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Magazine version of one of the chapters of the new book Nick. Gorkavy “Undiscovered Worlds” (St. Petersburg: “Astrel”, 2018).
Mathematicians are special people. They are so deeply immersed in abstract worlds that, “returning to Earth,” they often cannot adapt to real life and surprise others with unusual views and actions. We will talk about perhaps the most talented and extraordinary of them - Grigory Perelman.
In 1982, sixteen-year-old Grisha Perelman, who had just won a gold medal at the International Mathematical Olympiad in Budapest, entered Leningrad University. He was noticeably different from the other students. His supervisor, Professor Yuri Dmitrievich Burago, said: “There are a lot of gifted students who speak before they think. Grisha was not like that. He always thought very carefully and deeply about what he intended to say. He wasn't very quick to make decisions. Speed of solution means nothing; mathematics is not built on speed. Mathematics is about depth.”
After graduating from university, Grigory Perelman became an employee of the Steklov Mathematical Institute and published a number of interesting articles on three-dimensional surfaces in Euclidean spaces. The world mathematical community appreciated his achievements. In 1992, Perelman was invited to work at New York University.
Gregory ended up in one of the world centers of mathematical thought. Every week he went to a seminar in Princeton, where he once listened to a lecture by the eminent mathematician, Columbia University professor Richard Hamilton. After the lecture, Perelman approached the professor and asked several questions. Perelman later recalled about this meeting: “It was very important for me to ask him about something. He smiled and was very patient with me. He even told me a couple of things that he published only a few years later. He shared with me without hesitation. I really liked his openness and generosity. I can say that in this respect Hamilton was unlike most other mathematicians."
Perelman spent several years in the USA. He walked around New York wearing the same corduroy jacket, ate mostly bread, cheese and milk, and worked constantly. He began to be invited to the most prestigious universities in America. The young man chose Harvard and then encountered something that he categorically did not like. The hiring committee required the applicant to provide a CV and letters of recommendation from other scientists. Perelman’s reaction was harsh: “If they know my works, then they don’t need my biography. If they want my biography, then they don’t know my work.” He refused all offers and in the summer of 1995 returned to Russia, where he continued to work on the ideas that Hamilton had developed. In 1996, Perelman was awarded the European Mathematical Society Prize for Young Mathematicians, but he, who did not like any hype, refused to accept it.
When Gregory achieved some success in his research, he wrote a letter to Hamilton, hoping for joint work. However, he did not answer, and Perelman had to continue to act alone. But world fame awaited him ahead.
In 2000, the Clay Mathematics Institute published the “Millennium Problem List,” which included seven classic problems in mathematics that had not been solved for many years, and promised a million-dollar prize for proving any of them. Less than two years later, on November 11, 2002, Grigory Perelman published an article on a scientific website on the Internet, in which, on 39 pages, he summed up his many years of efforts to prove one problem from the list. American mathematicians who knew Perelman personally immediately began to discuss the article in which the famous Poincaré conjecture was proved. The scientist was invited to several US universities to give a course of lectures on his proof, and in April 2003 he flew to America. There, Gregory held several seminars in which he showed how he managed to turn the Poincaré conjecture into a theorem. The mathematical community recognized Perelman's lectures as an extremely important event and made significant efforts to verify the proposed proof.
Details for the curious
Poincaré problem
Jules Henri Poincaré (1854–1912) - an outstanding French mathematician, mechanic, physicist, astronomer and philosopher, head of the Paris Academy of Sciences and member of more than 30 academies of sciences around the world. The problem formulated by Poincare in 1904 belongs to the field of topology.
For topology, the main property of space is its continuity. Any spatial forms that can be obtained from one another using stretching and curvature, without cutting and gluing, are considered identical in topology (the transformation of a cup into a donut is often shown as an illustrative example). The Poincaré conjecture states that in four-dimensional space, all three-dimensional surfaces belonging to compact manifolds are topologically equivalent to a sphere.
The proof of the hypothesis by Grigory Perelman made it possible to develop a new methodological approach to solving topological problems, which is of great importance for the further development of mathematics.
Paradoxically, Perelman did not receive grants to prove the Poincaré conjecture, while other scientists testing its correctness received grants amounting to a million dollars. Verification was extremely important, because many mathematicians worked on the proof of this problem, and if it was actually solved, then they were left out of work.
The mathematical community tested Perelman's proof for several years and by 2006 concluded that it was correct. Yuri Burago wrote then: “The proof closes an entire branch of mathematics. After it, many scientists will have to switch to research in other areas.”
Mathematics has always been considered the most rigorous and accurate science, where there is no place for emotions and intrigue. But even here there is a struggle for priority. Passions began to boil around the proof of the Russian mathematician. Two young mathematicians, immigrants from China, having studied Perelman's work, published a much more voluminous and detailed - more than three hundred pages - article with a proof of the Poincaré conjecture. In it, they argued that Perelman's work contained many gaps that they were able to fill. According to the rules of the mathematical community, priority in proving the theorem belongs to those researchers who were able to present it in the most complete form. According to many experts, Perelman's proof was complete, although briefly stated. More detailed calculations did not introduce anything new into it.
When journalists asked Perelman what he thought about the position of Chinese mathematicians, Grigory replied: “I can’t say that I’m outraged, others do even worse. Of course, there are a lot of more or less honest mathematicians. But almost all of them are conformists. They themselves are honest, but they tolerate those who are not.” He then noted bitterly: “Those who violate ethical standards in science are not considered aliens. People like me are the ones who end up isolated.”
In 2006, Grigory Perelman was awarded the highest honor in mathematics, the Fields Medal. But the mathematician, who led a solitary, even reclusive lifestyle, refused to receive it. It was a real scandal. The President of the International Mathematical Union even flew to St. Petersburg and spent ten hours persuading Perelman to accept the well-deserved award, which was planned to be presented at a congress of mathematicians on August 22, 2006 in Madrid in the presence of the Spanish King Juan Carlos I and three thousand participants. This congress was supposed to be a historic event, but Perelman politely but adamantly said: “I refuse.” The Fields Medal, according to Gregory, did not interest him at all: “It doesn’t matter at all. Everyone understands that if the evidence is correct, then no other recognition of merit is required.”
In 2010, the Clay Institute awarded Perelman the promised million-dollar prize for proving the Poincaré conjecture, which he was about to receive at a mathematical conference in Paris. Perelman refused a million dollars and did not go to Paris.
As he himself explained, he does not like the ethical atmosphere in the mathematical community. In addition, he considered Richard Hamilton's contribution no less. Winner of many mathematical prizes, Soviet, American and French mathematician M. L. Gromov supported Perelman: “Great things require an unclouded mind. You should only think about mathematics. Everything else is human weakness. To accept a reward is to show weakness.”
Refusing a million dollars made Perelman even more famous. Many asked him to receive the prize and give it to them. Gregory did not respond to such requests.
Until now, the proof of the Poincaré conjecture remains the only solved problem on the millennium list. Perelman became the number one mathematician in the world, although he refused contacts with his colleagues. Life has shown that outstanding results in science were often achieved by individuals who were not part of the structure of modern science. That's how Einstein was. While working as a clerk in a patent office, he created the theory of relativity, developed the theory of the photoelectric effect and the principle of operation of lasers. This is how Perelman became, who neglected the rules of conduct in the scientific community and at the same time achieved maximum efficiency of his work by proving the Poincaré conjecture.
The Clay Mathematics Institute (Cambridge, USA) was founded in 1998 by businessman Landon Clay and mathematician Arthur Jaffee to increase and disseminate mathematical knowledge.
The Fields Medal has been awarded for excellence in mathematics since 1936.
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 United States, 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.
« 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 the 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
In the world of physics there is a hypothesis: 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.