https://physicsforstudents.com/the-saint-of-mathematics/ Skip to content * * * * Whatsapp +91 98302 19677 Email Us editor@physicsforstudents.com [cropped-Logo-2-header-2] [cropped-Logo-2-header-2] * Home * Articles * Videos * Godel's World * Student's Corner * Featuring * About + About us + Our Team * * Contact Search for: [ ] The Saint of Mathematics 1. Home > Articles > 2. The Saint of Mathematics [perelman2-1] Aug 9 2021 Admin The Meaning of Life For every one of us, life carries a different meaning. We grow up in life to do something. We aim to stand apart from the mass and show the world how different we are. Some dedicate their life on behalf of poor people, some to the nation, and some to research and study. For some, money does not matter at all. Hundreds, thousands maybe million dollars to them are useless....are... just nothing...Today, we are going to read the life of an unusual genius, one of the greatest mathematicians ever born on this earth, who proved something that unraveled the greatest mystery of the universe. "He might make thee know that man doth not live by bread only, but by every word that proceedeth out of the mouth of the Lord doth man live." (From the Bible, Deuteronomy 8: 2-3) The soul needs food and subsistence just as the body does. The soul needs fresh air, the soul needs to live on the nourishing power which emanates from an individual. How do we live without money? How do we live without fame? We can survive on what we need, yet we desire more. The person about whom we are talking is an ideal example of the phrase: "man doth not live by bread only" (Matthew 4:4) Our aspirations, our ideas, our strive for a better life, all revolve around a basic purpose, a material objective No, I am not saying that we do something and we do not expect any return, But can we stay detached from the work? Can we.....Just do the work and then enjoy relaxing back on it? Can we just 'renounce and enjoy?' Difficult, isn't it? As long as we stay attached to the work we cannot enjoy it. Let us do our work at our best and then sit back and enjoy. Can we then see the tranquility of the sky and hear the humming of the bees? We are talking about a person, who has done that He has done his work and then renounced it. For him, the key to happiness comes from renunciation. For him, the joy and nourishment of the soul lie in giving up things, not in accepting them. This person did the best, which no one could do. It required dedication, hard work, seclusion, renunciation and, the spark of a genius. He could have become the richest person on the earth or the most famous person. Yet, he repudiated all the honors and freed himself from the shackles of glory and acclamation, and that is why we call him 'the saint of mathematics.' The Birth Of A Genius On June 13, 1966, Lubov Lvovna and Yakov Perelman gave birth to a child who was named Grigori Yakovlevich Perelman. He was born in a place called Leningrad, the Soviet Union, now located in Saint Petersburg, Russia. Both of his parents were in the technical field, his father's profession as an electrical engineer and his mother working as a mathematics teacher, Born to a Russia-Jewish family, hatred, and racism was strong for the Jews and his surname dictated a lot of anti-Semitism which he suffered. In the later part of his life, his father moved to Israel, and his mother, being a mathematics teacher, left her work to raise his son and her daughter Elena, who later flourished as a brilliant mathematician. Proud of his son's talent in mathematics, his father always encouraged him to solve great mathematical puzzles and taught him to play the game of chess. The trace of his mathematical sparks dates back to his childhood. Grigori scored excellent marks in all the subjects barring physical education. This incident reminds us of another genius who had the same personality, Austrian mathematician and logician, Kurt Godel. When he reached the age of 10, Perelman's talent shone like a bright light and its effulgence radiated within his family. He started participating in different competitions and his mother enrolled him in a coaching club was run by Sergei Rukshin, a young mathematics undergraduate from Leningrad University. Grigori Perelman at young age Grigori Perelman from the third right and Sergey Kgorushan from the third left (Photo: https://bykm.ru/en/) Later in an interview, Rukshin recounts: "The first time I heard about Grisha was from Professor Nathanson. He said that his former student had a kid who was interested in mathematics and why would not I look at him?" (1) Rushkin helped him a lot to communicate in English and as a result, he took admission in Leningrad's Special Mathematics and Physics School Number 239 in September 1980. Two years later, in 1982, he got the chance into the team of Soviet Union's International Mathematical Olympiad, where he scored the best - fetching a gold medal and got directly into the School of Mathematics and Mechanics at the Leningrad State University. 1904: The Epoch Making Question Let us trace back to the year 1904 when the French mathematician Henri Poincare posed an epoch-making question: "If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere?" Demonstrating this with an example, if we extend a band around the outside part of an apple, then we can reduce it to a point, without tearing apart and without slipping or falling off from the surface. Similarly, if we try to imagine the same band which is made of rubber which is being stretched in the direction around the donut, then we cannot shrink the object to a single point without cutting or breaking the band or the donut. Technically we say the apple is "simply connected" but the surface of the donut is not simply connected. It was so simple to imagine but so difficult to prove! Towards the Answer Almost a century passed before the mathematical world got a proper answer. The initial success was lead by prominent mathematicians like: (1) In 1961 Stephen Smale of the University of California proved the conjecture to be true for spheres of 5 or more dimensions. (2) Michael Freeman proved the conjecture in 4 dimensions. (3) In 1999 Richard Hamilton published a paper that played a significant role in the progress of Poincare conjecture. It was Hamilton who first used Ricci flow (subject to further discussion) It was liking biting around the bush. Although Hamilton's proof made great strides towards the central problem yet there arose some singularities in Ricci flow which collapsed everything just as the singularity problem did so in a black hole. In September of 1992, Perelman came to New York for his internship in the Courant Institute of Mathematical Sciences working on manifolds with lower bounds on Ricci curvature. The Rendezvous In some part of our life, we all meet someone who carries a profound influence in our life. We can fall in love or our entire perspective changes, we become revolutionaries or we become spiritual. All happens at a specific moment. Moments tied together to form a beautiful garland, moments entwined together show a new horizon. For Perelman, this moment was destined. This moment would change the course of his entire life. He did not know that a young geometer, whose name is Hamilton would create a profound influence on his life. Was it only knowledge? Or his smiling face? Or... Richard Hamilton was a prolific mathematician. A graduate from Yale University and a Ph.D. from Princeton University he taught differential geometry and geometric analysis. Perelman had read Hamilton's papers and went to hear him give a talk at the Institute for Advanced Study. The meeting of Hamilton with Perelman was a crucial one, yet they exchanged very few words. Something was an inkling in Perlman's mind. Was that Hamilton? His works? His frankness? What was it? Was providence waiting for something? One day, he read a paper by Richard Hamilton and found he was stuck in a problem and cannot further proceed. Hamilton was stuck in a problem, which mathematicians called the singularity, a point at which a mathematical object is not defined. He has designed something called Ricci flow which was the centrifugal force behind proving the conjecture, however, he could not solve the problems with singularities. Perelman wrote to Hamilton that he thinks he could solve it. Hamilton did not reply. For Perelman, it meant, yes. Richard Hamilton - Davies Professor of Mathematics at the Columbia UniversityRichard Hamilton - Davies Professor of Mathematics at the Columbia University Photo:https://alchetron.com/Richard-S.-Hamilton Grigori Perelman headed towards St.Petersburg, where he could dedicate himself to solving the problem. When he arrived his father has left and her sister would soon be moving to Israel. Not one, not two, seven long years..... He shut himself from all his jobs, all his occupations, all his friends and relatives. He was obsessed with the idea of proving the problem - the Poincare conjecture. As we shall see Perelman never went forward to prove the conjecture, rather the proof came alongside much greater achievement. The solitude for seven long years served as salvation for what he was seeking. It was not easy to dedicate someone to such a problem. He has earned some savings from the US, so now he can concentrate on his own work. For him, nothing can be purer than mathematics. Mathematicians have the highest knowledge of ethics and hence the best morality that could manifest is its form in mathematics. Perelman never faced a problem that was more challenging than this. He locked himself up, devoid of any external disturbances, and did the mathematics. The world, for years, had been waiting for a solution for the most difficult problem in mathematics. Termed as the millennium problem by the Clay Mathematical Institute, it challenged the world's best brains. Perelman worked silently at his home, stayed with his mother and no one knew what he did. Since 1995, when he left the US most of his fellow mathematicians have forgotten him, including Gang Tian who drove him around the streets. For others, he was almost a dwindling star in the lost horizon. Perelman never forgot Richard Hamilton and the day when he met. He was working on his roads and improved his work which would earn him the greatest title, honor, and fame. The Proof On November 11, 2002, Perelman opens the website arXiv.org and submits his paper: "The entropy formula for the Ricci flow and its geometric applications." It was brief, 39 pages, written in English, and signs his name as "Grisha Perelman." The world of mathematics went into a state of utter pandemonium. First, the proof was too short, difficult to understand. Second, submitting proof, that too, solving a millennium problem, over the internet seemed a foolish idea. The arrival of Perelman was not treated with pomp and grandeur but everybody understood that his lectures carried real significance. The series of lectures, which he delivered in April, ushered a new era, the press considered this to be a major event, perhaps turning the history of mathematics. Presented amongst many dignitaries were Prof.Andrew Wiles (the one who proved Fermat's Last theorem), John Ball, John Forbes Nash Jr, The audience was astonished as Perelman said nothing about the Poincare. He was opening new gates in geometry. The audience was silent, they stared in awe, expecting to prove the conjecture but the Russian never mentioned anything about that. The conjecture was just a small case that he proved along the way. Grigoti Perelman delivering a lecture at Weaver Hall in 2003. Photo Credit: Frances M. RobertsGrigori Perelman delivering a lecture at Weaver Hall in 2003. Photo Credit: Frances M. Roberts By mid-July Perelman submitted his final two papers on the internet: (1) Ricci flow with surgery on three-manifolds and (2) Finite extinction time for the solutions to the Ricci flow on certain three-manifolds The mathematical world was shaken! Could this be the answer to the Millenium problem? Or is it still flawed? The history of this proof was flawed for years. Many mathematicians have tried to prove it but failed. He was invited for a series of lectures from April 2003 to visit, MIT, the famous Princeton University, Stony Brook University Columbia , and New York University to lecture his proof and make the world understand his mathematical interpretations. Mathematicians around the world gathered together to look into his proof. One team comprising of Bruce Kleiner and John Lott from the University of Michigan posted further details of Perelman's proof of the geometrization conjecture on the internet in arXiv.org. In June 2006, the Asian Journal of Mathematics published a paper giving a complete description of Perelman's proof of the Poincare and the geometrization conjectures. The June 2006 paper claimed: "This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow." (2) Declining the Fields Medal and Millennium Prize In May 2006, a committee of nine mathematicians voted to award Perelman a Fields Medal. Perelman declined to accept it. Sir John Ball, then president of the International Mathematical Union traveled to St. Petersburg to convince him to receive the money, but Perelman said: "The prize was completely irrelevant for me. Everybody understood that if the proof is correct, then no other recognition is needed." "I'm not interested in money or fame." On 2nd. August 2006, Perelman was publicly offered the medal at the International Congress of Mathematicians in Madrid. He did not attend the ceremony and declined to accept the medal. The Millennium Prize was awarded for a million-dollar prize. On 18 March 2010, he was awarded the Millennium Prize and in an official ceremony held at Institut Oceanographique, Paris his absence stunned the world! Perelman denied the prize and refused to accept the money of one million dollars. He stated that: "the main reason is my disagreement with the organized mathematical community. I don't like their decisions, I consider them unjust." (3) His argument was that Richard Hamilton is equally responsible for receiving the prize. If he has not been awarded for that then the mathematical society is corrupted. The ideology of Grigori Perelman A person who considers research and mathematics to be pure and cannot be tainted by anything which measures or compares it with a value. The value can be money or anything which is measurable. Can we really provide value to Perelman's talent? No, we cannot. So, he is beyond measurement. He is a saint, a monk of mathematics in all aspects. The address reads: Ulitsa Gubkina, 8, Moscow, Russia, 117966 and the plaque reads: Russian academy of sciences. St.Petersburg Department of Steklov Mathematical Institute. This is the place where Perelman worked and collaborated with numerous researchers. He resigned from the Steklov Institute in December 2005. Why do people do science? Why do people spend their entire life pursuing their passion? For fame, for money, for prominence. For Perelman, it is not. Why he declined the prizes? Well, "the answer my friend is blowing in the wind." Perelman stands resolute in his decision. Thousands of reporters gather around his house, waiting to talk to him. Many wait for days and nights to have a glimpse by the window. some try to take photographs of him as he walks down the alleys. I myself have seen a few footage on YouTube where he was seen shopping in malls, buying bread and milk. Often a passerby would greet him and he would do so with a smiling face. He never came in touch with any woman, neither he has any close fellow mate. He avoids boarding an elevator if there are many people and prefers to take the stairs down from his apartment. He is an ethical person, more ethical than anyone else. Mathematicians are more ethical as they have a strong sense of what is right and wrong. As mathematics always find the right way out, Perelman considered it not right to receive the award money. He considered Richard Hamilton to get a share of that, as he was the person, who showed him the light, which shone on the stage. He answered to the world: " I have nothing to say." (5) We can guess anything... An arrogant, cynical, haughty genius. In Perelman's logic: "To do great work, you have to have a pure mind." (6) Beethoven pointed out: "Even in poverty, I lived like a king for I tell you that nobility is the thing that makes a king." (7) He believed in nobility. He believed in his work, not in the fruits. He believed that the result of the work is important, rest are all fruitless, it might be a million-dollar or a fistful of the coin. Perelman's refusal, his seclusion, circumventing from society teaches us that people do science and mathematics, not for money. They do it because they love it, it because they live with it because they breathe the air within it. There are no such instances in the history of science where work is done in such a pure manner. The virtuosity in pursuing a passion is well defined in Perelman's journey. Devoid of earthly pleasure, money, fame, and establishment he pursued mathematics just for the sake of doing the work. The work became more important rather than anything else. What could you call this person? A SAINT OF MATHEMATICS --------------------------------------------------------------------- References: 1. Grigori Perelman documentary (in Russian as found in YouTube) 2. (http://www.ims.cuhk.edu.hk/~ajm/vol10/10_2.pdf) 3. (Interfax report: http://archive.boston.com/news/science/articles /2010/07/02/russian_math_whiz_rejects_1m_prize/) 4. (https://www.gutenberg.org/files/43592/43592-h/43592-h.htm) 5. Featured image collected from the internet. 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