Grigory Perelman biography and discoveries. Mathematician Yakov Perelman: contribution to science

, №7, 2014 , №8, 2014 , №10, 2014 , №12, 2014 , №1, 2015 , №4, 2015 , №5, 2015 , №6, 2015 , №7, 2015 , №9, 2015 , №1, 2016 , №2, 2016 , №3, 2016 , №6, 2016 , №8, 2016 , № 11, 2016 , № 2, 2017 , № 4, 2017 , № 6, 2017 , № 7, 2017 , №10, 2017 , №12, 2017 , №7, 2018 .

Magazine version of one of the chapters of the new book Nick. Gorkavy “Undiscovered Worlds” (St. Petersburg: “Astrel”, 2018).

Mathematicians are special people. They are so deeply immersed in abstract worlds that, “returning to Earth,” they often cannot adapt to real life and surprise others with unusual views and actions. We will talk about perhaps the most talented and extraordinary of them - Grigory Perelman.

In 1982, sixteen-year-old Grisha Perelman, who had just won a gold medal at the International Mathematical Olympiad in Budapest, entered Leningrad University. He was noticeably different from the other students. His supervisor, Professor Yuri Dmitrievich Burago, said: “There are a lot of gifted students who speak before they think. Grisha was not like that. He always thought very carefully and deeply about what he intended to say. He wasn't very quick to make decisions. Speed of solution means nothing; mathematics is not built on speed. Mathematics is about depth.”

After graduating from university, Grigory Perelman became an employee of the Steklov Mathematical Institute and published a number of interesting articles on three-dimensional surfaces in Euclidean spaces. The world mathematical community appreciated his achievements. In 1992, Perelman was invited to work at New York University.

Gregory ended up in one of the world centers of mathematical thought. Every week he went to a seminar in Princeton, where he once listened to a lecture by the eminent mathematician, Columbia University professor Richard Hamilton. After the lecture, Perelman approached the professor and asked several questions. Perelman later recalled about this meeting: “It was very important for me to ask him about something. He smiled and was very patient with me. He even told me a couple of things that he published only a few years later. He shared with me without hesitation. I really liked his openness and generosity. I can say that in this respect Hamilton was unlike most other mathematicians."

Perelman spent several years in the USA. He walked around New York wearing the same corduroy jacket, ate mostly bread, cheese and milk, and worked constantly. He began to be invited to the most prestigious universities in America. The young man chose Harvard and then encountered something that he categorically did not like. The hiring committee required the applicant to provide a CV and letters of recommendation from other scientists. Perelman’s reaction was harsh: “If they know my works, then they don’t need my biography. If they want my biography, then they don’t know my work.” He refused all offers and in the summer of 1995 returned to Russia, where he continued to work on the ideas that Hamilton had developed. In 1996, Perelman was awarded the European Mathematical Society Prize for Young Mathematicians, but he, who did not like any hype, refused to accept it.

When Gregory achieved some success in his research, he wrote a letter to Hamilton, hoping for joint work. However, he did not answer, and Perelman had to continue to act alone. But world fame awaited him ahead.

In 2000, the Clay Mathematics Institute published the “Millennium Problem List,” which included seven classic problems in mathematics that had not been solved for many years, and promised a million-dollar prize for proving any of them. Less than two years later, on November 11, 2002, Grigory Perelman published an article on a scientific website on the Internet, in which, on 39 pages, he summed up his many years of efforts to prove one problem from the list. American mathematicians who knew Perelman personally immediately began to discuss the article in which the famous Poincaré conjecture was proved. The scientist was invited to several US universities to give a course of lectures on his proof, and in April 2003 he flew to America. There, Gregory held several seminars in which he showed how he managed to turn the Poincaré conjecture into a theorem. The mathematical community recognized Perelman's lectures as an extremely important event and made significant efforts to verify the proposed proof.

Details for the curious

Poincaré problem

Jules Henri Poincaré (1854–1912) - an outstanding French mathematician, mechanic, physicist, astronomer and philosopher, head of the Paris Academy of Sciences and member of more than 30 academies of sciences around the world. The problem formulated by Poincare in 1904 belongs to the field of topology.

For topology, the main property of space is its continuity. Any spatial forms that can be obtained from one another using stretching and curvature, without cutting and gluing, are considered identical in topology (the transformation of a cup into a donut is often shown as an illustrative example). The Poincaré conjecture states that in four-dimensional space, all three-dimensional surfaces belonging to compact manifolds are topologically equivalent to a sphere.

The proof of the hypothesis by Grigory Perelman made it possible to develop a new methodological approach to solving topological problems, which is of great importance for the further development of mathematics.

Paradoxically, Perelman did not receive grants to prove the Poincaré conjecture, while other scientists testing its correctness received grants amounting to a million dollars. Verification was extremely important, because many mathematicians worked on the proof of this problem, and if it was actually solved, then they were left out of work.

The mathematical community tested Perelman's proof for several years and by 2006 concluded that it was correct. Yuri Burago wrote then: “The proof closes an entire branch of mathematics. After it, many scientists will have to switch to research in other areas.”

Mathematics has always been considered the most rigorous and accurate science, where there is no place for emotions and intrigue. But even here there is a struggle for priority. Passions began to boil around the proof of the Russian mathematician. Two young mathematicians, immigrants from China, having studied Perelman's work, published a much more voluminous and detailed - more than three hundred pages - article with a proof of the Poincaré conjecture. In it, they argued that Perelman's work contained many gaps that they were able to fill. According to the rules of the mathematical community, priority in proving the theorem belongs to those researchers who were able to present it in the most complete form. According to many experts, Perelman's proof was complete, although briefly stated. More detailed calculations did not introduce anything new into it.

When journalists asked Perelman what he thought about the position of Chinese mathematicians, Grigory replied: “I can’t say that I’m outraged, others do even worse. Of course, there are a lot of more or less honest mathematicians. But almost all of them are conformists. They themselves are honest, but they tolerate those who are not.” He then noted bitterly: “Those who violate ethical standards in science are not considered aliens. People like me are the ones who end up isolated.”

In 2006, Grigory Perelman was awarded the highest honor in mathematics, the Fields Medal. But the mathematician, who led a solitary, even reclusive lifestyle, refused to receive it. It was a real scandal. The President of the International Mathematical Union even flew to St. Petersburg and spent ten hours persuading Perelman to accept the well-deserved award, which was planned to be presented at a congress of mathematicians on August 22, 2006 in Madrid in the presence of the Spanish King Juan Carlos I and three thousand participants. This congress was supposed to be a historic event, but Perelman politely but adamantly said: “I refuse.” The Fields Medal, according to Gregory, did not interest him at all: “It doesn’t matter at all. Everyone understands that if the evidence is correct, then no other recognition of merit is required.”

In 2010, the Clay Institute awarded Perelman the promised million-dollar prize for proving the Poincaré conjecture, which he was about to receive at a mathematical conference in Paris. Perelman refused a million dollars and did not go to Paris.

As he himself explained, he does not like the ethical atmosphere in the mathematical community. In addition, he considered Richard Hamilton's contribution no less. Winner of many mathematical prizes, Soviet, American and French mathematician M. L. Gromov supported Perelman: “Great things require an unclouded mind. You should only think about mathematics. Everything else is human weakness. To accept a reward is to show weakness.”

Refusing a million dollars made Perelman even more famous. Many asked him to receive the prize and give it to them. Gregory did not respond to such requests.

Until now, the proof of the Poincaré conjecture remains the only solved problem on the millennium list. Perelman became the number one mathematician in the world, although he refused contacts with his colleagues. Life has shown that outstanding results in science were often achieved by individuals who were not part of the structure of modern science. That's how Einstein was. While working as a clerk in a patent office, he created the theory of relativity, developed the theory of the photoelectric effect and the principle of operation of lasers. This is how Perelman became, who neglected the rules of conduct in the scientific community and at the same time achieved maximum efficiency of his work by proving the Poincaré conjecture.

The Clay Mathematics Institute (Cambridge, USA) was founded in 1998 by businessman Landon Clay and mathematician Arthur Jaffee to increase and disseminate mathematical knowledge.

The Fields Medal has been awarded for excellence in mathematics since 1936.

Mathematicians are special people. They are so deeply immersed in abstract worlds that, “returning to Earth,” they often cannot adapt to real life and surprise others with unusual views and actions. We will talk about perhaps the most talented and extraordinary of them - Grigory Perelman.

In 2000, the Clay Mathematics Institute* published the “Millennium Problem List,” which included seven classic problems in mathematics that had not been solved for many years, and promised a million-dollar prize for proving any of them. Less than two years later, on November 11, 2002, Grigory Perelman published an article on a scientific website on the Internet, in which, on 39 pages, he summed up his many years of efforts to prove one problem from the list. American mathematicians who knew Perelman personally immediately began to discuss the article in which the famous Poincaré conjecture was proved. The scientist was invited to several US universities to give a course of lectures on his proof, and in April 2003 he flew to America. There, Gregory held several seminars in which he showed how he managed to turn the Poincaré conjecture into a theorem. The mathematical community recognized Perelman's lectures as an extremely important event and made significant efforts to verify the proposed proof.

In 2006, Grigory Perelman was awarded the highest award in the field of mathematics - the Fields Medal**. But the mathematician, who led a solitary, even reclusive lifestyle, refused to receive it. It was a real scandal. The President of the International Mathematical Union even flew to St. Petersburg and spent ten hours persuading Perelman to accept the well-deserved award, which was planned to be presented at a congress of mathematicians on August 22, 2006 in Madrid in the presence of the Spanish King Juan Carlos I and three thousand participants. This congress was supposed to be a historic event, but Perelman politely but adamantly said: “I refuse.” The Fields Medal, according to Gregory, did not interest him at all: “It doesn’t matter at all. Everyone understands that if the evidence is correct, then no other recognition of merit is required.”

Refusing a million dollars made Perelman even more famous. Many asked him to receive the prize and give it to them. Gregory did not respond to such requests.

From the book Nick. Gorky "Undiscovered Worlds". - St. Petersburg: “Astrel”. 2018.

Mathematicians all over the world have been working on it for decades. Now the scientist remains a mystery to the entire scientific community. And not only because he shocked everyone by refusing a million-dollar prize for his discovery. A great mathematician is a closed person. Lives in St. Petersburg, communicates with almost no one except his mother and leads a reclusive lifestyle. Perelman does not give interviews, does not talk about himself and does not answer any questions.

The only exception was the Ural director Andrei Grigoriev, who was making a film about a genius. On June 13, the mathematician turned 53 years old. On Perelman’s birthday, Andrei Grigoriev and the genius’s class teacher Valentina Berdova told KP - Petersburg about the scientist’s childhood and current life.

“GRISHA WAS ALWAYS SURROUNDED BY GIRLS”

Grisha Perelman studied with me from the 5th grade, admitted “KP - Petersburg” Perelman's teacher Valentina Vasilievna. - Having such a child in the class is a miracle. If necessary, he will defend himself by saying that the teacher gives all the material. His class was very good. And Grisha attracted the attention of not only teachers, but also children.

Recently the Internet was alarmed by the news that Perelman was dying. One of his friends called out that he saw the genius in an unusual image: “In very short and wrinkled pants, no socks at all (it’s minus 7 outside) and in very strange galoshes on his bare feet.” But as it turned out, the mathematician has been like this since childhood.

“He didn’t focus on his appearance,” explains the math teacher. - He didn’t always have his hair neatly combed, and he didn’t fasten a button. But he answered better than anyone else in class. The girls - his classmates - were all neatly dressed, combed and loved to hover around him. They teased him for his appearance: “Grisha, why are you like this?” He answered them very briefly and very correctly. The children just liked to hang around him. But they once told me about this: “You know, they’re making fun of him.” I called the girls and said: “What are you doing?” They replied, “We’re just wondering.” I asked them not to do that, and they left him alone. Grisha later told me that the girls walked around him for a long time, asking him something, but now they don’t come up to him. I played my role.

“THE MATH TEACHER LOVED TO DRINK”

Grigory Perelman has been interested in mathematics since school. And sometimes he knew her even better than the teacher. Therefore, the teacher always had to take the rap in class.

Grisha really didn’t like it when people lie,” admits Valentina Vasilyevna. - We had a good team of teachers. The mathematics teacher Sergei Mikhailovich was brilliant, but there was one “but”. He liked to drink, the children knew that. He could be rude, he could sometimes compose in class. This happened in any class. He lied outright. But Grisha quickly caught him on this. Once, twice. Seryozhka endured and endured, and then sat down at the table and said: “Sorry, guys, I didn’t prepare for the lesson today.”

Valentina Berdova then asked Grigory why he did this. And then for the first time Perelman voiced his position in life.

I then say: “Grisha, but how could you tell the teacher this? Well, he's wrong. The children still didn’t understand,” the teacher smiles. - And he answers: “Valentina Vasilievna, I don’t like it when people lie.” This continued throughout his life. There have always been a lot of lies in our lives. But the mathematics teacher did not lose his authority. The children loved him. Because he presented knowledge in such a way that you won’t want it, but you will remember it. Of course, he had to be fired several times because he was rude and called students names. He got punished for this.

“EVERYONE GOT FROM GRISHA”

True, it was not only the mathematics teacher who got it from Perelman, but also others. As a child, the future genius was interested in everything at once.

In geography lessons. “I was a novice teacher,” the teacher recalls. - I tell him: “How did you remember all of Africa?” And he: “Valentina Vasilyevna, I remember the image and it sticks.” He is certainly a multifaceted person. He was interested in everything: music, geography, history, and French. A foreign language teacher used to start speaking French, say something wrong, and Grisha would correct him immediately, but very delicately. But, of course, Sergei Alekseevich got more.

According to the teacher, Perelman still has a dislike for lying.

His protests are all because of this,” explains the teacher. - The King of Spain was supposed to present him with the prestigious Fields Medal in Madrid. He didn’t come, instead he went into the forest to pick mushrooms in Kupchino. I say: “Grish, why?” He never answered me. Everyone was waiting for him there, and he was picking mushrooms. But that's his business. As for mathematics, he takes after his mother. She is also a mathematician. I remember his dad, he kept saying: “Ask him more, he can do more.” His grandmother came. And now he forbade everyone: his sister, his father, his mother to talk about himself.

“I COULD BECOME A MUSICIAN”

Perelman, according to the teacher, could well have made a good musician. At school he liked to sing.

All the children told him: “Grisha, sing!”, and he sings, recalls Berdova. - At the same time, he sings in a clear voice. His voice was not strong, but very clear. And his favorite song: “The division marched forward through the valleys and over the hills.” I asked him how he knew the words. And he answered that these were grandfather’s songs. I listened to him with pleasure. But guys are an impatient people. If they were distracted, he said: “If they don’t want to listen to me, I won’t sing.” He also conducted political classes and talked about world events. But the dunces didn’t want to listen either. So he soon stopped that too.

Director Andrei Grigoriev also says that Perelman was always drawn to music. He managed to melt the heart of a genius thanks to the orchestra. At the director's request, the musicians played classical music under the windows of Perelman's house in the rain. Seeing this, the mathematician agreed to talk with Grigoriev.

Grigory Perelman used to play the violin, explains Grigoriev. “But Sergei Evgenievich Rubchin, his supervisor, discouraged him from playing musical instruments so that he would devote himself more to mathematics. Now we are preparing a film about him. When I talked with Perelman, the most surprising thing for him was that the scientists with whom he worked in the USA were interested in him. When I asked: “Why are these people immediately paralyzed at the mention of just your name, how do you have such power?” He felt good at that moment, he walked and smiled. He created himself and charmed millions of people.

The director also explained why Grigory Perelman is not making contact now.

The journalists traumatized him and pressed him hard,” says Andrei Grigoriev. - The deformation in his mind has passed, the media representatives put a little pressure on him. We have already met twice. The first time we talked for about two hours. And in my film I will try to convey the idea of who Grigory Perelman is and his inner world. The way he sees this world.

The film about Perelman will be released in 2021.

The brilliant mathematician Grigory Perelman shocked the scientific world by proving the Poincaré conjecture, one of the most difficult mysteries of the millennium. And ordinary people were surprised by the poor scientist’s refusal to accept a million-dollar bonus. Gradually, the genius himself and his reclusive lifestyle became a mystery, comparable in complexity to a proven theorem.

Childhood and youth

Grigory Yakovlevich leads a secretive lifestyle. Facts about the scientist’s childhood, youth and personal life are known from the words of neighbors, school teachers and classmates, and colleagues who worked with the mathematician.

Perelman was born on June 13, 1966 in Leningrad. The name of the brilliant mathematician speaks for itself about his nationality. Since childhood, the Jewish boy showed incredible abilities and interest in learning. While his peers were kicking a ball in the yard, little Grisha preferred to read books and play chess.

Contrary to popular belief, Yakov Isidorovich Perelman, the famous scientist, author of books and popularizer of science, is not a relative of Grigory Yakovlevich.

Gregory's father is an electrical engineer. In 1993, Perelman Sr. immigrated to his historical homeland of Israel, like thousands of his compatriots in the 90s. The mother of the future outstanding mathematician stayed with the children in Leningrad and taught mathematics at the school.

Grigory Yakovlevich has a younger sister who has built a scientific career. Having received a diploma in mathematics from St. Petersburg University, the woman later left for Sweden. Since 2007 he has been working as a programmer in Stockholm.

By the time the boy went to school, he was significantly superior to his classmates in knowledge and could easily count three-digit numbers in his head. Perelman’s teachers recall that the student had conversations on equal terms with adults.

The magic of logic and numbers attracted Grigory Yakovlevich. From the 5th grade, the boy attended the mathematics center at the Palace of Pioneers. The mentor of the young prodigies was Associate Professor of the Pedagogical University named after Sergei Rukshin. Young Grisha received awards for participating in Olympiads, including earning the highest score at the International Mathematical Olympiad.

After graduating from a nine-year school in an ordinary Leningrad school, the graduate moved to specialized physics and mathematics school No. 239. Without a doubt, the hardworking and talented Perelman was an ideal student. Physical training failed me. Failure to pass the GTO standards prevented the graduate from receiving a gold medal.

It is not surprising that after school, Gregory was accepted into the Faculty of Mathematics and Mechanics at Leningrad State University without entrance exams. At the university, Perelman continued to shine at the Olympiads and received the Lenin Prize for excellent educational results.

The science

After graduation, graduate school followed, then a doctorate. As a result, the gifted scientist remained to work at his home university as a senior researcher.

In the early 90s, the talented scientist went to the USA, where he visited several universities as part of an exchange of experience. In the United States, the mathematician gave lectures and met with colleagues. Soon, the ascetic Perelman became bored with America, and the scientist returned to his homeland.

Having resumed work at a Leningrad university, the mathematician begins to work hard on the riddle of the millennium, which the brilliant scientists of the century were unable to solve. It is worth noting that several years earlier Perelman’s passion for topology began. Previously, the mathematician was able to prove the soul hypothesis, which preceded the study of the Poincaré conjecture.

The meaning of proving a hypothesis, like the essence itself, cannot be described in simple language understandable to a person far from higher mathematics. The discoveries made by the mathematician are of great importance in the study of the Universe and in working with nanotechnology.

In addition, the hypothesis states that the peculiarity of the shape of the Universe leads to the fact that it can be compressed into one point. This, in turn, indirectly confirms the Big Bang theory. Proponents of the theological origins of the universe have had reason to doubt God as the creator of all things. Poincaré's conjecture proves that there is no God.

In 2002-2003, Perelman published articles revealing the essence of the proof. Three independent teams of mathematicians tested the arguments and confirmed the complete proof.

In 2003, Perelman visited the United States, gave lectures about his own discovery, and shared his experience with his compatriots. And in 2005, the scientist unexpectedly left the department and locked himself in an apartment in Kupchino, where he lived with his sick mother.

Personal life

A reclusive lifestyle leaves hundreds of questions. The main thing of interest to journalists and citizens is the reason why Grigory Perelman refused the money that rightfully belonged to him. We are talking about the Clay Institute Prize. The Mathematical Institute has compiled a list of seven riddles, the solution of which carries a million-dollar reward. The Poincaré conjecture was included in this list.

Of course, having learned about the discovery of the Russian scientist, the founders immediately turned to the scientist. Imagine everyone's surprise when the mathematician refused a million dollars without explanation.

Soon Grigory Yakovlevich stopped communicating with the press altogether. He simply ignores Russian journalists and refuses interviews to foreign ones. News of the scientist’s similar behavior led to rumors about Perelman’s illness. They claimed that the genius suffered from autism. However, reliable evidence or doctors’ opinions have not yet been made public.

It is known that the scientist lives with his mother, who is seriously ill. The mathematician has no wife. According to the stories of Grigory Yakovlevich’s teacher, who maintains a relationship with him, mother and son live poorly.

In 2018, information appeared that the mathematician had moved to Sweden. However, sources represented by neighbors and store sellers denied the rumors and confirmed that Perelman did not leave.

While working in the States, the scientist surprised his foreign colleagues with his unpretentiousness and detachment from everyday needs. The mathematician's favorite food was sandwiches with cheese, which Grigory Yakovlevich washed down with kefir or milk. Restaurants and an abundance of grocery stores did not interest the “strange Russian.”

As a child, Gregory was interested in music. The mother instilled in her son an adoration for classical composers. She, being a talented violinist, introduced Grisha to the instrument. Perelman enjoyed attending music school, and then he was faced with a difficult choice - to enter the conservatory or devote himself to the exact sciences.
Statements from conspiracy theorists have appeared on the Internet that Perelman is the most influential person on earth because he knows how to control the Universe. Of course, such a person did not escape the attention of the secret services, and communication with others is prohibited for the scientist.

Quotes

I know how to control the Universe. And tell me - why should I run for a million?

The whole world is permeated by emptiness, and it obeys formulas - this gives us limitless possibilities.

If you can train your arms and legs, then why can't you train your brain?

There is, perhaps, no unsolvable problem. Difficult to solve. That's more accurate.

Remember the biblical legend about how Jesus Christ walked on water as well as dry land? So I needed to calculate how fast he had to move through the waters so as not to fall through.

Awards and prizes

1991 - Prize “Young Mathematician” of the St. Petersburg Mathematical Society
1996 - European Mathematical Society Prize for Young Mathematicians
2006 - Fields Medal Award
2010 - Clay Mathematics Institute Prize