Mathematician Yakov Perelman: contribution to science. Famous Russian mathematician Grigory Perelman. Biography of Perelman and his mathematical discoveries

Grigory Yakovlevich Perelman(b. June 13, 1966, Leningrad, USSR) - an outstanding Russian mathematician who was the first to prove the Poincaré conjecture.

Grigory Perelman was born on June 13, 1966 in Leningrad into a Jewish family. His father Yakov was an electrical engineer who immigrated to Israel in 1993. Mother, Lyubov Leibovna, remained in St. Petersburg and worked as a mathematics teacher at a vocational school. It was his mother, who played the violin, who instilled in the future mathematician a love of classical music.

Until the 9th grade, Perelman studied at high school on the outskirts of the city, however, in the 5th grade he began studying at the mathematics center at the Palace of Pioneers under the guidance of RGPU associate professor Sergei Rukshin, whose students won many awards at mathematical Olympiads. In 1982, as part of a team of Soviet schoolchildren, he won a gold medal at the International Mathematical Olympiad in Budapest, receiving full marks for flawlessly solving all problems. Perelman graduated from the 239th Physics and Mathematics School in Leningrad. He played table tennis well and attended music school. I didn’t receive a gold medal only because of physical education, not passing the GTO standards.

He was enrolled in the Faculty of Mathematics and Mechanics of Leningrad State University without exams. He won faculty, city and all-Union student mathematical Olympiads. All the years I studied only with “excellent” marks. For academic success he received a Lenin scholarship. After graduating with honors from the university, he entered graduate school (headed by Academician A.D. Aleksandrov) at the Leningrad branch of the Mathematical Institute. V. A. Steklova (LOMI - until 1992; then - POMI). Having defended his Ph.D. thesis in 1990, he remained to work at the institute as a senior research fellow.

In the early 1990s, Perelman came to the USA, where he worked as a research assistant at various universities, where his attention was drawn to one of the most difficult, at that time unsolved, problems of modern mathematics - the Poincaré Conjecture. He surprised his colleagues with his ascetic lifestyle; his favorite foods were milk, bread and cheese. In 1996, he returned to St. Petersburg, continuing to work at POMI, where he worked alone on solving the Poincaré Problem.

In 2002-2003, Grigory Perelman published his three famous articles on the Internet, in which he briefly outlined his original method for solving the Poincaré Problem:

The entropy formula for the Ricci flow and its geometric applications
Ricci flow with surgery on three-manifolds
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

The appearance on the Internet of Perelman's first article on the entropy formula for the Ricci flow caused an immediate international sensation in scientific circles. In 2003, Grigory Perelman accepted an invitation to visit a number of American universities, where he gave a series of talks on his work on the proof of the Poincaré Problem. In America, Perelman spent a lot of time explaining his ideas and methods, both in public lectures organized for him and during personal meetings with a number of mathematicians. After his return to Russia, he answered numerous questions from his foreign colleagues by email.

In 2004-2006, three independent groups of mathematicians were engaged in the verification of Perelman’s results: 1) Bruce Kleiner, John Lott, University of Michigan; 2) Zhu Xiping, Sun Yat-sen University, Cao Huaidong, Lehigh University; 3) John Morgan, Columbia University, Gan Tian, Massachusetts Institute of Technology. All three groups concluded that Poincaré's Problem had been successfully solved, but Chinese mathematicians Zhu Xiping and Cao Huaidong, along with their teacher Yau Shintang, attempted plagiarism, claiming that they had found a "complete proof". They later retracted this statement.

In December 2005, Grigory Perelman resigned from his post as a leading researcher at the Laboratory of Mathematical Physics, resigned from POMI and almost completely broke off contacts with colleagues.

To further scientific career showed no interest. Currently lives in Kupchino in the same apartment with his mother, leads a secluded lifestyle, ignores the press.

Scientific contribution

Main article: Poincaré conjecture

In 1994 he proved the hypothesis about the soul (differential geometry).

Grigory Perelman, in addition to his outstanding natural talent, being a representative of the Leningrad geometric school, at the beginning of his work on the Poincaré Problem also had a broader scientific outlook than his foreign colleagues. In addition to other major mathematical innovations that made it possible to overcome all the difficulties faced by mathematicians dealing with this problem, Perelman developed and applied the purely Leningrad theory of Alexandrov spaces to analyze Ricci flows. In 2002, Perelman first published his innovative work devoted to the solution of one of the special cases of William Thurston's geometrization conjecture, from which the validity of the famous Poincaré conjecture, formulated by the French mathematician, physicist and philosopher Henri Poincaré in 1904, follows. The method of studying the Ricci flow described by the scientist was called Hamilton-Perelman theory.

Recognition and ratings

In 1996 he was awarded the European Mathematical Society Prize for Young Mathematicians, but refused to receive it.

In 2006, Grigory Perelman was awarded the international Fields Medal Prize for solving the Poincaré conjecture (the official wording for the award: “For his contribution to geometry and his revolutionary ideas in the study of the geometric and analytical structure of the Ricci flow”), but he refused it too.

In 2006, Science magazine named the proof of Poincaré's theorem the scientific breakthrough of the year. Breakthrough of the Year). This is the first work in mathematics to earn this title.

In 2006, Sylvia Nasar and David Gruber published the article "Manifold Destiny", which talks about Grigory Perelman, his work on solving the Poincaré Problem, ethical principles in science and the mathematical community, and also contains a rare interview with him. The article devotes considerable space to criticism of the Chinese mathematician Yau Shintan, who, together with his students, tried to challenge the completeness of the proof of the Poincaré Hypothesis proposed by Grigory Perelman. From an interview with Grigory Perelman:

In 2006, The New York Times published an article by Dennis Overbye, “Scientist at Work: Shing-Tung Yau. The Emperor of Math." The article is devoted to the biography of Professor Yau Shintan and the scandal associated with accusations against him of attempts to belittle Perelman's contribution to the proof of the Poincaré Hypothesis. The article cites a fact unheard of in mathematical science - Yau Shintan hired a law firm to defend his case and threatened to prosecute his critics.

In 2007, the British newspaper The Daily Telegraph published a list of “One Hundred Living Geniuses”, in which Grigory Perelman ranks 9th. In addition to Perelman, only 2 Russians were included in this list - Garry Kasparov (25th place) and Mikhail Kalashnikov (83rd place).

In March 2010, the Clay Mathematics Institute awarded Grigory Perelman a US$1 million prize for his proof of the Poincaré conjecture, the first ever prize awarded for solving one of the Millennium Problems. In June 2010, Perelman ignored a mathematical conference in Paris, at which the Millennium Prize was supposed to be awarded for the proof of the Poincaré conjecture, and on July 1, 2010, he publicly announced his refusal of the prize, citing the following reasons:

Note that such a public assessment of the merits of Richard Hamilton by the mathematician who proved the Poincaré Hypothesis may be an example of nobility in science, since, according to Perelman himself, Hamilton, who collaborated with Yau Shintan, noticeably slowed down in his research, encountering insurmountable technical difficulties.

In September 2011, the Clay Institute, together with the Henri Poincaré Institute (Paris), created a position for young mathematicians, the money for which will come from the Millennium Prize awarded but not accepted by Grigory Perelman.

In 2011, Richard Hamilton and Demetrios Christodoulou were awarded the so-called. The $1,000,000 Shao Prize in Mathematics, also sometimes called the Nobel Prize of the East. Richard Hamilton was awarded for creating a mathematical theory, which was then developed by Grigory Perelman in his work to prove the Poincaré conjecture. It is known that Hamilton accepted this award.

Interesting Facts

In his work “The entropy formula for Ricci flow and its geometric applications” (eng. The entropy formula for the Ricci flow and its geometric applications) Grigory Perelman, not without humor, modestly points out that his work was partially financed by personal savings saved during his visits to the Courant Institute mathematical sciences, State University of New York (SUNY), State University of New York at Stony Brook, and UC Berkeley, and thanks the organizers of these trips. At the same time, the official mathematical community allocated millions in grants to individual research groups in order to understand and test Perelman’s work.
When a member of the Stanford University hiring committee asked Perelman for C.V. (resume), and letters of recommendation, Perelman objected:

The Manifold Destiny article was noticed by the outstanding mathematician Vladimir Arnold, who proposed reprinting it in the Moscow journal Uspekhi Matematicheskikh Nauk, where he was a member of the editorial board. The magazine's editor-in-chief, Sergei Novikov, refused him. According to Arnold, the refusal was due to the fact that Chief Editor magazine feared retaliation from Yau, since he also worked in the USA.
The biographical book of Masha Gessen tells about the fate of Perelman “Perfect severity. Grigory Perelman: genius and the task of the millennium", based on numerous interviews with his teachers, classmates, co-workers and colleagues. Perelman's teacher Sergei Rukshin was critical of the book.

Grigory Perelman became the main character documentary film"The Spell of the Poincaré Hypothesis" directed by Masahito Kasuga, produced by the Japanese public broadcaster NHK in 2008.
In April 2010, the “Khrushchev Millionaire” episode of the talk show “Let Them Talk” was dedicated to Grigory Perelman. It was attended by Grigory’s friends, his school teachers, as well as journalists who communicated with Perelman.
In the 27th episode of “Big Difference” on Channel One, a parody of Grigory Perelman was presented in the hall. The role of Perelman was simultaneously performed by 9 actors.
It is a common misconception that the father of Grigory Yakovlevich Perelman is Yakov Isidorovich Perelman, a famous popularizer of physics, mathematics and astronomy. However, Ya. I. Perelman died more than 20 years before the birth of Grigory Perelman.
On April 28, 2011, Komsomolskaya Pravda reported that Perelman gave an interview to the executive producer of the Moscow film company President Film, Alexander Zabrovsky, and agreed to shoot a feature film about him. Masha Gessen, however, doubts that these statements are true. Vladimir Gubailovsky also believes that the interview with Perelman is fictitious.

Grigory Perelman has a younger sister, Elena (born 1976), also a mathematician, a graduate of St. Petersburg University (1998), who defended her Doctor of Philosophy (PhD) dissertation in Rehovot in 2003; Since 2007 he has been working as a programmer in Stockholm.

Until the 9th grade, Perelman studied at a high school on the outskirts of Leningrad, and then transferred to the 239th Physics and Mathematics School. He played table tennis well and attended music school. I didn’t receive a gold medal only because of physical education, not passing the GTO standards. From the 5th grade, Grigory studied at the mathematics center at the Palace of Pioneers under the guidance of RGPU associate professor Sergei Rukshin, whose students won many awards at mathematical Olympiads. In 1982, as part of a team of Soviet schoolchildren, he won a gold medal at the International Mathematical Olympiad in Budapest, receiving full marks for flawlessly solving all problems.

He was enrolled in the Faculty of Mathematics and Mechanics of Leningrad State University without exams. He won faculty, city and all-Union student mathematical Olympiads. All the years I studied only with “excellent” marks. For academic success he received a Lenin scholarship. After graduating with honors from the university, he entered graduate school (scientific supervisor - A.D. Aleksandrov) at (LOMI - until 1992; then - POMI). Having defended his Ph.D. thesis on “Saddle surfaces in Euclidean spaces” in 1990, he remained to work at the institute as a senior researcher.

In 2004-2006, three independent groups of mathematicians were involved in checking Perelman’s results:

Bruce Kleiner, John Lott, University of Michigan;
Zhu Xiping, Sun Yat-sen University, Cao Huaidong, Lehigh University;
John Morgan, Columbia University, Gan Tian, .

All three groups concluded that the Poincaré conjecture was completely proven, but Chinese mathematicians, Zhu Xiping and Cao Huaidong, along with their teacher Yau Shintong, attempted plagiarism by claiming that they had found a "complete proof". They later retracted this statement.

In September 2011, it became known that the mathematician refused to accept the offer to become a member of the Russian Academy of Sciences. In the same year, Masha Gessen’s book about the fate of Perelman was published “Perfect severity. Grigory Perelman: genius and the task of the millennium", based on numerous interviews with his teachers, classmates, co-workers and colleagues. Perelman's teacher Sergei Rukshin responded critically to the book.

Leads a secluded life, ignores the press. Lives in St. Petersburg in Kupchino with his mother. The press reported that since 2014 Gregory has been living in Sweden, but later it turned out that he visits there sporadically.

Scientific contribution

Recognition and ratings

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An excerpt characterizing Perelman, Grigory Yakovlevich

One group of Frenchmen stood close by the road, and two soldiers - the face of one of them was covered with sores - was tearing a piece of raw meat with their hands. There was something scary and animalistic in that quick glance that they cast at those passing by, and in that angry expression with which the soldier with the sores, looking at Kutuzov, immediately turned away and continued his work.
Kutuzov looked at these two soldiers carefully for a long time; Wrinkling his face even more, he narrowed his eyes and shook his head thoughtfully. In another place, he noticed a Russian soldier, who, laughing and patting the Frenchman on the shoulder, said something affectionately to him. Kutuzov shook his head again with the same expression.
- What are you saying? What? - he asked the general, who continued to report and drew the commander-in-chief’s attention to the captured French banners that stood in front of the front of the Preobrazhensky regiment.
- Ah, banners! - said Kutuzov, apparently having difficulty tearing himself away from the subject that occupied his thoughts. He looked around absently. Thousands of eyes from all sides, waiting for his word, looked at him.
He stopped in front of the Preobrazhensky Regiment, sighed heavily and closed his eyes. Someone from the retinue waved for the soldiers holding the banners to come up and place their flag poles around the commander-in-chief. Kutuzov was silent for a few seconds and, apparently reluctantly, obeying the necessity of his position, raised his head and began to speak. Crowds of officers surrounded him. He with an attentive look He circled the circle of officers, recognizing some of them.
– Thank you everyone! - he said, turning to the soldiers and again to the officers. In the silence that reigned around him, his slowly spoken words were clearly audible. “I thank everyone for their difficult and faithful service.” The victory is complete, and Russia will not forget you. Glory to you forever! “He paused, looking around.
“Bend him down, bend his head,” he said to the soldier who was holding the French eagle and accidentally lowered it in front of the banner of the Preobrazhensky soldiers. - Lower, lower, that’s it. Hooray! “Guys,” with a quick movement of his chin, turn to the soldiers, he said.
- Hurray rah rah! - thousands of voices roared. While the soldiers were shouting, Kutuzov, bending over the saddle, bowed his head, and his eye lit up with a gentle, as if mocking, shine.
“That’s it, brothers,” he said when the voices fell silent...
And suddenly his voice and expression changed: the commander-in-chief stopped speaking, and a simple man spoke, an old man, it is obvious that he now wanted to tell his comrades the very thing he needed.
There was a movement in the crowd of officers and in the ranks of soldiers to hear more clearly what he would say now.
- Here's what, brothers. I know it’s difficult for you, but what can you do? Be patient; not long left. Let's see the guests out and then rest. The king will not forget you for your service. It’s difficult for you, but you’re still at home; and they - see what they have come to,” he said, pointing to the prisoners. - Worse than the last beggars. While they were strong, we did not feel sorry for ourselves, but now we can feel sorry for them. They are people too. Right, guys?
He looked around him, and in the persistent, respectfully perplexed glances fixed on him, he read sympathy for his words: his face became lighter and lighter from an senile, meek smile, wrinkled like stars in the corners of his lips and eyes. He paused and lowered his head as if in bewilderment.
- And even then, who called them to us? Serves them right, m... and... in g.... - he suddenly said, raising his head. And, swinging his whip, he galloped, for the first time in the entire campaign, away from the joyfully laughing and roaring cheers that upset the ranks of the soldiers.
The words spoken by Kutuzov were hardly understood by the troops. No one would have been able to convey the content of the field marshal’s first solemn and, at the end, innocently old man’s speech; but the heartfelt meaning of this speech was not only understood, but that same, that very feeling of majestic triumph, combined with pity for the enemies and the consciousness of one’s rightness, expressed by this, precisely this old man’s, good-natured curse - this very (feeling lay in the soul of every soldier and was expressed by a joyful cry that did not cease for a long time. When after this one of the generals turned to him with a question about whether the commander-in-chief would order the carriage to arrive, Kutuzov, answering, unexpectedly sobbed, apparently being in great excitement.

November 8th is the last day of the Krasnensky battles; It was already dark when the troops arrived at their overnight camp. The whole day was quiet, frosty, with light, sparse snow falling; By evening it began to become clear. A black purple starry sky could be seen through the snowflakes, and the frost began to intensify.
The musketeer regiment, which left Tarutino in the number of three thousand, now, in the number of nine hundred people, was one of the first to arrive at the appointed place for the night, in a village on the high road. The quartermasters who met the regiment announced that all the huts were occupied by sick and dead Frenchmen, cavalrymen and staff. There was only one hut for the regimental commander.
The regimental commander drove up to his hut. The regiment passed through the village and placed the guns on the goats at the outer huts on the road.
Like a huge, multi-membered animal, the regiment set to work organizing its lair and food. One part of the soldiers scattered, knee-deep in the snow, into the birch forest that was to the right of the village, and immediately the sound of axes, cutlasses, the crackling of breaking branches and cheerful voices were heard in the forest; the other part was busy around the center of the regimental carts and horses, placed in a pile, taking out cauldrons, crackers and giving food to the horses; the third part scattered in the village, arranging headquarters premises, choosing dead bodies Frenchmen lying in the huts, taking away boards, dry firewood and straw from the roofs for fires and fences for protection.
About fifteen soldiers behind the huts, from the edge of the village, with a cheerful cry, were swinging the high fence of the barn, from which the roof had already been removed.
- Well, well, together, lie down! - voices shouted, and in the darkness of the night a huge fence covered with snow swayed with a frosty crack. The lower stakes cracked more and more often, and finally the fence collapsed along with the soldiers pressing on it. There was a loud, crudely joyful cry and laughter.
- Take two at a time! bring the horn here! that's it. Where are you going?
- Well, at once... Stop, guys!.. With a shout!
Everyone fell silent, and a quiet, velvety pleasant voice began to sing a song. At the end of the third stanza, at the same time as the end of the last sound, twenty voices cried out in unison: “Uuuu!” It's coming! Together! Pile on, kids!..” But, despite the united efforts, the fence moved little, and in the established silence one could hear heavy panting.
- Hey you, sixth company! Devils, devils! Help us... we will also come in handy.
Of the sixth company, about twenty people who were going to the village joined those dragging them; and the fence, five fathoms long and a fathom wide, bending, pressing and cutting the shoulders of the puffing soldiers, moved forward along the village street.
- Go, or what... Fall, Eka... What happened? This and that... The funny, ugly curses did not stop.
- What's wrong? – suddenly the commanding voice of a soldier was heard, running towards the carriers.
- Gentlemen are here; in the hut he himself was anal, and you, devils, devils, swearers. I'll! – the sergeant major shouted and hit the first soldier who turned up in the back with a flourish. – Can’t you be quiet?
The soldiers fell silent. The soldier who had been hit by the sergeant-major began, grunting, to wipe his face, which he had torn into blood when he stumbled upon a fence.
- Look, damn, how he fights! “My whole face was bleeding,” he said in a timid whisper when the sergeant-major left.
- Don’t you love Ali? - said a laughing voice; and, moderating the sounds of voices, the soldiers moved on. Having got out of the village, they spoke again just as loudly, peppering the conversation with the same aimless curses.
In the hut, past which the soldiers passed, the highest authorities had gathered, and over tea there was a lively conversation about the past day and the proposed maneuvers of the future. It was supposed to make a flank march to the left, cut off the viceroy and capture him.
When the soldiers brought the fence, kitchen fires were already flaring up from different sides. Firewood crackled, snow melted, and the black shadows of soldiers scurried back and forth throughout the occupied space trampled in the snow.
Axes and cutlasses worked from all sides. Everything was done without any orders. They hauled firewood for the night's reserves, erected huts for the authorities, boiled pots, and stored guns and ammunition.
The fence dragged by the eighth company was placed in a semicircle on the north side, supported by bipods, and a fire was laid out in front of it. We broke the dawn, made calculations, had dinner and settled down for the night by the fires - some mending shoes, some smoking a pipe, some stripped naked, steaming out lice.

It would seem that in those almost unimaginably difficult conditions of existence in which Russian soldiers found themselves at that time - without warm boots, without sheepskin coats, without a roof over their heads, in the snow at 18° below zero, without even the full amount of provisions, it would not always be possible to keeping up with the army - it seemed that the soldiers should have presented the saddest and most depressing sight.
On the contrary, never, in the best material conditions, has the army presented a more cheerful, lively spectacle. This happened because every day everything that began to despondency or weaken was thrown out of the army. Everything that was physically and morally weak had long been left behind: only one color of the army remained - in terms of strength of spirit and body.
The largest number of people gathered at the 8th company, which bordered the fence. Two sergeants sat down next to them, and their fire burned brighter than others. They demanded an offering of firewood for the right to sit under the fence.
- Hey, Makeev, what are you... disappeared or were you eaten by wolves? “Bring some wood,” shouted one red-haired soldier, squinting and blinking from the smoke, but not moving away from the fire. “Go ahead and carry some wood, crow,” this soldier turned to another. Red was not a non-commissioned officer or a corporal, but he was a healthy soldier, and therefore commanded those who were weaker than him. A thin, small soldier with a sharp nose, who was called a crow, obediently stood up and went to carry out the order, but at that time the thin, beautiful figure of a young soldier carrying a load of firewood entered the light of the fire.
- Come here. That's important!
They broke the firewood, pressed it, blew it with their mouths and overcoat skirts, and the flames hissed and crackled. The soldiers moved closer and lit their pipes. The young, handsome soldier who had brought the firewood leaned his hands on his hips and began to quickly and deftly stamp his chilled feet in place.
“Ah, mamma, the cold dew is good, and like a musketeer...” he chanted, as if hiccupping on every syllable of the song.
- Hey, the soles will fly off! – the red-haired man shouted, noticing that the dancer’s sole was dangling. - What poison to dance!
The dancer stopped, tore off the dangling skin and threw it into the fire.
“And that, brother,” he said; and, sitting down, took a piece of French blue cloth from his knapsack and began to wrap it around his leg. “We’ve had a couple of hours,” he added, stretching his legs towards the fire.
- New ones will be released soon. They say, we'll beat you to the last ounce, then everyone will get double goods.
- And you see, Son of a bitch Petrov, after all, fell behind,” said the sergeant major.
“I’ve noticed him for a long time,” said another.
- Yes, little soldier...
“And in the third company, they said, nine people were missing yesterday.”
- Yes, judge how your feet ache, where will you go?
- Eh, this is empty talk! - said the sergeant major.
“Ali, do you want the same thing?” - said the old soldier, reproachfully turning to the one who said that his legs were chilling.
– What do you think? - suddenly rising from behind the fire, a sharp-nosed soldier, who was called a crow, spoke in a squeaky and trembling voice. - He who is smooth will lose weight, but the skinny will die. At least I would. “I have no urine,” he suddenly said decisively, turning to the sergeant major, “they told me to send him to the hospital, the pain has overcome me; otherwise you will still fall behind...
“Well, yes, yes,” the sergeant major said calmly. The soldier fell silent and the conversation continued.
“Today you never know how many of these Frenchmen they took; and, to put it bluntly, none of them are wearing real boots, just a name,” one of the soldiers began a new conversation.
- All the Cossacks struck. They cleaned the hut for the colonel and took them out. It’s a pity to watch, guys,” said the dancer. - They tore them apart: so the living one, believe it, babbles something in his own way.
“They’re pure people, guys,” said the first. - White, just like a birch is white, and there are brave ones, say, noble ones.
- How do you think? He has recruited from all ranks.
“But they don’t know anything our way,” the dancer said with a smile of bewilderment. “I say to him: “Whose crown?”, and he babbles on. Wonderful people!
“It’s strange, my brothers,” continued the one who was amazed at their whiteness, “the men near Mozhaisk said how they began to remove the beaten, where the guards were, so after all, he says, theirs lay dead for almost a month.” Well, he says, it lies there, he says, theirs is how the paper is white, clean, and doesn’t smell of gunpowder.
- Well, from the cold, or what? - asked one.
- You're so smart! By cold! It was hot. If only for the cold, ours wouldn’t have gone rotten either. Otherwise, he says, when you come up to ours, he’s all rotten with worms, he says. So, he says, we’ll tie ourselves with scarves, and, turning our muzzle away, we’ll drag him; no urine. And theirs, he says, is as white as paper; There is no smell of gunpowder.
Everyone was silent.
“It must be from the food,” said the sergeant major, “they ate the master’s food.”
Nobody objected.
“This man said, near Mozhaisk, where there was a guard, they were driven away from ten villages, they carried them twenty days, they didn’t bring them all, they were dead. What are these wolves, he says...
“That guard was real,” said the old soldier. - There was only something to remember; and then everything after that... So, it’s just torment for the people.
- And that, uncle. The day before yesterday we came running, so where they won’t let us get to them. They quickly abandoned the guns. On your knees. Sorry, he says. So, just one example. They said that Platov took Polion himself twice. Doesn't know the words. He’ll take it: he’ll pretend to be a bird in his hands, fly away, and fly away. And there is no provision for killing either.
“It’s okay to lie, Kiselev, I’ll look at you.”
- What a lie, the truth is true.
“If it were my custom, I would have caught him and buried him in the ground.” Yes, with an aspen stake. And what he ruined for the people.
“We’ll do it all, he won’t walk,” said the old soldier, yawning.
The conversation fell silent, the soldiers began to pack up.
- See, the stars, passion, are burning! “Tell me, the women have laid out the canvases,” said the soldier, admiring the Milky Way.
- This, guys, is for a good year.
“We’ll still need some wood.”
“You’ll warm your back, but your belly is frozen.” What a miracle.
- Oh my God!
- Why are you pushing, is the fire about you alone, or what? See... it fell apart.
From behind the established silence, the snoring of some who had fallen asleep was heard; the rest turned and warmed themselves, occasionally talking to each other. A friendly, cheerful laugh was heard from the distant fire, about a hundred paces away.
“Look, they’re roaring in the fifth company,” said one soldier. – And what a passion for the people!
One soldier got up and went to the fifth company.
“It’s laughter,” he said, returning. - Two guards have arrived. One is completely frozen, and the other is so courageous, dammit! Songs are playing.
- Oh oh? go have a look... - Several soldiers headed towards the fifth company.

The fifth company stood near the forest itself. A huge fire burned brightly in the middle of the snow, illuminating the tree branches weighed down with frost.
In the middle of the night, soldiers of the fifth company heard footsteps in the snow and the crunching of branches in the forest.
“Guys, it’s a witch,” said one soldier. Everyone raised their heads, listened, and out of the forest, into the bright light of the fire, two strangely dressed human figures stepped out, holding each other.
These were two Frenchmen hiding in the forest. Hoarsely saying something in a language incomprehensible to the soldiers, they approached the fire. There was one taller, wearing an officer's hat, and seemed completely weakened. Approaching the fire, he wanted to sit down, but fell to the ground. The other, small, stocky soldier with a scarf tied around his cheeks, was stronger. He raised his comrade and, pointing to his mouth, said something. The soldiers surrounded the French, laid out an overcoat for the sick man, and brought porridge and vodka to both of them.
The weakened French officer was Rambal; tied with a scarf was his orderly Morel.
When Morel drank vodka and finished a pot of porridge, he suddenly became painfully cheerful and began to continuously say something to the soldiers who did not understand him. Rambal refused to eat and silently lay on his elbow by the fire, looking at the Russian soldiers with meaningless red eyes. Occasionally he would let out a long groan and then fall silent again. Morel, pointing to his shoulders, convinced the soldiers that it was an officer and that he needed to be warmed up. The Russian officer, who approached the fire, sent to ask the colonel if he would take the French officer to warm him up; and when they returned and said that the colonel had ordered an officer to be brought, Rambal was told to go. He stood up and wanted to walk, but he staggered and would have fallen if the soldier standing next to him had not supported him.
- What? You will not? – one soldier said with a mocking wink, turning to Rambal.
- Eh, fool! Why are you lying awkwardly! It’s a man, really, a man,” reproaches to the joking soldier were heard from different sides. They surrounded Rambal, lifted him into his arms, grabbed him, and carried him to the hut. Rambal hugged the necks of the soldiers and, when they carried him, spoke plaintively:
- Oh, nies braves, oh, mes bons, mes bons amis! Voila des hommes! oh, mes braves, mes bons amis! [Oh well done! O my good, good friends! Here are the people! O my good friends!] - and, like a child, he leaned his head on the shoulder of one soldier.
Meanwhile Morel sat on best place surrounded by soldiers.
Morel, a small, stocky Frenchman, with bloodshot, watery eyes, tied with a woman's scarf over his cap, was dressed in a woman's fur coat. He, apparently drunk, put his arm around the soldier sitting next to him and sang a French song in a hoarse, intermittent voice. The soldiers held their sides, looking at him.
- Come on, come on, teach me how? I'll take over quickly. How?.. - said the joker songwriter, who was hugged by Morel.
Vive Henri Quatre,
Vive ce roi vaillanti –
[Long live Henry the Fourth!
Long live this brave king!
etc. (French song) ]
sang Morel, winking his eye.
Se diable a quatre…
- Vivarika! Vif seruvaru! sit-down... - the soldier repeated, waving his hand and really catching the tune.
- Look, clever! Go go go go!.. - rough, joyful laughter rose from different sides. Morel, wincing, laughed too.
- Well, go ahead, go ahead!
Qui eut le triple talent,
De boire, de battre,
Et d'etre un vert galant...
[Having triple talent,
drink, fight
and be kind...]
– But it’s also complicated. Well, well, Zaletaev!..
“Kyu...” Zaletaev said with effort. “Kyu yu yu...” he drawled, carefully protruding his lips, “letriptala, de bu de ba and detravagala,” he sang.
- Hey, it’s important! That's it, guardian! oh... go go go! - Well, do you want to eat more?
- Give him some porridge; After all, it won’t be long before he gets enough of hunger.
Again they gave him porridge; and Morel, chuckling, began to work on the third pot. Joyful smiles were on all the faces of the young soldiers looking at Morel. The old soldiers, who considered it indecent to engage in such trifles, lay on the other side of the fire, but occasionally, raising themselves on their elbows, they looked at Morel with a smile.
“People too,” said one of them, dodging into his overcoat. - And wormwood grows on its root.
- Ooh! Lord, Lord! How stellar, passion! Towards the frost... - And everything fell silent.
The stars, as if knowing that now no one would see them, played out in the black sky. Now flaring up, now extinguishing, now shuddering, they busily whispered among themselves about something joyful, but mysterious.

X
The French troops gradually melted away in a mathematically correct progression. And that crossing of the Berezina, about which so much has been written, was only one of the intermediate stages in the destruction of the French army, and not at all a decisive episode of the campaign. If so much has been written and written about the Berezina, then on the part of the French this happened only because on the Berezina broken bridge the disasters suffered French army previously evenly, here they suddenly grouped into one moment and into one tragic spectacle that remained in everyone’s memory. On the Russian side, they talked and wrote so much about the Berezina only because, far from the theater of war, in St. Petersburg, a plan was drawn up (by Pfuel) to capture Napoleon in a strategic trap on the Berezina River. Everyone was convinced that everything would actually happen exactly as planned, and therefore insisted that it was the Berezina crossing that destroyed the French. In essence, the results of the Berezinsky crossing were much less disastrous for the French in terms of the loss of guns and prisoners than Krasnoye, as the numbers show.
The only significance of the Berezin crossing is that this crossing obviously and undoubtedly proved the falsity of all plans for cutting off and the justice of the only possible course of action demanded by both Kutuzov and all the troops (mass) - only following the enemy. The crowd of Frenchmen fled with an ever-increasing force of speed, with all their energy directed towards achieving their goal. She ran like a wounded animal, and she could not get in the way. This was proven not so much by the construction of the crossing as by the traffic on the bridges. When the bridges were broken, unarmed soldiers, Moscow residents, women and children who were in the French convoy - all, under the influence of the force of inertia, did not give up, but ran forward into the boats, into the frozen water.
This aspiration was reasonable. The situation of both those fleeing and those pursuing was equally bad. Remaining with his own, each in distress hoped for the help of a comrade, for a certain place he occupied among his own. Having given himself over to the Russians, he was in the same position of distress, but he was on a lower level in terms of satisfying the needs of life. The French did not need to have correct information that half of the prisoners, with whom they did not know what to do, despite all the Russians’ desire to save them, died from cold and hunger; they felt that it could not be otherwise. The most compassionate Russian commanders and hunters of the French, the French in Russian service could not do anything for the prisoners. The French were destroyed by the disaster in which the Russian army was located. It was impossible to take away bread and clothing from hungry, necessary soldiers in order to give it to the French who were not harmful, not hated, not guilty, but simply unnecessary. Some did; but this was only an exception.

After graduating from school without exams, he was enrolled in the Faculty of Mathematics and Mechanics of Leningrad State University (now St. Petersburg State University). During his student years, Perelman repeatedly won mathematics Olympiads. After graduating with honors from the university, he entered graduate school at the Leningrad branch of the Mathematical Institute. V.A. Steklov (since 1992 - St. Petersburg Department of the Mathematical Institute).

In 1990, he defended his Ph.D. thesis and was retained at the institute as a senior researcher.

In 1992, the scientist received an invitation to give a course of lectures at New York University and Stony Brook University, and then worked for some time at the University of Berkeley (USA). While in the USA, Perelman worked as a research fellow at American universities.
In 1996, he returned to St. Petersburg, where he worked at the St. Petersburg branch of the Mathematical Institute until December 2005.

Between November 2002 and July 2003, Perelman wrote three articles in which he revealed the solution to one of the special cases of William Thurston's geometrization conjecture, from which the validity of the Poincaré conjecture follows. The method of studying Ricci flow described by Perelman was called the Hamilton-Perelman theory, since the American mathematician Richard Hamilton was the first to study it.

Poincaré's conjecture was formulated by French mathematician Henri Poincaré in 1904 and is a central problem in topology, the study of the geometric properties of bodies that do not change when the body is stretched, twisted, or compressed. Poincaré's theorem was considered one of the unsolvable mathematical problems.

The mathematician is known for being emphatic and speaking publicly.

According to media reports, in 2014, Grigory Perelman received a Swedish visa for 10 years and moved to Sweden, where a local private company engaged in scientific development offered him a well-paid job. However, it was later reported that he lives in St. Petersburg, and visits Sweden as needed.

In 2011, it was published about the life and actions of the Russian scientist Grigory Perelman.

After graduating from school, without exams, he was enrolled in the Faculty of Mathematics and Mechanics of Leningrad State University (now St. Petersburg State University). During his student years, Perelman repeatedly won mathematics Olympiads. After graduating with honors from the university, he entered graduate school at the Leningrad branch of the Mathematical Institute. V.A. Steklov (since 1992 - St. Petersburg Department of the Mathematical Institute).

In 1990, he defended his Ph.D. thesis and was retained at the institute as a senior researcher.

The mathematician is known for being emphatic and speaking publicly.

In 2011, it was published about the life and actions of the Russian scientist Grigory Perelman.

The hero of the new issue of the “Icon of the Era” column is Russian mathematician Grigory Perelman. What is known about him is that he gave up a million dollars by proving the Poincaré Conjecture, which, in turn, is known to be extremely difficult to understand. Moreover, the sequence here is exactly this - the fact of refusing money excited the respectable public much more than “some kind of abstract mathematical calculation.” Now that the hype around this decision has subsided, let’s figure out who Grigory Perelman is for mathematics and what mathematics is for him.

Grigory Perelman

Born in 1966 in Leningrad

mathematician

Life path

Soviet Union had an outstanding mathematical tradition, so it is impossible to talk about Perelman’s childhood without mentioning the phenomenon of Soviet mathematical schools. In them, talented children were trained under the guidance of the best mentors; such an environment served as fertile ground for future outstanding achievements. However, despite the competent organization of the learning process, there was also discrimination inherent in the Soviet system, when even the presence unusual surname could cost a place in the city’s national team or admission to a university.

Henri Poincaré

Perelman grew up in an intelligent family and showed interest in mathematics from childhood. However, once he got into the mathematical circle, he did not immediately become a leader. The first failures spurred him to work harder and influenced his character - unyielding and stubborn. These qualities helped the scientist solve the main problem of his life.

Following a gold medal at the International Mathematical Olympiad in Budapest in 1982 and a brilliant graduation (there were not enough GTO standards passed for the gold medal) followed by Mathematical and Mechanics of St. Petersburg State University, and later graduate school, where Perelman also studied exclusively with “excellent” marks. When the Soviet Union ceased to exist, the scientist was faced with reality: science was experiencing a severe crisis. An internship in the USA unexpectedly took place, where the young scientist first met Richard Hamilton. The American mathematician made serious progress in solving the famous Poincaré problem. Moreover, he even outlined a plan, following which this decision could be reached. Perelman managed to communicate with him, and Hamilton made an indelible impression on him: he was open and spared no effort in explaining.

Institute building named after. Steklova in St. Petersburg

Despite offers to stay, at the end of the internship, Perelman returned to Russia, to his home apartment in a nine-story building in St. Petersburg in Kupchino (the notorious "ghetto" in the south of the city), and began working at the Mathematical Institute. Steklova. In his free time, he reflected on the Poincaré Hypothesis and the ideas that Hamilton had told him about. At this time, the American, judging by the publications, was unable to advance further in his reasoning. Soviet education gave Perelman the opportunity to look at the problem from the other side, using his own approach. Hamilton no longer responded to letters, and this became the “green light” for Perelman: he began working on solving the Hypothesis.

Every simply connected compact three-dimensional manifold without boundary is homeomorphic to a three-dimensional sphere.

The Poincaré conjecture belongs to topology, the branch of mathematics that studies the most general properties space. Like any other branch of mathematics, topology is extremely specific and precise in its formulations. Any simplifications and retellings in a “more accessible form” distort the essence and have little in common with the original. That is why in this article we will not talk about the well-known thought experiment with a mug that, through continuous deformation, turns into a donut. Out of respect for the main character, we simply admit that it is difficult to explain the Poincaré Hypothesis to people far from mathematics. And for those who are ready to devote time and effort to this, we will provide several materials for independent study.

The three-dimensional sphere is the object referred to in the formulation of the Poincaré Hypothesis

It took Perelman seven years to solve this problem. He did not recognize conventions and sent his works to scientific journals I did not submit it for review (a common practice among scientists). In November 2002, Perelman published the first part of his calculations on arXiv.org, followed by two more. In them, in an extremely concise form, a problem even more general than the Poincaré Conjecture was solved - this is the Thurston Geometrization Conjecture, from which the first was a simple consequence. However, the scientific community received these works with caution. I was confused by the brevity of the solution and the complexity of the calculations that Perelman presented.

After the publication of the decision, Perelman again went to the United States. For several months he held seminars at various universities, talking about his work and patiently answering all questions. However, the main purpose of his trip was to meet with Hamilton. It was not possible to communicate with the American scientist a second time, but Perelman again received an invitation to stay. He received a letter from Harvard asking him to send them his resume, to which he irritably replied: “If they know my work, they don’t need my CV. If they need my CV, they don't know my work."

Fields Medal

The next few years were marred by an attempt by Chinese mathematicians to claim credit for the discovery.(their interests were supervised by Professor Yau, a brilliant mathematician, one of the creators of the mathematical apparatus of String Theory), the unbearably long wait for verification of the work, which was carried out by three groups of scientists, and the hype in the press.

All this went against Perelman’s principles. Mathematics attracted him with its categorical honesty and unambiguity, which is the basis of this science. However, the intrigues of his colleagues, concerned about recognition and money, shook the scientist’s faith in the mathematical community, and he decided not to study mathematics anymore.

And although Perelman’s contribution was eventually appreciated, and Yau’s claims were ignored, the mathematician did not return to science. No Fields Medal (analogue Nobel Prize for mathematicians), nor the Millennium Prize (million dollars) he didn't accept. Perelman was extremely skeptical about the hype in the press and minimized contacts with former colleagues. To this day he lives in the same apartment in Kupchino.

Timeline

Born in Leningrad.

As part of a team of schoolchildren, he participated in the International Mathematical Olympiad in Budapest.

Perelman was invited to spend a semester each at New York University and Stony Brook University.

Returned to the institute. Steklova.

november
2002 -
July 2003

Perelman posted three scientific articles on the website arXiv.org, which in an extremely condensed form contained a solution to one of the special cases of William Thurston’s Geometrization Hypothesis, leading to a proof of the Poincaré Hypothesis.

Perelman gave a series of lectures in the United States on his works.

Perelman's results were verified by three independent groups of mathematicians. All three groups concluded that Poincaré's Problem had been successfully solved, but Chinese mathematicians Zhu Xiping and Cao Huaidong, along with their teacher Yau Shintang, attempted plagiarism, claiming that they had found a "complete proof".