conjecture,

253
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.

254
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.

255
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.

256
00:29:59,559 --> 00:30:03,079
Perelman is offended. The world of mathematics is rotten.

257
00:30:03,179 --> 00:30:07,021
Ethics has deserted it.
You can buy, sell, and steal everything.

258
00:30:07,366 --> 00:30:15,151
He said that the world of mathematics is becoming corrupt,
much like the rest of society.

259
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.

260
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.

261
00:30:35,681 --> 00:30:38,762
But he doesn't need this gold medal.

262
00:30:40,636 --> 00:30:51,947
Grisha nursed a grudge not only against the international,
but also against the Russian mathematical community

263
00:30:52,047 --> 00:30:59,520
because none of those people tried to restore the truth.
And he was right.

264
00:31:03,166 --> 00:31:09,599
In August 2006 at the award ceremony in Madrid
there are 3000 mathematicians present.

265
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.

266
00:31:31,880 --> 00:31:36,804
But there is confusion – while the king came, Perelman didn't.

267
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.

268
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.

269
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.”

270
00:32:08,085 --> 00:32:16,981
Mathematicians have a very clear criterion
of what is right and wrong.

271
00:32:17,081 --> 00:32:23,914
It is often subjective but it still is very important.

272
00:32:24,014 --> 00:32:33,040
People can't falsify the truth.
If they do, they stop being professionals.

273
00:32:35,627 --> 00:32:43,714
Perelman's grievances accumulate within him.
He becomes more reclusive.

274
00:32:44,565 --> 00:32:49,978
Kleiner and Lott sent him one of the first versions
of their manuscript with a note:

275
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.”

276
00:32:57,352 --> 00:33:00,939
He replied, “No. I don't want to read your manuscript.”

277
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.

278
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.

279
00:33:14,781 --> 00:33:19,967
You have to be very persistent to concentrate
on one thing for seven years.

280
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.

281
00:33:29,258 --> 00:33:39,093
In 2006, after four years of review, the experts present
their final conclusion – the proof is correct.

282
00:33:39,193 --> 00:33:43,629
Its author is Grigori Perelman and nobody else.

283
00:33:46,590 --> 00:33:53,685
This means that Perelman deserves a Millennium Prize.

284
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.

285
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.

286
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.

287
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.

288
00:34:43,781 --> 00:34:49,465
It is also almost a million dollars.
The brilliant Mikhail Gromov is one of its winner.

289
00:34:50,546 --> 00:34:53,709
Mathematicians don't care about money and prizes.

290
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.

291
00:34:58,486 --> 00:35:00,438
But it doesn't change anything.

292
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.

293
00:35:14,019 --> 00:35:22,539
Here in the Clay Institute at Cambridge,
this elegant piece of glass is still kept.

294
00:35:23,544 --> 00:35:27,756
It is the Millennium Prize which has made so much noise.

295
00:35:28,328 --> 00:35:31,664
This formula is the Poincare conjecture.

296
00:35:31,764 --> 00:35:39,720
Mathematicians, like poets, try to express complex
situations with a few carefully chosen words.

297
00:35:40,374 --> 00:35:47,868
The news that Perelman is going to get a million dollars
spreads quickly. It causes a mass hysteria.

298
00:35:47,968 --> 00:35:50,032
He is not prepared for this.

299
00:35:50,132 --> 00:35:57,702
They lie in wait for him around his building.
Call his home. They compose songs, poems, jokes about him.

300
00:35:57,802 --> 00:36:02,163
Quickly publish his biographies and write fake interviews.

301
00:36:02,608 --> 00:36:06,443
What's the difference, they need a sensation.

302
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:

303
00:36:16,952 --> 00:36:21,129
“I have nothing to tell you.”

304
00:36:21,769 --> 00:36:26,282
And he is right. What they are discussing is pointless.

305
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.

306
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:

307
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;

308
00:37:01,210 --> 00:37:08,407
Stephen Smale, who proved the Poincare conjecture
for the five-dimensional space;

309
00:37:08,507 --> 00:37:13,305
Bruce Kleiner, John Morgan and his co-author Gang Tian;

310
00:37:13,405 --> 00:37:18,389
and Misha Gromov, one of the best geometers of our time.

311
00:37:20,591 --> 00:37:25,400
The decision has been made. But it doesn't make Perelman happy.

312
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.

313
00:37:37,302 --> 00:37:40,988
It is more than he needed to prove the theorem.

314
00:37:41,088 --> 00:37:47,261
They are waiting for his answer again.
But now he is not ready with the answer.

315
00:37:47,412 --> 00:37:52,270
(Perelman's voice) I have not decided yet.
The Clay Institute will know it first.

316
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.

317
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.

318
00:38:12,931 --> 00:38:18,918
And his mother confirmed it on the phone,
that Grisha was thinking.

319
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.

320
00:38:30,952 --> 00:38:37,682
When we were discussing it in our community,
we also decided that Perelman and Hamilton,

321
00:38:37,782 --> 00:38:39,895
they both deserve the award.

322
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

323
00:38:48,504 --> 00:38:52,385
about the Ricci flow and the Poincare conjecture.

324
00:38:53,216 --> 00:38:59,262
Perelman always said that the contribution of Hamilton
is none less significant than his.

325
00:38:59,362 --> 00:39:04,378
I think that without Hamilton it would
have been difficult to do anything.

326
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.

327
00:39:12,218 --> 00:39:17,396
It is strange that Perelman himself rejects
an ethical rule of mathematics.

328
00:39:19,235 --> 00:39:26,894
In all mathematical results of this level, you always
rely on the previous results.

329
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.

330
00:39:35,794 --> 00:39:40,875
Besides, the decision of the committee can't be changed.

331
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.

332
00:39:53,346 --> 00:39:58,332
“I don't like their decisions, I find them unjust.”

333
00:40:01,688 --> 00:40:07,157
In June 2010 the first Millennium Prize ceremony is held in Paris.

334
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.

335
00:40:20,709 --> 00:40:26,114
Everyone in this room knows – Perelman will not come
and will not accept the money.

336
00:40:27,911 --> 00:40:32,096
Perelman is a national hero. A national hero.

337
00:40:32,196 --> 00:40:35,701
People talk about it, and here is one.

338
00:40:36,173 --> 00:40:41,132
They tried to buy him and failed. Without a chance.

339
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.

340
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.

341
00:41:08,985 --> 00:41:14,779
First of all, he impoverished his own mother.
She didn't deserve that.

342
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.

343
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.

344
00:41:33,602 --> 00:41:38,431
I think he is living on the edge of a nervous breakdown.

345
00:41:39,035 --> 00:41:46,120
He is a great mathematician. He doesn't teach anybody,
doesn't interact. He is wasting his talent.

346
00:41:46,220 --> 00:41:52,227
A lot of energy was used on him. Many people taught him,
he interacted with them.

347
00:41:52,327 --> 00:41:56,718
And now he's gone and not giving it back.
It is not ethical.

348
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.

349
00:42:06,274 --> 00:42:08,304
What has he left? Only music.

350
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.

351
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.

352
00:42:27,135 --> 00:42:34,160
He lives in the world where the mysteries
of the universe are unraveled not for money.

353
00:42:34,260 --> 00:42:38,392
To take this money meant to betray your principles.

354
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.

355
00:42:54,573 --> 00:42:59,149
Now people talk about mathematician
Grigori Perelman in the past tense.

356
00:42:59,602 --> 00:43:07,698
When he was in geometry, he was
the best geometer in the world, when he functioned.

357
00:43:09,043 --> 00:43:12,284
What will his name say to future generations?

358
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.

359
00:43:24,597 --> 00:43:29,131
[Subtitles credits.
 Chief editor: Lloyd Unverferth. Editors: Amor Fati, K. Z. Khor,
 Suren Ganesh, Andrew O'Desky. Translation: Roman Kunin.]