Grigory Perelman's birthday. Grigory Perelman: alive, well, doing science
The history of mankind knows many people who, thanks to their outstanding abilities, became famous. However, it should be said that rarely any of them managed to become a real legend during their lifetime and achieve fame not only in the form of placing portraits in school textbooks. Few celebrities have reached such a pinnacle of fame, which was confirmed by the conversations of both the world scientific community and grandmothers sitting on a bench at the entrance.
But in Russia there is such a person. And he lives in our time. This is the mathematician Perelman Grigory Yakovlevich. The main achievement of this great Russian scientist was the proof of the Poincaré hypothesis.
The fact that Grigory Perelman is the most famous mathematician in the world is known even to any ordinary Spaniard. After all, this scientist refused to receive the Fields Prize, which he was supposed to be awarded by the King of Spain himself. And, without any doubt, only the greatest people are capable of such a thing.
A family
Grigory Perelman was born on 06/13/1966 in the northern capital of Russia - the city of Leningrad. The father of the future genius was an engineer. In 1993 he left his family and emigrated to Israel.
Grigory's mother, Lyubov Leibovna, worked as a mathematics teacher at a vocational school. She, owning the violin, instilled in her son a love of classical music.
Grigory Perelman was not the only child in the family. He has a sister who is 10 years younger than him. Her name is Elena. She is also a mathematician, she graduated from St. Petersburg University (in 1998). In 2003, Elena Perelman defended her dissertation for the degree of Doctor of Philosophy at the Reitzman Institute in Rehovot. Since 2007 she has been living in Stockholm where she works as a programmer.
School years
Grigory Perelman, whose biography is such that today he is the most famous mathematician in the world, was a shy and quiet Jewish boy as a child. However, despite this, in terms of knowledge, he significantly surpassed his peers. And this allowed him to communicate with adults almost on an equal footing. His peers were still playing in the yard and sculpting sand cakes, and Grisha was already learning the basics of mathematical science with might and main. The books that were available in family library. The mother of the future scientist, who was simply in love with this exact science, also contributed to the acquisition of knowledge. Also, the future Russian mathematician Grigory Perelman was passionate about history and played chess well, which his father taught him.
No one forced the boy to sit over his textbooks. Grigory Perelman's parents never tormented their son with moralizing that knowledge is power. He discovered the world of science quite naturally and without any strain. And this was entirely facilitated by the family, the main cult of which was not money at all, but knowledge. Parents never scolded Grisha for a lost button or a dirty sleeve. However, it was considered shameful, for example, to go out of tune while playing a melody on the violin.
The future mathematician Perelman went to school at the age of six. By this age, he was thoroughly savvy in all subjects. Grisha easily wrote, read and performed mathematical operations using three digit numbers. And it was a time when his classmates only learned to count to a hundred.
At school, the future mathematician Perelman was one of the strongest students. He repeatedly became the winner of the All-Russian mathematical competitions. Until the 9th grade, the future Russian scientist attended a secondary school located on the outskirts of Leningrad, where his family lived. Then he moved to the 239th school. She had a physical and mathematical bias. In addition, from the fifth grade, Grigory attended the mathematical center opened at the Palace of Pioneers. Classes were held here under the guidance of Sergei Rukshin - Associate Professor of the Russian State Pedagogical University. The students of this mathematician constantly won awards at various mathematical Olympiads.
In 1982, Grigory, as part of the team Soviet schoolchildren, defended the honor of the country at the International Mathematical Olympiad, held in Hungary. Our guys took first place then. And Perelman, who scored maximum amount possible points, received a gold medal for the impeccable performance of all the tasks proposed at the Olympiad. To date, we can say that this was the last award that he accepted for his work.
It would seem that Grigory, an excellent student in all subjects, without any doubt, should have graduated from school with a gold medal. However, he was let down by physical education, according to which he could not pass the required standard. The class teacher had to simply beg the teacher to give the boy a B in his certificate. Yes, Grisha did not like sports loads. However, on this occasion, he did not complex at all. Physical education simply did not occupy him as much as other disciplines. He always said that he was convinced that our body needs training, but at the same time he preferred to train not his arms and legs, but his brain.
Relationships in the team
At school, the future mathematician Perelman was a favorite. He was sympathized not only with teachers, but also with classmates. Grisha was not a crammer and a nerd. He did not allow himself to trump his knowledge, the depth of which sometimes confused even teachers. He was just a talented child who was fond of not only proving complex theorems, but also classical music. The girls valued their classmate for his originality and intelligence, and the boys for his firm and calm character. Grisha not only studied with ease. He also helped his lagging classmates in mastering knowledge.
In Soviet times, a strong student was assigned to each loser, who helped him to pull himself up in any subject. The same order was given to Gregory. He had to help a classmate who was absolutely not interested in studying. In less than two months of classes, Grisha made a solid good student out of a loser. And there is nothing surprising in this. After all, the presentation of complex material at an accessible level is one of the unique abilities of the famous Russian mathematician. Largely due to this quality, in the future, Grigory Perelman proved the Poincaré theorem.
Student years
After successfully graduating from school, Grigory Perelman became a student at the Leningrad state university. Without any examinations, he was enrolled in the Faculty of Mathematics and Mechanics of this higher educational institution.
Perelman did not lose his interest in mathematics even in his student years. He constantly became the winner of university, city, and all-Union Olympiads. The future Russian mathematician studied just as successfully as at school. For excellent knowledge he was awarded the Lenin Scholarship.
Further education
After graduating with honors from the university, Grigory Perelman entered graduate school. His supervisor in those years was the famous mathematician A.D. Alexandrov.
Postgraduate studies were located at the Leningrad branch of the Institute of Mathematics. V.A. Steklov. In 1992, Grigory Yakovlevich defended his PhD thesis. The topic of his work concerned saddle surfaces in Euclidean spaces. Later, Perelman remained to work at the same institute, taking the position of senior researcher in the laboratory of mathematical physics. During this period, he continued to study the theory of space and was able to prove several hypotheses.
Work in the USA
In 1992, Grigory Perelman was invited to Stony Brook University and New York University. These educational establishments America offered the scientist to spend one semester there.
In 1993, Grigory Yakovlevich continued to teach at Berkeley, at the same time leading scientific work. It was at this time that Perelman Grigory became interested in the Poincaré theorem. It was the most difficult problem of modern mathematics that had not been solved at that time.
Return to Russia
In 1996, Grigory Yakovlevich returned to St. Petersburg. He again received the post of researcher at the Institute. Steklov. At the same time, he worked alone on the Poincaré conjecture.
Description of the theory
The problem arose in 1904. It was then that the French scientist Andry Poincaré, who was considered a mathematical universal in scientific circles due to the development of new methods of celestial mechanics and the creation of topology, put forward a new mathematical hypothesis. He suggested that the space around us is a three-dimensional sphere.
It is quite difficult to describe the essence of the hypothesis for a simple layman. There are too many scientific calculations in it. As an example, consider the usual balloon. In the circus, a wide variety of figures can be made from it. It can be dogs, horses and flowers. And what is the result? The ball from this remains the same. He doesn't change his physical properties, no molecular composition.
The same is true of this hypothesis. Her topic is related to topology. This is a branch of geometry that studies the diversity that spatial objects have. Topology considers various, outwardly dissimilar objects and finds common features in them.
Poincare also tried to prove the fact that our universe has the shape of a sphere. According to his theory, all simply connected three-dimensional manifolds have the same structure. They are simply connected due to the presence of a single continuous area of the body in which there are no through holes. It can be a sheet of paper and a glass, a rope and an apple. But a colander and a cup with a handle belong to completely different objects in their essence.
The notion of geomorphism follows from topology. It includes the concept of geomorphic objects, that is, those when one can be obtained from one another by stretching or compressing. For example, a ball (a piece of clay), from which a potter makes an ordinary pot. And if the master does not like the product, then he can immediately turn it back into a ball. If the potter decides to mold a cup, then the handle for it will have to be made separately. That is, he creates his object in a different way, obtaining not an integral, but a composite product.
Suppose that all objects in our world consist of an elastic, but at the same time non-adhesive substance. This material does not allow us to glue individual parts and seal holes. With it, you can only squeeze or extrude. Only in this case will a new form be obtained.
This is the main meaning of the Poincare conjecture. It says that if you take any three-dimensional object that does not have holes, then it, when performing various manipulations, but without gluing and cutting, can take the form of a ball.
However, the hypothesis is only a stated version. And this continues until the moment when she finds an exact explanation. Poincare's assumptions remained so until they were confirmed by the exact calculations of a young Russian mathematician.
Working on a problem
Grigory Perelman spent several years of his life proving the Poincaré conjecture. All this time he thought only about his work. He was constantly looking for the right ways and approaches to solving the problem and understood that the proof was somewhere nearby. And the mathematician was not mistaken.
Even in his student years, the future scientist often liked to repeat the phrase that there are no unsolvable problems. There are only intractable ones. He always believed that everything depends only on the initial data and the time spent searching for the missing ones.
During his stay in America, Grigory Yakovlevich often attended various events. Of particular interest to Perelman were the lectures given by the mathematician Richard Hamilton. This scientist also tried to prove the Poincare conjecture. Hamilton even developed his own method of Ricci flows, which, rather, was not related to mathematics, but to physics. However, all this was very interested in Grigory Yakovlevich.
After returning to Russia, Perelman literally plunged headlong into working on the problem. And after a short period of time, he managed to make significant progress in this matter. He approached the solution of the problem in a completely non-standard way. As a tool of proof, he used Ricci flows.
Perelman sent his calculations to an American colleague. However, he did not even try to delve into the calculations of the young scientist and flatly refused to carry out joint work.
Of course, his doubts can be easily explained. After all, citing evidence, Perelman relied more on the postulates available in theoretical physics. The topological geometric problem was solved by him with the help of related sciences. This method was at first glance completely incomprehensible. Hamilton did not understand the calculations and was skeptical about the unexpected symbiosis for him, which was used as evidence.
He did what he was interested in
In order to prove the Poincaré theorem (the mathematical formula of the Universe), Grigory Perelman did not appear in scientific circles for seven long years. Colleagues did not know what he was developing, what was the scope of his work. Many could not even answer the question "Where is Grigory Perelman now?".
Everything was resolved in November 2002. It was during this period that Perelman's 39-page work appeared on one of the scientific resources, where one could get acquainted with the latest developments and articles of physicists, in which proofs of the geometrization theorem were given. The Poincaré hypothesis was considered as a particular example to explain the essence of the study.
Simultaneously with this publication, Grigory Yakovlevich sent the work he had done to Richard Hamilton, as well as the mathematician Ren Tian from China, with whom he had communicated back in New York. The proof of the theorem was also obtained by several other scientists, whose opinion Perelman especially trusted.
Why was the work of several years of a mathematician's life so easily released, because these proofs could simply be stolen? However, Perelman, who completed the work for a million dollars, did not at all want to get hold of it or emphasize his uniqueness. He believed that if there was an error in his proofs, then they could be taken as a basis by other scientists. And that would give him satisfaction.
Yes, Grigory Yakovlevich was never an upstart. He always knew exactly what he wanted from life, and had his own opinion on any occasion, which often differed from the generally accepted one.
Money can not buy happiness
Why is Grigory Perelman famous? Not only by proving a hypothesis included in the list of seven mathematical problems millennia unsolved by scientists. The fact is, Grigory Perelman refused a million-dollar bonus, which the Boston Institute of Mathematics. Clay. And it didn't come with any explanation.
Of course, Perelman really wanted to prove the Poincaré conjecture. He dreamed of solving the puzzle, the solution of which was not received by anyone. And here the Russian scientist showed the passion of the researcher. At the same time, it was intertwined with the intoxicating feeling of self-awareness as a discoverer.
Grigory Yakovlevich's interest in the hypothesis moved into the category of "accomplished deeds." Does a true mathematician need a million dollars? Not! The main thing for him is a sense of his own victory. And it is simply impossible to measure it by earthly standards.
According to the rules, the Clay Prize can be awarded when a person who has solved one or several "millennium problems" at once sends his scientific article to the editors of the institute's journal. Here it is examined in detail and carefully checked. And only two years later, a verdict can be issued that will confirm or refute the correctness of the decision.
Verification of the results obtained by Perelman was carried out from 2004 to 2006. Engaged in this work three independent groups of mathematicians. All of them made an unambiguous conclusion that the Poincaré conjecture was proved completely.
The prize was awarded to Grigory Perelman in March 2010. For the first time in history, the award was to be given for solving one of the problems on the list of "mathematical problems of the millennium". However, Perelman simply did not come to the conference in Paris. On July 1, 2010, he publicly announced his refusal of the award.
Of course, for many people, Perelman's act seems inexplicable. The man simply refused honors and glory, and also missed the chance to move to America and live comfortably there until the end of his days. However, for Grigory Yakovlevich, all this does not carry any semantic load. Just like it used to be school lessons physical education.
retreat
To date, Grigory Perelman does not remind himself of himself in word or deed. Where does this outstanding person live? In Leningrad, in one of the usual high-rise buildings in Kupchino. Grigory Perelman lives with his mother. His personal life did not work out. However, the mathematician leaves no hope of starting a family.
Grigory Yakovlevich does not communicate with Russian journalists. He kept his contacts only with the foreign press. However, despite the seclusion, interest in this person does not fade away. Books are written about him. Grigory Perelman is often mentioned in scientific articles and essays. Where is Grigory Perelman now? Still at home. Many believe that they will hear this name more than once, and perhaps in connection with the solution of the next “millennium problem”.
The brilliant mathematician Grigory Perelman shocked the scientific world by proving the Poincare conjecture - one of the most difficult riddles millennium. And the townsfolk were surprised by the refusal of a poor scientist from the prescribed bonus of a million dollars. 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 life. The facts of the scientist's childhood, youth and personal life are known from the words of neighbors, school teachers and classmates, 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 nationality. The Jewish boy from childhood showed incredible abilities and interest in learning. At a time when peers were chasing 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 sciences, is not a relative of Grigory Yakovlevich.
Gregory's father is an electrical engineer. In 1993, Perelman Sr. immigrated to his historical homeland in Israel, like thousands of his compatriots in the 90s. The mother of the future outstanding mathematician stayed with the children in Leningrad, taught mathematics at the school.
Grigory Yakovlevich has a younger sister who has built a scientific career. After receiving a degree in mathematics at 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 significantly surpassed his classmates in knowledge, he easily counted three-digit numbers in his mind. Perelman's teachers recall that the student had conversations on an equal footing with adults.
The magic of logic and numbers attracted Grigory Yakovlevich. From the 5th grade, the boy attended the mathematical center at the Palace of Pioneers. The young geeks were mentored by an associate professor Pedagogical University named after Sergei Rukshin. Young Grisha received awards for participating in olympiads, including highest mark at the International Mathematical Olympiad.
After graduating from a nine-year school in an ordinary Leningrad school, the graduate moved to a specialized physical and mathematical school No. 239. Without a doubt, the hardworking and talented Perelman studied perfectly. Summed up physical training. The failure to pass the TRP standards prevented the graduate from getting a gold medal.
It is not surprising that after the school bench, Gregory without entrance exams admitted to the Leningrad State University at the Faculty of Mathematics and Mechanics. At the university, Perelman continued to shine at the Olympiads, and received the Lenin Prize for excellent learning outcomes.
The science
After graduation, postgraduate studies followed, then a doctoral defense. As a result, the gifted scientist remained at his home university as a senior research fellow.
In the early 90s, the talented scientist went to the USA, where he visited several universities as part of the exchange of experience. In the United States, the mathematician gave lectures and met with colleagues. Soon the ascetic Perelman got 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 Perelman's passion for topology began a few years earlier. Earlier, the mathematician was able to prove the soul hypothesis, which preceded the study of the Poincaré hypothesis.
The meaning of the proof of the hypothesis, however, as well as the very essence, cannot be described plain language, understandable to those far from higher mathematics person. The discoveries made by the mathematician great value in studying the Universe, in working with nanotechnologies.
In addition, the hypothesis states that the peculiarity of the shape of the universe leads to the fact that it can be contracted to a single point. This, in turn, indirectly confirms the theory big bang. Proponents of the theological origin of the universe got a reason to doubt God as the creator of all things. The Poincaré hypothesis proves that there is no God.
In 2002-2003, Perelman published articles revealing the essence of the proof. Three independent groups of mathematicians, having checked the arguments, confirmed the complete proof.
In 2003, Perelman visited the United States, lectured about his own discovery, and shared his experience with his compatriots. And in 2005, the scientist suddenly leaves the department and locks himself in an apartment in Kupchino, where he lives with his sick mother.
Personal life
A reclusive lifestyle leaves hundreds of questions. The main one that interests journalists and citizens is the reason why Grigory Perelman refused the money that rightfully belongs to him. It's about about the Clay Institute Prize. The Mathematical Institute has compiled a list of seven riddles for which a million dollar reward is due. The Poincaré hypothesis was included in this list.
Of course, having learned about the discovery of the Russian scientist, the founders immediately turned to the scientist. What was everyone's surprise when the mathematician refused a million dollars without explanation.
Soon, Grigory Yakovlevich completely stopped communicating with the press. He simply ignores Russian journalists and refuses to give interviews to foreign ones. News of the scientist's similar behavior led to rumors about Perelman's illness. It was claimed that the genius suffers from autism. However, reliable evidence or conclusions of doctors have not yet been made public.
It is known that the scientist lives with his mother, who is seriously ill. The mathematician does not have a wife. According to the stories of the teacher Grigory Yakovlevich, who maintains a relationship with him, mother and son live in poverty.
In 2018, information appeared that the mathematician had moved to Sweden. However, sources in the person of neighbors and store sellers denied the rumors and confirmed that Perelman did not leave anywhere.
- While working in the States, the scientist surprised his foreign colleagues with his unpretentiousness and detachment from everyday needs. The favorite food of the mathematician 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 fond of music. Mother instilled in her son the adoration of classical composers. She, being a talented violinist, introduced Grisha to the instrument. Perelman attended music school with pleasure, and then he faced a difficult choice - to enter the conservatory or to devote himself to the exact sciences.
- Statements by conspiracy theorists have appeared on the Web that Perelman is the most powerful 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 not train your brain?
There is no such thing as an unsolvable problem. Difficult to solve. So more precisely.
Remember the biblical legend about how Jesus Christ walked on water, like dry land? So I had 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 Institute of Mathematics Award
Friends and neighbors of the world-famous mathematician dispelled rumors about his "oppressed state."
Grigory Perelman, the world-famous Russian mathematician who proved the Poincaré conjecture and subsequently refused a $1 million prize, reluctantly fell into the public spotlight again. The reason for the disturbing rumors was the post of a resident of St. Petersburg, who wrote on his page that he had recently seen Mr. Perelman. According to the Petersburger, appearance famous mathematician left much to be desired and in general he “dies”, and “ is at the line beyond which only starvation follows».
Many Internet users who read this post decided to look for Perelman to give him all possible help. However, a day later, the author of the publication for some reason deleted his news. Fortunately, one of the scientist's friends was immediately found, Mikhail Bogomolov, who hastened to calm the alarmed public.
According to Mr. Bogomolov, Perelman found. He is alive and well and continues to quietly and modestly engage in science. A familiar mathematician in a media commentary said that worries about a scientist today are groundless, since next to him there is a close person who supports him in everything, as such brilliant people should be. It also became known that Perelman not alien to the Internet, but he does not pay attention to all sorts of "fuss" around him.
Gossip about the “sad fate” of a mathematician in an interview with the media was also dispelled by one of the neighbors Grigory Perelman. According to the woman, she also does not understand all the commotion that the public made around the scientist. A neighbor mathematician said that Grigory Yakovlevich he never paid much attention to his appearance, especially since he was never bothered by wrinkled trousers or a shirt.
It is known that Perelman goes outside infrequently and does so only when absolutely necessary, such as going to the grocery store. At the same time, he always tries to go unnoticed, for which he puts on huge glasses, pulls a scarf over his face and covers himself with a hood.
The mathematician lives very quietly, he does not bother the neighbors, and he turned off the home phone in the apartment a long time ago, because he does not use it at all. The bell does not work in the apartment, the intercom is turned off, and in general, guests in his house are a rare phenomenon. However, if, willy-nilly, any meeting occurs, Perelman always greets, smiles politely, but at the same time hurries to go further faster.
The scientist's neighbors have long been accustomed to the oddities of their illustrious neighbor, and prefer not to interfere with him in the space in which the mathematician is very comfortable. Residents of the house note that when Perelman alarming reports appeared in the press, various journalists began to appear in the yard, which is why the mathematician can now completely “get stuck” in his apartment, since excessive attention, especially from the media, obviously irritates him greatly.
The scientist's neighbors also noticed that he did not need help from strangers, but even if he needed it, he would hardly accept it due to his character and life habits.
About life Perelman also told another person who monitors his activities. According to the Petersburger, the scientist maintains contacts with some of his colleagues via the Internet. Those, by the way, are also interested in his life and health, offer help, but he always categorically refuses any outside help, even from his good friends in science.
Alexander Shevchenko
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Magazine version of one of the chapters of the new book Nick. Gorky "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 received a gold medal at the International Mathematical Olympiad in Budapest, entered Leningrad University. He was noticeably different from 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 was not very quick in making decisions. The speed of the solution does not mean anything, mathematics is not built on speed. Mathematics depends on depth."
After graduating from the university, Grigory Perelman became an employee of the Steklov Mathematical Institute, published a number of interesting articles on three-dimensional surfaces in Euclidean spaces. The world mathematical community appreciated his achievements on merit. In 1992, Perelman was invited to work at New York University.
Gregory ended up in one of the world's centers of mathematical thought. Every week he went to a seminar in Princeton, where one day he listened to a lecture by the eminent mathematician, professor at Columbia University, Richard Hamilton. After the lecture, Perelman approached the professor and asked a few questions. Perelman later recalled 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 didn't publish until a few years later. He shared it with me without hesitation. I really liked his openness and generosity. I can say that in this Hamilton was not like most other mathematicians.
Perelman spent several years in the USA. He walked around New York in the same corduroy jacket, ate mostly bread, cheese and milk, and worked non-stop. He began to be invited to the most prestigious universities in America. The young man chose Harvard and then faced the fact that he categorically did not like it. The recruitment committee required an autobiography and letters of recommendation from other scientists from the applicant. Perelman's reaction was harsh: “If they know my work, then they don't need my biography. If they want my biography, they don't know my work." He refused all offers and returned to Russia in the summer of 1995, where he continued to work on the ideas that Hamilton 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 made some progress in his research, he wrote a letter to Hamilton, hoping for a joint work. However, he did not answer, and Perelman had to proceed alone. But ahead of him was waiting for world fame.
In 2000, the Clay Mathematics Institute published a Millennium Problem List, which included seven classic mathematics problems that have been unsolved 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 he summed up his many years of efforts to prove one problem from the list on 39 pages. American mathematicians, who knew Perelman personally, immediately began to discuss the article, which proved the famous Poincaré conjecture. 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, where he showed how he managed to turn the Poincaré conjecture into a theorem. The mathematical community recognized Perelman's lectures exclusively important event and made considerable efforts to verify the proposed evidence.
Details for the curious
Poincare problem
Jules Henri Poincaré (1854-1912) - an outstanding French mathematician, mechanic, physicist, astronomer and philosopher, head of the Paris Academy of Sciences and a member of more than 30 academies of sciences in 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, which can be obtained from one another by stretching and bending, without cuts and gluing, are considered the same in topology (as an illustrative example, the transformation of a cup into a donut is often shown). 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 conjecture by Grigory Perelman made it possible to develop a new methodological approach to solving topological problems, which is of great importance for further development mathematics.
Paradoxically, Perelman did not receive grants to prove the Poincaré hypothesis, and other scientists who tested his correctness received grants worth a million dollars. Verification was extremely important, because many mathematicians worked on the proof of this problem, and if it was really solved, then they remained out of work.
The mathematical community tested Perelman's proof for several years and by 2006 came to the conclusion that it was correct. Yuri Burago then wrote: “The proof closes a whole 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 precise science, where there is no place for emotions and intrigues. But even here there is a struggle for priority. Passions boiled around the proof of the Russian mathematician. Two young mathematicians, immigrants from China, having studied the work of Perelman, 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 contains many gaps that they managed to fill. According to the rules of the mathematical community, the priority in proving a theorem belongs to those researchers who managed to present it in the most complete form. According to many experts, Perelman's proof was complete, although brief. 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 cannot say that I am outraged, the rest are doing even worse. Of course, there are many 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: “It is not those who violate ethical standards in science that are considered outsiders. People like me are the ones who end up in isolation.”
In 2006, Grigory Perelman was awarded the highest honor in mathematics, the Fields Medal. But the mathematician, leading 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 for ten hours persuaded Perelman to accept a well-deserved award, which was planned to be presented at the 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 to be historical event However, Perelman politely but adamantly said: "I refuse." The Fields medal, according to Gregory, did not interest him at all: “It does not matter. Everyone understands that if the proof 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 was going to be presented to him 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 the contribution of Richard Hamilton no less. The winner of many mathematical prizes, the Soviet, American and French mathematician M. L. Gromov supported Perelman: “For great things, a clear mind is needed. You have to think only about mathematics. Everything else is human weakness. To accept a reward is to show weakness."
The rejection of 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 Poincare conjecture remains the only solved problem from the list of the millennium. Perelman became the number one mathematician in the world, although he refused to contact his colleagues. Life has shown that outstanding results in science were often achieved by individuals who were not part of the structure modern science. That was Einstein. 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 was Perelman, who neglected the rules of conduct in the scientific community and at the same time achieved the maximum efficiency of his work, proving the Poincaré hypothesis.
The Clay Institute of Mathematics (Cambridge, USA) was founded in 1998 by businessman Landon Clay and mathematician Arthur Jeffey to increase and disseminate mathematical knowledge.
The Fields Prize for Excellence in Mathematics has been awarded since 1936.
Grigory Yakovlevich Perelman(b. June 13, 1966, Leningrad, USSR) - outstanding, the first to prove the Poincare conjecture.
Grigory Perelman was born on June 13, 1966 in Leningrad into a Jewish family. His father Yakov was an electrical engineer and emigrated to Israel in 1993. Mother, Lyubov Leibovna, remained in St. Petersburg, worked as a mathematics teacher at a vocational school. It was the mother, who played the violin, who instilled in the future mathematician a love for classical music.
Until grade 9, Perelman studied at high school on the outskirts of the city, however, in the 5th grade he began studying at the mathematical center at the Palace of Pioneers under the guidance of associate professor of the Russian State Pedagogical University Sergey 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 a full score for the perfect solution of all problems. Perelman graduated from the 239th Physics and Mathematics School in Leningrad. He played table tennis well, attended a music school. gold medal I didn’t get it only because of physical education, without passing the TRP standards.
He was enrolled without exams in the Faculty of Mathematics and Mechanics of the Leningrad State University. He won at faculty, city and all-Union student mathematical Olympiads. All the years I studied only "excellently". For academic success, he received a Lenin scholarship. After graduating with honors from the university, he entered graduate school (supervisor - Academician A. D. Aleksandrov) at the Leningrad Department 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 researcher.
In the early 1990s, Perelman came to the United States, where he worked as a researcher at various universities, where one of the most difficult, at that time not yet solved, problems of modern mathematics, the Poincaré Conjecture, attracted his attention. He surprised his colleagues with the austerity of life, his favorite food was milk, bread and cheese. In 1996 he returned to St. Petersburg, continuing to work at POMI, where he worked alone on solving the Poincare Problem.
In 2002-2003, Grigory Perelman published his three famous articles on the Internet, in which he summarized his original method for solving the Poincare 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 made a series of presentations on his work in proving the Poincare 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 e-mail.
In 2004-2006, three independent groups of mathematicians were engaged in verification of Perelman's results: 1) Bruce Kleiner, John Lott, University of Michigan; 2) Zhu Xiping, Sun Yat-sen University, Cao Huaidong, Lehai University; 3) John Morgan, Columbia University, Gan Tian, Massachusetts technological Institute. All three groups concluded that the Poincaré problem had been successfully solved, but Chinese mathematicians Zhu Xiping and Cao Huaidong, along with their teacher Yau Xingtang, attempted to plagiarize, claiming that they had found a "complete proof". They subsequently retracted this statement.
In December 2005, Grigory Perelman resigned as a leading researcher at the Laboratory of Mathematical Physics, resigned from POMI, and almost completely cut off contacts with colleagues.
To further scientific career showed no interest. Currently, he lives in Kupchino in the same apartment with his mother, leads a secluded life, ignores the press.
Scientific contribution
Main article: Poincare 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 school of geometry, at the beginning of his work on the Poincare Problem, 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 pioneering work on solving one of the special cases of William Thurston's geometrization conjecture, from which the famous Poincaré conjecture, formulated by the French mathematician, physicist and philosopher Henri Poincaré in 1904, follows. The method described by the scientist for studying the Ricci flow is called Hamilton-Perelman theories.
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 for solving the Poincaré conjecture (the official wording of the award was: “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.
In 2006, the journal Science named the proof of Poincaré's theorem the Scientific Breakthrough of the Year. Breakthrough of the Year). This is the first work in mathematics that has earned such a title.
In 2006, Sylvia Nazar and David Gruber published "Manifold Destiny," an article about Grigory Perelman, his work on the Poincare Problem, ethical principles in science and the mathematical community, and a rare interview with him. The article devotes considerable space to the criticism of the Chinese mathematician Yau Xingtang, who, together with his students, tried to challenge the completeness of the proof of the Poincare Conjecture 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 Shintang and the scandal associated with accusations against him of trying to belittle Perelman's contribution to the proof of the Poincaré Hypothesis. The article cites a fact unheard of in mathematics - Yau Shintang hired a law firm to defend his case and threatened to sue his critics.
In 2007, the British newspaper The Daily Telegraph published a list of "One Hundred Living Geniuses", in which Grigory Perelman takes 9th place. In addition to Perelman, only 2 Russians made it to this list - Garry Kasparov (25th place) and Mikhail Kalashnikov (83rd place).
In March 2010, the Clay Mathematical Institute awarded Grigory Perelman a $1 million prize for proving the Poincaré Conjecture, the first ever award for solving a Millennium Problem. In June 2010, Perelman ignored a mathematical conference in Paris, which was supposed to present the Millennium Prize for proving the Poincaré conjecture, and on July 1, 2010 he publicly announced his refusal of the prize, motivating it as follows:
Note that such a public assessment of the merits of Richard Hamilton by a mathematician who proved the Poincare Conjecture 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, faced with insurmountable technical difficulties.
In September 2011, the Clay Institute, together with the Henri Poincaré Institute (Paris), established 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 Christodoul were awarded the so-called. The $1,000,000 Shao Prize in Mathematics, also sometimes referred to as the Nobel Prize of the East. Richard Hamilton was awarded for the creation of a mathematical theory, which was then developed by Grigory Perelman in his work on the proof of the Poincaré conjecture. It is known that Hamilton accepted this award.
Interesting Facts
- In his work "The entropy formula for the Ricci flow and its geometric applications" (Eng. The entropy formula for the Ricci flow and its geometric applications) Grigory Perelman, not without humor, modestly indicates that his work was partially financed by personal savings saved during his visits to the Courant Institute mathematical sciences, the State University of New York (SUNY), the State University of New York at Stony Brook, and the University of California at Berkeley, and would like to thank the organizers of these trips. At the same time, the official mathematical community allocated millions of grants to individual research groups in order to understand and test Perelman's work.
- When a member of the hiring committee at Stanford University asked Perelman for C.V. (summary), as well as letters of recommendation, Perelman opposed:
- The article Manifold Destiny was noticed by the eminent mathematician Vladimir Arnold, who offered to reprint it in the Moscow journal Uspekhi matematicheskikh nauk, where he was a member of the editorial board. The editor-in-chief of the magazine, Sergei Novikov, refused him. According to Arnold, the refusal was due to the fact that Chief Editor magazine was afraid of revenge from Yau, as he also worked in the United States.
- 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, colleagues and colleagues. Perelman's teacher Sergei Rukshin was critical of the book.
- Grigory Perelman became the main actor documentary film The Enchantment of the Poincaré Hypothesis directed by Masahito Kasuga, filmed by the Japanese public broadcaster NHK in 2008.
- In April 2010, the release of the “Millionaire from Khrushchev” talk show “Let them talk” was dedicated to Grigory Perelman. Grigory's friends, his school teachers, as well as journalists who communicated with Perelman took part in it.
- In the 27th edition of "Big Difference" on Channel One, a parody was presented in the hall on Grigory Perelman. 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 well-known popularizer of physics, mathematics and astronomy. However, Ya. I. Perelman died more than 20 years before the birth of Grigory Perelman.
- April 28, 2011 TVNZ"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 claims are true. Vladimir Gubailovsky also believes that the interview with Perelman is fictitious.
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