Mathematician Grigory Perelman, who solved one of the seven problems of the millennium

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

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 those around them with unusual looks and actions. We will talk about almost 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 markedly different from other students. Its scientific advisor, Professor Yuri Dmitrievich Burago, said: “There are a lot of gifted students who speak before they think. Grisha was not like that. He always thought very carefully and deeply about what he intended to say. He was not very quick at making decisions. Solution speed does not mean anything, mathematics is not built on speed. Mathematics depends on depth."

After graduation, Grigory Perelman became an employee of the Steklov Mathematical Institute, published a number of interesting articles on three-dimensional surfaces in Euclidean spaces. The world mathematical community appreciated his achievements. 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 at Princeton, where he once attended a lecture by the distinguished mathematician, Columbia University professor Richard Hamilton. After the lecture, Perelman approached the professor and asked several questions. Later Perelman recalled this meeting: “It was very important for me to ask him about something. He smiled and was very patient with me. He even told me a couple of things that he only published a few years later. He did not hesitate to share with me. I really liked his openness and generosity. I can say that in this Hamilton was unlike most other mathematicians."

Perelman spent several years in the United States. He walked around New York in the same corduroy jacket, ate mostly bread, cheese and milk, and worked continuously. He began to be invited to the most prestigious universities in America. The young man chose Harvard and then faced the fact that he categorically did not like it. The recruiting committee demanded an autobiography from the applicant and letters of recommendation from other scientists. Perelman's reaction was harsh: “If they know my work, then they don't need my biography. If they want my biography, they don’t know my work.” He turned down all offers and returned to Russia in the summer of 1995, where he continued to work on the ideas developed by Hamilton. In 1996, Perelman was awarded the prize of the European Mathematical Society 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 a joint work. However, he did not answer, and Perelman had to act further alone. But ahead of him was world fame.

In 2000, the Clay Mathematical Institute * published a "Millennium Problem List," which included seven classical problems in mathematics that have 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 he summed up his many years of efforts to prove one problem from the list on 39 pages. American mathematicians, who knew Perelman personally, immediately began to discuss the article in which the famous Poincaré conjecture was proved. The scientist was invited to several US universities to give a course of lectures on its proof, and in April 2003 he flew to America. There, Gregory held several seminars at which he showed how he managed to turn Poincaré's conjecture into a theorem. The mathematical community recognized Perelman's lectures as extremely important and made significant efforts to test the proposed proof.

Paradoxically, Perelman did not receive grants to prove Poincaré's hypothesis, and other scientists who test its correctness received grants worth a million dollars. Verification was extremely important, because many mathematicians worked on the proof of this problem, and if it was really solved, then they were out of work.

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

Mathematics has always been considered the science of the most rigorous and precise, where there is no place for emotions and intrigues. But even here there is a struggle for priority. Passions boiled around the proof of the Russian mathematician. Two young mathematicians from China, having studied the work of Perelman, published a much more voluminous and detailed - more than three hundred pages - article proving Poincaré's conjecture. In it, they argued that Perelman's work contains 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, albeit summarized. More detailed calculations did not add anything new to it.

When journalists asked Perelman what he thought about the position of Chinese mathematicians, Grigory replied: “I cannot say that I am outraged, the others are doing even worse. Of course, there are plenty of more or less honest mathematicians. But practically all of them are conformists. They themselves are honest, but they tolerate those who are not. " Then he bitterly noted: “Outsiders are not those who violate ethical standards in science. People like me are the ones who find themselves isolated."

In 2006, Grigory Perelman was awarded the highest honor in mathematics - the Fields Prize **. But the mathematician, leading a secluded, 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 ten hours persuaded Perelman to accept the well-deserved award, the presentation of which was planned at the congress of mathematicians on August 22, 2006 in Madrid in the presence of the Spanish king Juan Carlos I and three thousand participants. This congress was 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. Everyone understands that if the proof is correct, then no other recognition of merit is required."

In 2010, the Clay Institute awarded Perelman the promised prize of a million dollars for proving the Poincaré conjecture, which was going to be presented to him at a mathematical conference in Paris. Perelman refused a million dollars and did not go to Paris.

As he himself explained, he does not like the ethical atmosphere in the mathematical community. In addition, he considered the contribution of Richard Hamilton to be no less. The laureate of many mathematical prizes, the Soviet, American and French mathematician ML Gromov supported Perelman: “Great deeds require an unclouded mind. You should only think about math. Everything else is human weakness. To accept an award is to show weakness."

The abandonment of the million dollars made Perelman even more famous. Many asked him to receive the prize and give it to them. Gregory did not answer such requests.

Until now, the proof of the Poincaré conjecture remains the only solved problem from the list of the millennium. Perelman became the number one mathematician in the world, although he refused to contact colleagues. Life has shown that outstanding results in science were often achieved by loners who were not part of the structure of modern science. This was Einstein. 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. Such was Perelman, who neglected the rules of behavior in the scientific community and at the same time achieved the maximum efficiency of his work, proving Poincaré's hypothesis.