Chapter 34 This is going to cause a sensation Lu Shan clicked into his mailbox and found that there was an attachment. The attached content is the entire paper on the Poincare conjecture proved by Gregory Perelman. The paper is in English and is twenty-two pages long. The title of the paper is: "Ricci fall with surgery on three-manifolds." Lu Shan and Poincare worked together day and night, and had already mastered most of academic English. He was fascinated by the paper. During this period, Poincare also proved that any simply connected, closed three-dimensional manifold must be homeomorphic to a three-dimensional sphere. Lu Shan was watching while he was proving it. So when Lu Shan read this paper, he felt as if he had suddenly realized something. The Poincare conjecture is not only a mathematical problem, but also a physics problem.
The proof of the conjecture has an impact in the fields of physics and engineering, especially in describing and simulating the universe, providing new ideas and methods. Because the evening self-study class had just ended, more and more people came to the Internet cafe. That’s what high school is like, there’s endless energy. Some people waste their youth under the desk lamp, some waste their youth under the monitor, and some waste their youth vigorously in bed. Just when Lu Shan was watching with great interest, a fat man behind him patted Lu Shan on the shoulder and asked curiously, "Brother, what game cheat code is this?" Lu Shan: “Three-dimensional manifold.” "What kind of game is Three-Manifold? Third-rate? The one with colors? The one with the secret passage? Take me with you!" "Can I remove the mosaic by entering the cheat code?" Lu Shan: “…” You can’t finish reading a paper in an Internet cafe. Fortunately, the printing shop outside the school does not close until 12 o'clock in order to meet the students' needs for printing materials. After Lu Shan sent an email to Zou Yao, he left the Internet cafe and went to the printing shop to log into his email again and print out the paper. After returning home, Lu Shan added the paper to the transfer list and brought it into the laboratory. [Remaining points: ] When Poincare saw Lu Shan coming in, his eyes lit up. He quickly put down the pen in his hand and crawled out from the pile of draft papers. "Chérie, j'ai réussi!" Excited, Poincare grabbed Lu Shan's hand and uttered something in French. After spending so much time with Poincare, Lu Shan felt that he might be able to speak French in no time.
Poincare pulled Lu Shan to the table and placed a thick pile of draft paper in front of him. Lu Shan took a look at the contents of the draft paper! I go! This is not proof that a three-dimensional manifold must be homeomorphic to a three-dimensional sphere. In other words, Poincaré proved the Poincaré conjecture. Lu Shan wants to cry! Poincaré was surprised and asked, "I have proved it, shouldn't you be happy? Why are you crying? Is my proof wrong?" "I think it's right! I have verified it many times." Lu Shan really wanted to cry! Poincare is really great! If calculated in real time, it's only been a month. Poincare proved his conjecture. But there was more than a hundred years between Poincare and Perelman. The reason why Perelman was able to prove the Poincare conjecture was that he stood on the shoulders of countless giants. Lu Shan wants to cry! If the Poincare conjecture had not been proven yet, would I be able to earn a lot of points by publishing this paper? If I were reborn a few years earlier, would I be able to win the one million dollar prize from the Clay Mathematics Institute? Don’t you want to cry after missing out on the thesis and the million-dollar knife? Lu Shan said: "I am just excited. Finally there is a result." Poincare looked at what Lu Shan was holding and asked, "What is that in your hand?" "The proof of the conjecture named after you, that a three-dimensional manifold must be homeomorphic to a three-dimensional sphere, is the same as what you proved." "It was proved by the Russian Grigori Perelman." "Oh?" Poincare was curious and took the paper handed over by Lu Shan. Watch and evaluate. "This kid is pretty smart!" "E - Approaching the appropriate part of the gradually formed circular cylinder... This can be optimized, but the proof is still too complicated!" Poincare optimized the paper as he read it. Lu Shan was also watching and found that Poincare's proof had a little more advantages. And the most important point is that Poincare unified the dimensions of this problem and gave a unified and complete discussion. The Poincare conjecture was proved to hold for closed manifolds with dimensions greater than 5 in 1960 and for closed manifolds with dimensions greater than 4 in 1982.
Since the high-dimensional Poincare conjecture has been proved, only the 3-dimensional case remains. Perelman's proof was mainly for the three-dimensional case, and in Poincare's view, the proof was rather cumbersome. Poincare's own proof is not just a proof of the three-dimensional case, nor is it a separation of the proof of higher dimensions, but rather a unity of opposites between three dimensions and higher dimensions. It uses a unified, complete and simple narrative, and also provides a complete set of formulas. That’s really cool. If Perelman's paper is regarded as a description of the history of a certain dynasty, then Poincare's paper is a description of human history and provides the laws. When Lu Shan saw this, he got goosebumps! Poincaré's paper can still be published! This is an optimization and unification of the Poincare conjecture. This is a perfect ending to the Poincare conjecture. Lu Shan told Poincare his idea and said temptingly: "Once the paper is published, you will have enough points to upgrade the lab and get the computer you want." Poincare was excited: "I have done a lot of English reading, read a lot of books, and even mentioned computers. What kind of magical thing is this?" "For the sake of your computer, I will reorganize the proof and complete the paper." Of course Lu Shan will also participate in it, and this is also a learning process for Lu Shan. Soon, New Year's Day 2008 arrived. Although the high school students only have two days off, it can be considered a break from their intense studies. After attending a class reunion and completing business trips in Jiangzhou, Fang Lan also returned to Shenzhen. During this time, she had already written a press release and felt that she was going to be famous. The title of the news with the highest number of comments is: "Is the college entrance examination really fair? The counterattack of a poor student. " The title is thrilling enough, it's eye-catching enough, and the content is even more explosive. The content is based on Lu Shan, and tells the story of a poor student who relies on his family background to get a place in a competition, and then continues to use his connections to be admitted to a prestigious school without having to take the college entrance examination. Most of the content was narrated by Zhang Sufen, and was artistically processed (explosive and exaggerated) by Fang Lan. Although Lu Shan's name was not mentioned in the article, a student named Lu and Jiangzhou University were mentioned. What is the most important thing about a commentary article? It should tell you what really happened and expose social phenomena in a profound way. Student Lu is a student taught by Zhang Sufen. He really exists, and this phenomenon also really exists, so there is nothing wrong with the article. As for artistic processing, it is also reasonable. The editor-in-chief of "Nanyun Weekend" thought that this article was very good, criticizing current social ills and reflecting social phenomena and key areas of public concern. After review, it was published on the front page of the New Year's Day special edition of "Nanyun Weekend". Those who follow this book are all handsome guys, and they definitely want to get rich overnight! (End of this chapter)