« Millennium Challenge", solved by a Russian mathematical genius, has to do with the origin of the Universe. Not every mathematician can understand the essence of the riddle...
MIND GAME
Until recently, mathematics did not promise either fame or wealth to its “priests”. They weren't even given the Nobel Prize. There is no such nomination. After all, according to a very popular legend, Nobel’s wife once cheated on him with a mathematician. And in retaliation, the rich man deprived all their crooked brethren of his respect and prize money.
The situation changed in 2000. The private mathematical Clay Mathematics Institute selected seven of the most difficult problems and promised to pay a million dollars for solving each one.
They looked at the mathematicians with respect. In 2001, the film “A Beautiful Mind” was even released, the main character of which was a mathematician.
Now only people far from civilization are not aware: one of the promised millions - the very first - has already been awarded. The prize was awarded to a Russian citizen, a resident of St. Petersburg Grigory Perelman. He proved the Poincaré conjecture, a puzzle that had eluded anyone for more than 100 years and which, through his efforts, became a theorem.
Our cute 44-year-old bearded man has rubbed his nose in the eyes of the whole world. And now it continues to keep it - the world - in suspense. Since it is unknown whether the mathematician will take the honestly deserved million dollars or refuse. The progressive public in many countries is naturally worried. At least newspapers on all continents chronicle the financial and mathematical intrigue.
And against the background of these fascinating activities - fortune telling and dividing other people's money - the meaning of Perelman's achievement was somehow lost. The President of the Clay Institute, Jim Carlson, of course, stated at one time that the purpose of the prize fund was not so much a search for answers as an attempt to increase the prestige of mathematical science and to interest young people in it. But still, what is the point?
Grisha in his youth - even then he was a genius.
POINCARE HYPOTHESIS - WHAT IS IT?
The riddle solved by the Russian genius touches on the basics of a branch of mathematics called topology. Its topology is often called “rubber sheet geometry.” It deals with the properties of geometric shapes that are preserved if the shape is stretched, twisted, or bent. In other words, it is deformed without tears, cuts or gluing.
Topology is important to mathematical physics because it allows us to understand the properties of space. Or evaluate it without being able to look at the shape of this space from the outside. For example, to our Universe.
When explaining the Poincaré conjecture, they begin like this: imagine a two-dimensional sphere - take a rubber disk and pull it over the ball. So that the circumference of the disk is collected at one point. In a similar way, for example, you can tie a sports backpack with a cord. The result is a sphere: for us - three-dimensional, but from the point of view of mathematics - only two-dimensional.
Then they offer to pull the same disk onto a donut. It seems like it will work out. But the edges of the disk will converge into a circle, which can no longer be pulled to a point - it will cut the donut.
As another Russian mathematician, Vladimir Uspensky, wrote in his popular book, “unlike two-dimensional spheres, three-dimensional spheres are inaccessible to our direct observation, and it is as difficult for us to imagine them as it was for Vasily Ivanovich to imagine the square trinomial from the famous joke.”
So, according to the Poincaré hypothesis, a three-dimensional sphere is the only three-dimensional thing whose surface can be pulled to one point by some hypothetical “hypercord”.
Grigory Perelman: - Just think, Newton's binomial...
Jules Henri Poincaré suggested this in 1904. Now Perelman has convinced everyone who understands that the French topologist was right. And turned his hypothesis into a theorem.
The proof helps to understand what shape our Universe has. And it allows us to very reasonably assume that it is that same three-dimensional sphere.
But if the Universe is the only “figure” that can be contracted to a point, then, probably, it can be stretched from a point. This serves as an indirect confirmation of the Big Bang theory, which states that the Universe originated from a point.
It turns out that Perelman, together with Poincaré, upset the so-called creationists - supporters of the divine beginning of the universe. And they shed grist to the mill of materialist physicists.
The brilliant mathematician from St. Petersburg Grigory Perelman, who became famous throughout the world for proving the Poincaré conjecture, finally explained his refusal of the million-dollar prize awarded for this. According to Komsomolskaya Pravda, the reclusive scientist revealed himself in a conversation with a journalist and producer of the President-Film film company, which, with Perelman’s consent, will film the feature film “Formula of the Universe” about him.
Alexander Zabrovsky was lucky enough to communicate with the great mathematician - he left Moscow for Israel several years ago and guessed to first contact Grigory Yakovlevich’s mother through the Jewish community of St. Petersburg, providing her with help. She talked to her son, and after her good characterization, he agreed to a meeting. This can truly be called an achievement - the journalists were not able to “catch” the scientist, although they sat at his entrance for days.
As Zabrovsky told the newspaper, Perelman gave the impression of an “absolutely sane, healthy, adequate and normal person”: “Realistic, pragmatic and sensible, but not without sentimentality and passion... Everything that was attributed to him in the press, as if he was “out of his mind” - complete nonsense! He knows exactly what he wants and knows how to achieve his goal."
The film, for which the mathematician made contact and agreed to help, will not be about himself, but about the cooperation and confrontation of the three main world mathematical schools: Russian, Chinese and American, which are the most advanced in the path of studying and managing the Universe.
When asked why Perelman refused the million, he replied:
“I know how to control the Universe. And tell me, why should I run for a million?”
The scientist is offended by what he is called in the Russian press
Perelman explained that he does not communicate with journalists because they are not interested in science, but in matters of a personal and everyday nature - from the reasons for refusing a million to the question of cutting hair and nails.
He doesn’t want to contact the Russian media specifically because of the disrespectful attitude towards him. For example, in the press they call him Grisha, and such familiarity offends him.
Grigory Perelman said that since his school years he was accustomed to what is called “training the brain.” Recalling how, as a “delegate” from the USSR, he received a gold medal at the Mathematical Olympiad in Budapest, he said: “We tried to solve problems where the ability to think abstractly was a prerequisite.
This distraction from mathematical logic was the main point of daily training. To find the right solution, it was necessary to imagine a “piece of the world.”
As an example of such a “difficult to solve” problem, he gave the following: “Remember the biblical legend about how Jesus Christ walked on water as well as on dry land. So I needed to calculate how fast he had to move through the waters so as not to fall through.” .
Since then, Perelman has devoted all his activities to the study of the problem of studying the properties of the three-dimensional space of the Universe: “This is very interesting. I am trying to embrace the immensity. But any immensity is also embraceable,” he argues.
The scientist wrote his dissertation under the guidance of Academician Alexandrov. “The topic was not difficult: “Saddle-shaped surfaces in Euclidean geometry.” Can you imagine surfaces of equal size and unevenly spaced from each other at infinity? We need to measure the “hollows” between them,” the mathematician explained.
What does Perelman’s discovery mean, frightening the world’s intelligence services?
Poincaré's statement is called the “formula of the Universe” because of its importance in the study of complex physical processes in the theory of the universe and because it provides an answer to the question of the shape of the Universe. This evidence will play a big role in the development of nanotechnology."
“I learned to calculate voids, together with my colleagues we are learning the mechanisms of filling social and economic “voids,” he said. “Voids are everywhere. They can be calculated, and this provides great opportunities ...
As the publication writes, the scale of what Grigory Yakovlevich discovered, actually moving ahead of today's world science, made him an object of constant interest for intelligence services, not only Russian, but also foreign.
He acquired some super-knowledge that helps him understand the universe. And here questions of this kind arise: “What will happen if his knowledge finds practical implementation?”
Essentially, the intelligence services need to know whether Perelman, or more precisely, his knowledge, poses a threat to humanity? After all, if with the help of his knowledge it is possible to collapse the Universe into a point and then expand it, then we can die or be reborn in a different capacity? And then will it be us? And do we even need to control the Universe?
AND AT THIS TIME
Mom of a genius: “Don’t ask us questions about money!”
When it became known that the mathematician had been awarded the Millennium Prize, a crowd of journalists gathered in front of his door. Everyone wanted to personally congratulate Perelman and find out whether he would take his rightful million.
We knocked on the flimsy door for a long time (if only we could replace it with bonus money), but the mathematician did not open it. But his mother quite clearly dotted the i’s right from the hallway.
We don’t want to talk to anyone and we’re not going to give any interviews,” Lyubov Leibovna shouted. - And don’t ask us questions about this bonus and money.
People living in the same entrance were very surprised to see the sudden interest in Perelman.
Has our Grisha really gotten married? - one of the neighbors grinned. - Oh, I received a prize. Again. No, he won't take it. He doesn’t need anything at all, he lives on pennies, but he’s happy in his own way.
They say that the day before the mathematician was seen with full bags of groceries from the store. I was preparing to “hold the siege” with my mother. The last time there was a fuss about the award in the press, Perelman didn’t leave his apartment for three weeks.
BY THE WAY
Why else would they give a million dollars...
In 1998, with funds from billionaire Landon T. Clay, the Clay Mathematics Institute was founded in Cambridge (USA) to popularize mathematics. On May 24, 2000, the institute's experts selected the seven most, in their opinion, puzzling problems. And they assigned a million dollars for each.
1. Cook's problem
It is necessary to determine whether checking the correctness of a solution to a problem can take longer than obtaining the solution itself. This logical task is important for specialists in cryptography - data encryption.
2. Riemann hypothesis
There are so-called prime numbers, such as 2, 3, 5, 7, etc., which are only divisible by themselves. It is not known how many there are in total. Riemann believed that this could be determined and a pattern of their distribution could be found. Whoever finds it will also provide cryptography services.
3. Birch and Swinnerton-Dyer conjecture
The problem involves solving equations with three unknowns raised to powers. You need to figure out how to solve them, regardless of complexity.
4. Hodge conjecture
In the twentieth century, mathematicians discovered a method for studying the shape of complex objects. The idea is to use simple “bricks” instead of the object itself, which are glued together and form its likeness. It is necessary to prove that this is always permissible.
5. Navier - Stokes equations
It’s worth remembering them on the plane. The equations describe the air currents that keep it in the air. Now equations are solved approximately, using approximate formulas. We need to find the exact ones and prove that in three-dimensional space there is a solution to the equations that is always true.
6. Yang - Mills equations
There is a hypothesis in the world of physics: if an elementary particle has mass, then there is a lower limit to it. But which one is not clear. We need to get to him. This is perhaps the most difficult task. To solve it, it is necessary to create a “theory of everything” - equations that unite all forces and interactions in nature. Anyone who can do it will probably receive a Nobel Prize.
The oddities of a great man are commensurate with his genius. Therefore, when the mathematical world learned that the reclusive St. Petersburg mathematician Grigory Yakovlevich Perelman refused a million-dollar prize for proving the Poincaré conjecture, everyone understood that a new Carl Friedrich Gauss had appeared in Russia, who hid his discovery of non-Euclidean geometry in secret.
The story is like this. In 2006, Science magazine called Perelman’s proof of Poincaré’s theorem a scientific breakthrough, and a year later, the British newspaper The Daily Telegraph published a list of “One Hundred Living Geniuses,” in which Grigory Perelman ranks 9th. Besides Perelman, only 2 Russians were included in this list - Garry Kasparov and Mikhail Kalashnikov.
G. Perelman's discovery was awarded the highest mathematical award - the international Fields Medal Prize, equivalent to the Nobel Prize (as is known, there is no Nobel Prize for work in the field of mathematics). 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”). And in March 2010, the Clay Mathematics Institute awarded Grigory Perelman a prize of one million US dollars for proving the Poincaré conjecture. This marked the first time in history that a prize had been awarded for solving one of the Millennium Problems. So: Perelman refused both Fields and the prize, citing the following reason: “I refused. You know, I had a lot of reasons in both directions. That's why it took me so long to decide. In short, the main reason is disagreement with the organized mathematical community. I don't like their decisions, I think they are unfair. I believe that the contribution of the American mathematician Hamilton to solving this problem is no less than mine.”
My task does not include either an analysis of the Poincaré problem or Perelman’s argumentation (see Appendix) - these questions are far from the understanding of the “intellectual majority”, which, if they are interested in the Perelmans, is not in their discoveries, but in their deviations from the norm. And Perelman’s deviations from the norm really overwhelmed him: an unsociable man-mystery, who voluntarily left a prestigious job, chose the lifestyle of an ascetic in a tiny apartment in a St. Petersburg Khrushchev building, for many years after Poincaré’s proven hypothesis did not work anywhere, who declared that he was done with science, did not fundamentally giving an interview and surviving from bread and water on the meager pension of his elderly mother and only once declaring: “There is nothing to live on.”
I do not claim that the homeland abandoned its hero. They say that some St. Petersburg university invited him to teach, offering the would-be millionaire a salary of $300. Perelman refused the pitiful handout, believing that it was impossible to consider science as a commodity...
However, the point is not in the assessment of work, but in moral criteria and something else hidden. Because despite all the oddities of this undeniably great man, he agreed to work in a Swedish company engaged in scientific development and guaranteed him a decent life, comfortable housing and doing what he loved.
Israeli television producer Alexander Zabrovsky, who was eager to make a feature film about Perelman and spent several years persuading the mathematician to agree to this, said that it was he who helped Grigory Yakovlevich find a job he liked and solve his financial problems:
- He was given a decent monthly salary and given housing in one of the small towns in Sweden. Now he is doing what he loves and no longer experiences financial problems. Mom went with him. Grigory Yakovlevich’s half-sister is also there. Science knows no geographical or national barriers. The main thing is that his mind benefits society and that he himself feels good and comfortable. The work is related to nanotechnology.
Perelman received a foreign passport and a visa valid for 10 years; the documents indicated the reason for the trip - “scientific activity.”
Vladimir Fok, a mathematics teacher at the University of Strasbourg, comments on the situation: “Russian scientists have two main problems - very low wages and dependence on an incompetent administration. People who have nothing to do with science like to put a spoke in the wheels, although they should help.
I myself went to Strasbourg for this reason, although I tried to stay in Russia and worked on temporary contracts. But my institute, in my opinion, ceased to exist as a scientific institution and I was forced to emigrate. Now about 80% of students go abroad. And eminent scientists are also leaving the country. To all the difficulties of a scientist there is also added public condemnation - in our country, being a man of science is the same as being a fool. While in the West such social status commands respect.”
Apparently, Grigory Yakovlevich decided to be closer to his family, to his sister, who also received a mathematical education. He took his old mother with him.
“I feel infinitely sorry for Grisha’s mother,” Sergei Rukshin, a teacher and friend of the Fields laureate, commented on the situation. “She has long needed good medicine and special care, which Grisha could not provide. I and other people who knew him closely repeatedly offered help, including financial help, but he constantly refused. He is always extremely scrupulous with money.
It is almost impossible to stop emigration from Russia. Western countries still look attractive to residents of the ravaged country. This applies both to material well-being and to the stability associated with respect for civil liberties and peace, which intellectuals crave. The loss of millions of their fellow citizens in the 20th century, and far from the worst, is a very bitter lesson for Russia.
Academician Ludwig Faddeev, director of the Mathematical Institute. V.A. Steklova, in one of the issues of the magazine “In the World of Science” (2014, No. 2) wrote: “Our institute had 110 employees, of which 70 were doctors. 40 left.” That is, more than half of the highly qualified scientists emigrated ... They didn’t just leave, they changed the face of the science of sciences - foreign mathematics...”
At the Institute of High Pressure Physics named after. Vereshchagin RAS in 1988 employed 700 people, now - 150... In my NSC KIPT - 6500, now - 2300...
The number of highly qualified specialists who left Russia has more than doubled in three years - from 20 thousand people in 2013 to 44 thousand people in 2016. The chief scientific secretary of the Presidium of the Russian Academy of Sciences, Nikolai Dolgushkin, spoke about this at the general meeting of the Russian Academy of Sciences. “The average age of a researcher exceeded 50 years, and one in three has reached retirement age,” he added. “Since 1990, the number of researchers in the country has decreased by 2.7 times, and the average annual reduction in personnel involved in research and development has been 1.3% per year since 2000,” Dolgushkin said. In the European Union and the USA, the number of scientists during this time increased by 2-3%, and in Brazil, Korea and China - from 7% to 10%.
Russian economist Leonid Grigoriev said that “two million democrats have left Russia over the past ten years,” and Alexander Shchetinin called the brain drain “a flight from the zombie-box empire.” The author of the article “The general flight of Russians from Russia” (http://besttoday.ru/read/5404.html) writes: “We have turned into a third world country in terms of infrastructure and security. We don't have proper schools, hospitals or universities. Any contact with the state requires money, nerves and papers, and more and more. Literally any part of the free living space is filled with bureaucratic instructions, just as in a locked room oxygen is replaced by carbon dioxide. And when the people who perpetrated the kirdyk on Russia explain to us what the problem is, they say: “It’s because there are enemies around.”
Number of people employed in science only from 1991 to 1999. in Russia decreased by more than half (from 878.5 thousand to 386.8 thousand people), and tens of thousands of Russian scientists moved to the United States alone. According to official statistics, up to 60% of Russians - winners of international Olympiads - go to work abroad. The most serious situation has developed in applied areas: the best specialists are leaving for foreign companies.
A few specific examples. Mikhail Leonidovich Gromov is a world-famous mathematician, Doctor of Physical and Mathematical Sciences, Abel Prize laureate. Emigrated in 1974 to the USA. The Abel Prize in mathematics is also considered the equivalent of the Nobel Prize. It was awarded to Mikhail Leonidovich Gromov for “his revolutionary contribution to geometry.”
David (Dmitry Aleksandrovich) Kazhdan is an Israeli, former Soviet and American mathematician. He emigrated from the USSR in the mid-1970s to the USA, and in 2002 he moved to Israel. David Kazhdan is a member of the US National Academy of Sciences, the American Academy of Arts and Sciences, and the Israeli Academy of Sciences. In 2012 he became a laureate of the State Prize in Mathematics and Computer Science. Professor Kazhdan made major contributions to the development of group theory, which is the cornerstone of mathematics, but its principles also extend to physics, quantum theory and computer science.
Voevodsky Vladimir Aleksandrovich is a Russian and American mathematician, one of the outstanding innovating scientists of our time in the field of algebraic geometry. In 2002, Vladimir Voevodsky became the winner of the John Fields Prize, the highest award of the International Congress of Mathematicians. After graduating from Moscow State University, he completed an internship at Harvard and immigrated to the USA. Now he is a professor at the Institute for Advanced Studies at Princeton.
Andrei Konstantinovich Geim is a famous physicist, winner of the 2010 Nobel Prize in Physics, a member of the Royal Society of London, known as one of the discoverers of graphene, a two-dimensional allotropic modification of carbon. On December 31, 2011, by decree of Queen Elizabeth II, he was awarded the title of knight for services to science with the official right to add the title “sir” to his name. The achievements of Phystech graduates Andrei Geim and Konstantin Novoselov are now proud of as their own in the UK.
Abrikosov Aleksey Alekseevich is a famous physicist, Nobel Prize laureate in physics (2003), academician of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences. The main work was done in the field of condensed matter physics. In 1991 he moved to the USA.
Lev Petrovich Gorkov - Soviet-American physicist, academician of the USSR Academy of Sciences, academician of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences. In 1991, Gorkov immigrated to the United States, where he worked at the University of Illinois at Urbana-Champaign and then as director of the National High Magnetic Field Laboratory in Tallahassee, Florida. In 2005, Lev Petrovich was elected a member of the US National Academy of Sciences.
Simon Smith Kuznets is an economist, statistician, demographer and economic historian. Winner of the 1971 Nobel Prize in Economics "for his empirically based interpretation of economic growth, which has led to new and deeper understanding of economic and social structure and the development process as a whole." The name of Kuznets is associated with the formation of economics as an empirical scientific discipline and the development of quantitative economic history.
Leonid Solomonovich Gurvich - economist, honorary professor at the University of Minnesota. Worked on the Coles Commission and won the 2007 Nobel Prize in Economics. Known as one of the founders of the theory of optimal mechanisms.
Professor Andrey Gudkov, Senior Vice-President of the Oncological Institute named after. Roswell Park, Buffalo, USA, author of more than a hundred scientific papers in the field of cancer treatment writes:
- You can talk about a feeling of gratitude and debt to the society that raised you and gave you knowledge. For me, such an unpaid debt is, first of all, education, which I could pass on to young people while living in Russia. But, on the other hand, I am sincerely convinced that I bring more benefit to science with my work abroad, since the technical capabilities and speeds available there make it possible to achieve incomparable results per unit of time. I'm happy where I'm working now. There are about 40 Russian-speaking families in Buffalo - we are creating a micro-society, no one is forcing us to change our culture. There is no ideology here, we are trying to work in the Russian Federation, but it is unlikely that I will return: firstly, I am many years old, and secondly, it seems to me that it is more useful to continue an existing business than to start something here again.
Today's Russia is still unable to compete for talent in the global labor market, so scientists prefer to look for work abroad, these are the conclusions of a study by the Boston Consulting Group, which involved 24 thousand respondents from Russia. According to the results of this study: exactly half of Russian scientists seek to get a job abroad, as well as 52% of top managers, 54% of IT specialists, 49% of engineering workers and 46% of doctors. 65% of potential emigrants are “digital talent”: artificial intelligence specialists, scrum masters, user interface designers, etc. Moreover, 57% of them are young people under the age of 30. Among students, this share reaches 59%. “Working in Russia means swimming without water”, “Study, study and rush away” - these are the slogans of the paravalitists.
Among the reasons for leaving are: increased qualifications, a higher standard of living and expanded career opportunities. In addition, reasons often cited included economic instability in the home country and higher quality of government services abroad - in health, education and child care.
Every year, 100 thousand people leave Russia for developed countries, according to RANEPA data. This figure cited by host countries is 7 times higher than the official figure of Rosstat.
In October 2009, scientists who left Russia in the early 90s and made successful careers abroad wrote an open letter to the President and Prime Minister of the Russian Federation, drawing attention to the disastrous state of fundamental science in the country and the consequence of this problem - a massive outflow of scientists abroad . On the same days, 407 doctors of science working at institutes of the Russian Academy of Sciences (RAN) wrote an open letter of similar content to the country’s authorities. Two letters to a single address, sent from different parts of the planet, are the last desperate attempts to save Russian science.
“Due to the age structure of scientific and teaching personnel, Russia has 5-7 years left for qualified scientists and teachers of the older generation to prepare a new generation for science, education and high-tech industries. If within this timeframe it is not possible to attract young people to the scientific and educational sphere, then we will have to forget about plans for building an innovative economy...” - write 407 doctors of science from academic institutes in Moscow, St. Petersburg, Nizhny Novgorod, Ivanovo and other Russian cities. Russian scientists who have gone abroad and established themselves there are also in solidarity with their colleagues. “The regression of science continues, the scale and severity of the danger of this process are underestimated. The level of funding for Russian science sharply contrasts with the corresponding indicators of developed countries.” Indeed, during the Soviet era, the budget of the Academy of Sciences was equal to 2% of GDP, but now it is less than 0.3%.
APPENDIX ON THE POINCARES HYPOTHESIS
The problem Perelman solved relates to a branch of mathematics called topology. It is often called "rubber sheet geometry". It deals with the properties of geometric shapes that are preserved if the shape is stretched, twisted, or bent. In other words, it is deformed without tears, cuts or gluing.
Topology is important for mathematics and mathematical physics because it allows us to understand the properties of space. Or evaluate it without being able to look at the shape of this space from the outside. For example, to our Universe.
To explain the Poincaré conjecture, it is necessary to: imagine a two-dimensional sphere - a rubber circle stretched over a ball. In a similar way, you can tie a sports backpack with a cord. The result will be a sphere: from the outside - three-dimensional, but from the point of view of mathematics - only two-dimensional. Then they offer to pull the same circle onto the donut. It seems like it will work out. But the edges of the disk will converge into a circle, which can no longer be pulled to a point - it will cut the donut.
What follows is much more complicated: you need to imagine a three-dimensional sphere stretched over a four-dimensional ball. As another Russian mathematician, Vladimir Uspensky, wrote, “unlike two-dimensional spheres, three-dimensional spheres are inaccessible to our direct observation, and it is as difficult for us to imagine them as it was for Vasily Ivanovich to imagine the square trinomial from the famous joke.”
So, according to the Poincaré hypothesis, a three-dimensional sphere is the only three-dimensional thing whose surface can be pulled to one point by some hypothetical “hypercord”. Jules Henri Poincaré suggested this in 1904. Now Perelman has convinced all topologists that the great French mathematician was right. And turned his hypothesis into a theorem.
The proof helps to understand what shape our Universe has. And it allows us to very reasonably assume that it is that same three-dimensional sphere. But if the Universe is the only “figure” that can be contracted to a point, then, probably, it can be stretched from a point. This serves as an indirect confirmation of the Big Bang theory, which states that the Universe originated from a point.
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
Grigory Yakovlevich Perelman. Born on June 13, 1966 in Leningrad (now St. Petersburg). Russian mathematician who proved the Poincaré conjecture.
By nationality - Jewish.
Father - Yakov Perelman, an electrical engineer, emigrated to Israel in 1993.
Mother - Lyubov Leibovna Shteingolts, worked as a mathematics teacher at a vocational school, after her husband left for Israel, she remained in St. Petersburg.
The younger sister is Elena (born 1976), mathematician, graduate of St. Petersburg University (1998), defended her PhD thesis at the Weizmann Institute in Rehovot in 2003, and has been working as a programmer in Stockholm since 2007.
Some sources mistakenly attribute Perelman to being related to Yakov Isidorovich Perelman, a famous physicist, mathematician and astronomer. But they are just namesakes.
Gregory's mother played the violin and instilled in him a love of classical music from an early age; he graduated from music school. He played table tennis well.
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.
Until the 9th grade, Perelman studied at a high school on the outskirts of Leningrad, then transferred to the 239th physics and mathematics school. I did not receive a gold medal due to a low grade in physical education.
After graduating from school, without exams, he was enrolled in the Faculty of Mathematics and Mechanics of Leningrad State University. 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 the Leningrad branch of the Mathematical Institute. V. A. Steklova (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 1991, he was awarded the “Young Mathematician” Prize of the St. Petersburg Mathematical Society for his work “Aleksandrov spaces with curvature bounded from below.”
In the early 1990s, Perelman came to the United States, where he worked as a researcher at various universities. He surprised his colleagues with his ascetic lifestyle; his favorite foods were milk, bread and cheese.
In 1994 proved the soul hypothesis(differential geometry). He proved several key statements in the Alexandrov geometry of spaces of curvature bounded below.
In 1996, he returned to St. Petersburg, continuing to work at POMI, where he worked alone on proving the Poincaré conjecture.
In 1996, the European Mathematical Society Prize for Young Mathematicians was awarded, but he refused to receive it.
Entropy formula for Ricci flow and its geometric applications;
- Ricci flow with surgery on three-dimensional manifolds;
- Finite decay time for solutions of Ricci flow on some three-dimensional 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 reports on his work to prove the Poincaré conjecture.
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 involved in checking 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 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 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.
In 2006, Grigory Perelman was awarded the international Fields Medal for his solution to the Poincaré conjecture - “For his contribution to geometry and his revolutionary ideas in the study of the geometric and analytical structure of the Ricci flow.” However, he refused it.
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, marking the first time in history that the prize had been 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 proving the Poincaré conjecture, and on July 1, 2010, he publicly announced his refusal of the prize. He motivated as follows: “I refused. You know, I had a lot of reasons in both directions. That's why it took me so long to decide. In short, the main reason is disagreement with the organized mathematical community. I don't like their decisions, I think they are unfair. I believe that the contribution of the American mathematician Hamilton to solving this problem is no less than mine.”
“Simply, the essence of Poincaré’s theory can be stated as follows: if a three-dimensional surface is somewhat similar to a sphere, then it can be straightened into a sphere. Poincaré's statement is called the “Formula of the Universe” because of its importance in the study of complex physical processes in the theory of the universe and because it provides an answer to the question of the shape of the Universe. That’s why they struggled with its proof for so many years. I know how to control the Universe. And tell me, why should I run for a million?”, he said in an interview.
Such a public assessment of the merits of Richard Hamilton by the mathematician who proved the Poincaré conjecture can be an example of nobility in science, since, according to Perelman himself, Hamilton, who collaborated with Yau Shintun, 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. Hamilton accepted the award.
In 2011, Masha Gessen’s book 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.
In September 2011, it became known that the mathematician refused to accept the offer to become a member of the Russian Academy of Sciences.
Personal life of Grigory Perelman:
Not married. Have no children.
Leads a secluded life, ignores the press. Lives in St. Petersburg in Kupchin with his mother.
There were reports in the press that since 2014 Gregory has been living in Sweden, but later it turned out that he only visits there sporadically.
Grigory Yakovlevich Perelman(b. June 13, 1966, Leningrad, USSR) - outstanding, 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 a 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 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 researcher.
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.
He showed no interest in a further scientific career. 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 partly financed by personal savings during his visits to the Courant Institute of Mathematical Sciences, the State University of New York (SUNY), the State University of New York at Stony Brook and the University of California in 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), as well as letters of recommendation, Perelman opposed:
- 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 the editor-in-chief of the 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 protagonist of the documentary film “The Spell of the Poincaré Hypothesis” directed by Masahito Kasuga, filmed 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.
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