"To the public, the Poincaré conjecture is likely to be an unfamiliar term. Pen & Fun & Pavilion www.biquge.info"

"Let's start with something that can be of interest, the Poincaré conjecture is one of the Millennium Prize puzzles."

The Millennium Prize Puzzle, also known as the World's Seven Mathematical Problems, is seven mathematical conjectures published by the Clay Institute of Mathematics (CMI) on May 24, 2000. The only reason why Fermat's theorem, a puzzle that has been around for more than 300 years, was not chosen was that it had been solved by him. According to the rules set by the Clay Institute for Mathematics, the solution of any conjecture published in a mathematical journal and verified for two years will be awarded a prize of one million dollars. ”

"I would say that this is really not a Nobel Prize, although the difficulty of these seven mathematical problems ......"

"So, what exactly is Poincaré's guess?"

"Poincaré was a famous French mathematician, theoretical scientist and philosopher of science. In 1904, Poincaré proposed the famous Poincaré conjecture, which has puzzled mathematicians around the world for more than 100 years. The emergence of the Poincaré conjecture is closely related to the development of geometry. ”

"Mathematics, especially geometry, deals with objects that are universal and abstract. They are related to the things of life, but they do not come from these concrete things, so the study of geometry in ancient Greece was considered the most effective way to seek truth. It is said that at the entrance of Plato's Academy, it was written: Those who do not learn geometry are not allowed to enter. ”

……

"In 1904, the French mathematician Henri Poincaré proposed a topological conjecture: any single-connected, closed three-dimensional manifold must be homogeneous to a three-dimensional sphere."

If you think this is too abstract, we might as well imagine this: we imagine a spherical house, the walls of the house are made of steel, very strong, there are no windows and no doors, and we take a balloon in such a spherical house. Any balloon can be used (in fact, there are requirements for this balloon). This balloon is not deflated, but has been blown into a certain shape, any shape can be (there are certain requirements for the shape). But this balloon, we can continue to blow it up. It is also assumed that the skin of this balloon is infinitely thin. ”

"Okay, then we're going to keep blowing up this balloon and keep blowing it. What happens at the end of the blow? Monsieur Poincaré guessed that the surface of the balloon must have been tightly attached to the surface of the walls of the whole spherical house, and there was no gap in between. ”

"Let's think about it another way: if we stretch the rubber belt around the surface of an apple, then we can neither tear it off nor let it off the surface, so that it slowly moves and shrinks to a point. On the other hand, if we imagine that the same rubber belt is stretched on a tire face in the appropriate direction, then there is no way to shrink it to a point without tearing off the rubber belt or tire face. We say that the apple surface is "single-connected", while the tread is not. ”

"Doesn't it seem like it's easy to figure it out? But mathematics is not something that can prove a conjecture by "just thinking about it", it requires rigorous mathematical reasoning and logical reasoning. For more than a century, countless scientists have racked their brains and even devoted their lives to proving it, but to no avail. ”

What I want to say next may disappoint Ning Yun's fans. The Poincaré conjecture has been proved by the Russian mathematician Grigory Perelman in three papers published between November 2002 and July 2003. ”

"As a result of this achievement, the International Mathematical Union (IMU) decided to award the Fields Medal to Perelman at the International Mathematical Congress held in Madrid, Spain, in August 2006."

"I really don't want to explain anymore that the Fields Medal is known to the public as the "Nobel of Mathematics", the difference is that it is awarded every four years. My student begged me to write it because he said the article would be watched by many fans of Ning Yun, Emma Watson, and Emma Stone. (Seems to have forgotten something?) ）”

"Some people will ask, is it so important for a proven conjecture to be proven again? As a cutting-edge mathematical researcher, yes, it is very important! The process of the development of mathematics is very important to the human mind, to nature and to the pursuit of truth. ”

"The Poincaré conjecture is a fundamental proposition in topology that will help humans better study three-dimensional space, and the results will deepen people's understanding of the nature of manifolds. Perelman's contributions, those who are interested, can go to SCI to inquire or find information. Ning Yun's contribution will have to wait until my second article, and the specific journal in which it will be published has not yet been determined. ”

"In fact, I am still in the final stages of research on Ning Yun's thesis."

"Some people may wonder, it's been three weeks since you got the article, and it's still not final? Or rather, haven't you understood it yet? ”

"Yes, that's it, there's nothing to be embarrassed about. It wasn't until nearly four years after Perelman published the first of his three articles that the mathematical community really reached a consensus: Perelman tackled one of the discipline's most awe-inspiring problems. ”

Of course, part of the reason why Poincaré's conjecture took a long time to verify was that Perelman's proof was difficult to read because of the lack of detail. After about two years of hard work by several groups of mathematicians, the details of Poincaré's conjecture were finally completed. While Perelman's proof is somewhat flawed, they can all be fixed. ”

"Without Perelman's contribution, if I hadn't studied the subject a few years ago, three weeks would have been far from my commitment to the validation of this new method of interpretation."

"Before the formal thesis, I would like to briefly mention the contribution made by Ning Yun here. After Perelman solved the Poincaré conjecture, there were still many remaining questions. ”

And Ning Yun's new proof method solves the smooth four-dimensional Poincaré conjecture. i.e., whether there is a smooth four-dimensional space, which is homogeneous to a four-dimensional sphere but not differentially homogeneous to a four-sphere. ”

Prior to Ning Yun's proof, the smooth four-dimensional Poincaré conjecture was considered to be very difficult. It is a very important problem in mathematics, how to determine a smooth structure, and is there a method of differential geometry? These are questions that many mathematicians try to answer. Now, Ning Yun has completed this work. ”

"Again, for the sake of understanding for fans, I really have a wonderful sense of absurdity writing here. Very unrigorous and unworthy of academic recognition, if Perelman's contribution is 100, Ning Yun's contribution is about 50, which is half a Fields Medal, laughs :)"

"Many people don't understand, what contribution will such theoretical mathematics have to mankind? I think everyone knows about the contribution of calculus, right? Is there really anything you don't know? If you haven't reached the tenth grade yet. Calculus is not only closely related to the natural sciences, almost all basic sciences are deeply dependent on calculus, it can be said that calculus is an important theory and method for human beings to understand the objective world, explore the mysteries of the universe and even various problems of human beings themselves. ”

Geometric studies such as the Poincaré conjecture mentioned above belong to basic mathematics, and they are not motivated by "usefulness" at first, but are all in pursuit of a truth. But in fact it is extremely "useful", and geometry is used in many ways in our lives. I'll give you an example, CT (computer-aided X-ray tomography), which we all hear about, allows doctors to observe the distribution of tiny lesions and lesions inside the human body, and can take appropriate treatment measures at an early stage. Its mathematical basis is the Radon transform. The Radon transform was not immediately applied when it was first discovered, but that doesn't mean it doesn't have meaning and value. So mathematics is very useful, but some of the research results have not yet been applied in practice. ”

"This is Ning Yun's contribution to this world."

"The purpose of writing this article in advance is that my students told me that on the Internet, including some websites and traditional media, they swear to tell the public that the easter eggs were not filmed by Ning Yun."

When I heard this, I laughed. This sense of absurdity is so strong that this joke is enough to circulate in the mathematical community for a hundred years, well, at least twenty years! ”

"Shooting such an easter egg (yes, I have seen it once), I don't know that there is a director who can do it, but hiding a paper that proves the Poincaré conjecture in such an easter egg, solving the smooth four-dimensional Poincaré conjecture, the only thing the whole world can do at this point in time is Ning Yun."

"I want to ask, you guys, what should you be called, Directors Guild? Is there also a director who is essentially a mathematician? ”

"Then you must introduce me to you!"

"Later I realized that this could be some very boring business competition, and Ning Yun was involved in it because he was criticized for something he did."

"Honestly, I don't really care. I still secretly thought, such a genius should return to the mathematical world and be a director? ”

"But my students told me maybe he was different!"

"I really understand that. There are so many mathematicians and geniuses like no other. ”

"Perelman, whom we have mentioned many times, is a genius like no other. In 1996, he turned down the European Mathematical Society's Outstanding Young Mathematician Award, in 2006 he turned down the Fields Medal, and in 2010 he turned down a million-dollar award from the Clay Institute of Mathematics. His paper proving that the Poincaré conjecture shocked the entire mathematical community was published on the site, and not in any top journal. ”

"He refused all interviews, including magazines like Science and Nature."

In 2003, shortly after publishing his findings, the bearded scholar with the style of a hermit disappeared from view. Perelman has lived a reclusive life, rarely leaving his home except for a regular visit to a grocery store not far from his home. He turned down a lot of money from Stanford University and many other internationally renowned universities, preferring instead to "look for mushrooms in the forests near St. Petersburg." ”

"Under what circumstances did he refuse material rewards?"

After leaving the institute in 1994, Perelman joined the ranks of the unemployed. He has no savings, and the little money he has is just enough to cover his and his mother's living expenses such as rent and travel. A few years ago, a friend asked him, "Do you have a girlfriend?" "I don't even have the money to buy a concert ticket, what kind of girl would be with me?" Now, Perelman and his son are living on a meagre pension of £30 a month. ”

"I'm not sure it's accurate, it's that Perelman is too mysterious and doesn't like people to bother him. Poverty and rejection of million-dollar rewards, no doubt. ”

"Ning Yun, who proved Poincaré's conjecture in another way, may also be a strange, unusual person. My students told me that Ning Yun rarely gives any interviews and doesn't like people caring about his privacy. This is very different from a director who needs to be known, and it is not like the manager of a company, or rather, it is impossible to be a manager of a company at all. ”

"This is consistent with what my Harvard counterparts know."

"In terms of money, he has almost no more than his two gossip girlfriends."

"Even if he is the generation that we think is growing up with the Internet, the generation that needs social interaction and material things the most."

Harvard likes to say that they produce students who are martyrdom seekers of truth, not fame and fortune seekers. Harvard advocates serving society, contributing to society, and helping to improve society. ”

"Harvardians certainly shouldn't monopolize such spiritual pursuits. But Ning Yun is indeed a typical example. It is ridiculous and even more pathetic to criticize Ning Yun on the Internet for being eroded by fame and fortune. ”

"If the critics regard fame and fortune as a sweet spring, the person who provoked all this would have already fallen to his knees at the feet of fame and fortune and praised it!"

"People who have made such contributions to this world should not be treated like this, should not be misunderstood by the public, and should not be slandered by some people with evil intentions!"

"It's not my style to express it emotionally. I just want to say, Ning Yun, you did a good job! ”

"As my students say, if making a film is a break for inspiration, then do it! I will take my daughter to the theater to support you! ”

"Also, MPAA, mathematicians don't shoot R-ratings!"

(To be continued.) )