Poincare conjecture _ Sun

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ification: headache of centurlos angeles tax lawyery challenges takeaway: If we stretch around a rubber band on the surface of the Apple, so we can neither snapped it and not let it leave the surface, make it move slowly shrink a point. On the other hand, if we imagine the same rubber band in an appropriate direction is an expansion in the tire surface, then do not tear the rubber band or tire surface, there is no way to shrink to the point. We say, "Apple surface is simply connected," while the tire surface is not. About a hundred years ago, Poincare already know, 2-dimensional spherical nature may be represented by a single connectivity to characterize, he raised three-dimensional spherical (four-dimensional space and origin have unit distance point of the whole) of the corresponding issue. The question immediately becomes more difficult, since then, the mathematicians in this struggle. A mathematical historians have called 1854 was born Henry Poincare (HenriPoincare): "some people seemed to be born in order to prove the existence of genius, every time I see Henry, I'd heard the annoying voice sounded in my ear. " The great Poincare as mathematicians, and not entirely because he has solved many problems, but he has put forward a lot of meaning, with a foundation of big issues. Poincare conjecture is one of them. 1904, Poincare in a paper presented a seemingly very simple topological guess: in a three-dimensional space, where every piece of closed curves can shrink to the point, the space must be a three-dimensional sphere. But 1905 found error in the reference, and was modified to be promoted as: "any n-dimensional spherical homotopy n-dimensional manifold must be closed with the embryo in n-dimensional sphere. " Later, this conjecture was extended to three-dimensional space above, referred to as" high-dimensional Poincare conjecture ". w>br> If you think this is too abstract, we may wish to do such a imagination: we imagine such a House, this space is a ball. Or, imagine a huge football, filled with gas, we drill into it, this is a spherical House. We may suppose that this spherical house walls are made of steel, very strong, there is no door without Windows, we are now at such a spherical House. Now get a balloon, to the spherical House. Just what the balloon can (actually this balloon is required). This balloon is not flat, but already blown a certain shape, what shapes you can (for shape also has certain requirements). But the balloon, we can continue to blow it, and assuming that the skin of the balloon, the special setting will certainly not be blown out. Also suppose that the balloon is infinite thin skin. Well, now we continue to blow up this balloons, always blow. The blow to immigration? Poincare conjecture, to Mr. J Mr., it all spherical surface and the entire Internet balloon on a wall surface firmly attached to what live, no gaps. We can swap a method like: If we stretch around a rubber band on the surface of the Apple, so we can neither snapped it and not let it leave the surface, make it move slowly shrink a point; on the other hand, if we imagine the same rubber band in an appropriate direction is an expansion in the tire surface, then do not tear the rubber band or tire surface, there is no way to shrink to the point. Why because Apple surface "single connected," but not the tire surface. Looks like this is not very easy to make it clear? but mathematics can not "just think" can prove a conjecture, which requires strict mathematical reasoning and logic. More than a century, numerous scientists to prove it, his brains and evengave his life or fruitless. Difficult to prove road on 24 May 2000, the United States Clay Mathematics Institute of the Scientific Advisory Committee of the Poincare conjecture as seven "Millennium challenges" (also known as the world's largest math challenges), the Institute of seven road issues were considered "important classic problem, after many years is still not resolved. " Cray Mathematics Institute's Board of Directors decided to set up seven million prize fund, each of the" Millennium Prize problems "solution receives million dollar bonus. Another six "Millennium Prize problems" are: NP complete problem that's conjecture (Hodge), Riemann hypothesis (Riemann), Yang-Mills theory (Yang-Mills), the Navier-Stokes equations (Navier-Stokes, hereinafter referred to as NS equation), BSD conjecture (Birch andSwinnerton-Dyer). Raised this conjecture, Poincare once believed himself has proven it. But it was not long before, the proof of error will be exposed. Thus, topological scientists began to prove it. First, early proof of 20th century ago, Poincare conjecture of only a few isolated cases. But suddenly, BritishCountries mathematician Whitehead (Whitehead) on this issue had a keen interest. He once claimed that he completed the proof, but soon withdrew papers, losing the roundabouts, East of resumption. But in the process, he found a three-dimensional manifold of some interesting special case, and these exceptions, are now collectively known as the white sea currents. 1930s to the 1960s, some famous mathematicians claim that he resolved the Poincare conjecture, famous guest (R.Bing), Haken (Haken), maeuser (Moise) and Papa cilac Proos (Papa-kyriakopoulos) have therein. Papa cilac prospect is 1964 of Veblen prize winners, a Greece mathematician. Because his name is very long so read, weall call him the "Papa" (Papa). In 1948, Papa has been working with mathematical rings keep a certain distance away, until being invited as a guest at Princeton University. Papa to prove that the famous "Dean lemma" (Dehn'sLemma) is composed of mathematicians, like John Milnor (JohnMilnor) had to do this, write a Limerick: "unfriendly by Dean lemma/every topological's natural enemies/until Papa cilac Proos/proof it was painless. " However, this wise Greece, but the final topology on the Poincare conjecture of proof. In the Princeton University going around a story. Until 1976, before his death, Papa is still attempting to prove that the Poincare conjecture, deathbed, he put a stack of thick manuscripts to a mathematician friends, however, only turned a few pages, the mathematician discovered the error, but in order for the Papa quietly away, and finally statements must not selected. Second, at breakthrough during this period the Poincare conjecture topology home, although they did not produce the desired results, however, has therefore developed a low-dimensional topology this subject. Again attempt failed, allowing the Poincare conjecture of became known difficult mathematical problems of proof. However, because it is the basis for the study of geometric topology, mathematicians can't be thrown aside. At this point, things appear. 1966 fields Prize winner Bensmail (Smale), in the 1960s came up with a genius idea: If the Poincare conjecture three-dimensional insurmountable, the higher will be easier? 1960 to 1961, in Rio de Janeiro waterfront, often you can see a person holding a scratch paper and pencil, thoughts on the sea. He is the Smail. In the summer of 1961, nonlinear vibration in Kiev, Smail announced himself on the Poincare conjecture of the five-dimensional space and five-dimensional above proves that caused a sensation at the time. 10 years later in 1983, the United States mathematician Faurie de man (Freedman) will prove that it was a step forward. At Donaldson, on the basis of his card out of the four-dimensional space Poincare conjecture, and therefore access to fields. However, moving forward, and stagnation. Topology of three-dimensional Poincare conjecture no progress, some people began to think of other tools. Thurston (Thruston) is one of them. He introduced the geometric structure of method on three-dimensional manifold for cutting, and thus won the prize of the fields in 1983. "Like Fermat's last theorem, when the Valley Mountain Shimura conjecture is that, although people also do not see a specific prospect, but all the people are. Because one can solve the problem of the tool. Tsinghua University, Department of Mathematics "Man Chi-ying says. Third, final decisive battle Poincare conjecture, however, still have not been proved. People are looking forward to a new tool. However, address the Poincare conjecture of tools ? tool. Richard Hamilton, born in 1943, 6-year-old than qiuchengtong big. Although joking, qiuchengtong would jokingly said that more than 30 years history, like surfing, tourism and girlfriend of old "Playboy", but his achievements in mathematics, but only praise and fretted. 1972, qiuchengtong and Weiguang cooperation, developed a method of nonlinear differential geometry of theory. Qiuchengtong this way proves the Calabi conjecture and get fields prize. In 1979, at Cornell University in a class, then a Professor of mathematics at Stanford University's qiuchengtong saw Hamilton. "At that time, the Hamilton just doing the Ricci flow, others do not know, told me. I think this thing is not very easy to do. Unexpectedly, in 1980, he made the first important results. "Qiuchengtong said," so I told him, you can use this result to prove the Poincare conjecture, and three-dimensional space. " Ricci flow is to Italy mathematician Ridge (GregOrio Ricci) named an equation. With it you can complete a series of topological operations, construction geometry structure, the irregular manifold into rules of manifold, thereby solving three-dimensional Poincare conjecture. See the importance of this equation, qiuchengtong immediately follow your own several students follow Hamilton of Ricci flow. Including his first students from mainland China huaidong Cao. First met Cao huaidong, is in superstring Assembly Qiuchengtong reports on the Poincare conjecture. Although that time, almost all of the media looking for Cao huaidong, but wearing a bright big t-shirt for him in the Hall to go several times, but still no one recognized. No wonder. The vast majority of mathematicians, remains far from the public eye in the person of the ivory tower, even the name dynamic world where tweeten (Witten), sitting in the back seat, if it is big but to the city. 1982, Cao huaidong studied in doctoral qiuchengtong. In 1984, when qiuchengtong go to UC San Diego Campus Faculty, Cao huaidong also follow up. However, the vast majority of his time, and this time also from Cornell University go to Diego's Hamilton "bubble together." At this time, four PhD Qiuchengtong, all in the follow direction on Hamilton. Where do the best, is Shi Wan-hung. He wrote many of the most beautiful essays, raised a lot of good ideas, but, because of personality and environmental reasons, without the University's tenure, Shi Wan-should give up to do math. Lift the Shi Wan-hung, remain today, qiuchengtong waffle if any regrets. A although not help but make people think deeply on the assumption that if, at the time of ShiWan-keep it up and on the story of the Poincare conjecture,will being overwritten? Ricci flow is used for transformation, to later, there was unable to control the direction of the point. These points, called singularity. How to control their movements, as demonstrated by the three-dimensional Poincare conjecture. In reference to the qiuchengtong and Weiguang in nonlinear differential equations of the work, in 1993, Hamilton published an article on understanding the singular point of important papers. It was at this point, qiuchengtong felt that solve the Poincare conjecture, is just around the corner. And at the same time, the other end of the Earth, one called Grigori Perelman mathematician in �� spent eight years on the foot with a century-old math problem after three key papers in the manuscript in November 2002 and July 2003, paste it into a specialized publication of maths and physics papers Web site and email notification for a couple of mathematician. Claims proved geometry of conjecture. To October 2005, several experts announced that verify the certificate, consistent support almost reached the views. "If your wish to separate the at.this on promotion, there - to - < sucstressed="" 'mig-at="" perelman,="" it."="" who="" "i="" have="" done,="" i="" can="" published="" wish="" for="" the="" public="" to="" w.t.=""> Perelman's practices for Cray Research Institute for mathematics. This is because, according to the Institute's rules, that solved the human need to guess the regular magazine and approved by experts, to get $ 1 million in prize money. Obviously, Perelman and don't want to put the 100 million dollars into his meager income. For grigory perelman, people is poorly understood. At.this mathematical genius, was not related born in 1966, 13 June, his talent led him began to specialize in care on mathematics and physics. 16 forhis outstanding achievements in it, the International mathematical Olympiad mig-at 1982 that the medal. In addition, the gold he 's a talented violinist, billiard and beat well. From St. Petersburg University, PhD, has been working in Russia Academy of Perelman in St. Petersburg, Steklov mathematical Institute of the work. Last century, the late 1980s, he visited the United States universities to do post-doctoral research. About 10 years ago, he returned to the Steklov mathematical Institute, continuing his cosmic shapes that work. Prove the Poincare conjecture the key role that the exposure to the public soon Perelman vision, but he did not like to deal with the media. It is said that a reporter would like to give him a photo, be he shouted stop; and on the nature of science such fame magazine interview, he also asked for some help. "I think what I said nothing to talk of possible public interest. " Perelman said," I don't want to say because I value the privacy of their own, or I just want to hide any of the things I do. There is no top secret, but I only think that the public interest to me. "He insisted that he should not be so concerned about, and expressed the slightest feilai strikes. 2003, published his research results shortly after, this is the implicit ' style beard scholars from people's perspective. It is said that he and his mother, sister together live in St. Petersburg in the suburbs of a small house, and the Jewish families rarely open to the public. IV. final of settlement in this way, in the continuous efforts of our predecessors, the Poincare conjecture of became a winner. 3 June 2006, Sun Yat-sen University professors and Cao XI ping to a huaidong up to 300 pages of paper, the way to the special issue published in United States, published by the Asian mathematics journals on June has Perelman, complete the proof of vulnerability, gives the Poincare conjecture full proof. Explains the mathematics community concern about 100 years of significant challenges �� the Poincare conjecture. Use of Hamilton and Perelman, theoretical basis, Zhu Xi and Cao huaidong first successfully processed the conjecture in the "singularity" challenges to completely solve the puzzle world's mathematicians of the Poincare conjecture for years. In the future, "Poincare conjecture" is going to be called "Poincare theorem��"! however, because there are other people claim to prove the conjecture, including Perelman, Hamilton is on this issue has a great contribution, Perelman was once claimed to prove the conjecture, and Zhu Xi and Cao huaidong but completed the final cap, who was the first proof that there is controversy. Who is the most important proof? Perelman US 23 June arrived in St. Petersburg, a special interview Perelman. And before that was never interviewed Perelman. Before us, the President of the International Union of mathematicians JohnBall secret visited Perelman, his sole purpose is to persuade Perelman to accept to be in the August issue of the International Congress of mathematicians fields prize. Everyone knows that this is the field's highest honor, the total of 44 mathematician honored, nobody refused to accept the honor. But in the face of Professor Ball for two days of 10 hours of persuasion, Perelman's answer is "I refuse to. " He told us:" if my proved correct, way of recognition is not necessary. " Perelman visit United States in 1992, his life is extremely frugal eats bread, cheese and milk. In the New York University, he met the young Chinese mathematicians tiangang, each week they drove to Princeton to participate in the discussions of the higher Institute. Perelman read Hamilton article on streaming Clank, also in the higher Institute of listening to him for a report. Perelman said: "you don't have to be great mathematicians can also be seen on the geometry of be useful. " Perelman began in 1993, Berkeley for two-year access, falls Hamilton to school for a series of lectures. After the last report, Hamilton told Perelman his biggest obstacles, one of which is called "cigars," a kind of singularity. Perelman is aware that he wrote no published articles may be useful to solve this problem, ask Hamilton is aware of this article. But Hamilton does not seem to understand the importance of this article. In 1994, Perelman was written out a few very original papers and invited at the International Congress report. mathematician Several universities, including Stanford and Princeton, invited him to apply for jobs. But he refused to provide a number of schools, in the summer of 1995, and returned to St. Petersburg. He said: "I realized I was in Russia will work better. " Stanford Eliashberg says he returned to Russia in order to solve the Poincare conjecture, Perelman on this statement has not objected. In Russia he work alone, only through the Internet to gather the knowledge he needed. Gromov, who worked with Perelman's famous geometers said: "he doesn't need any help, like a person. He reminds me of Newton, obsessed with their own ideas, not to ignore the advice of others. "In 1995, Hamilton published an article, which describes his complete proof of the Poincare conjecture for some ideas. Perelman said to us, from the article "I don't see him in 1992 after any progress. May even earlier he was stuck in there. "Yet they think they see Perelman had to solve the problem. In 1996, he gave Hamilton wrote a long letter, describes his thoughts, hopes to Hamilton in his cooperation. However, Perelman said: "he did not answer. So I decided to start his own stem. "11 November 2002, Perelman in mathematical base arxiv.org posted on his first article, he passed the email sent to the article summary in United States of some mathematicians, includingHamilton, tiangang and qiuchengtong. Before he had not discussed with anyone in this article, because "I don't want to trust discuss my work. " For free to publish on the Internet is so important questions may bring risks, such as certificates or flawed but make shaming him, and even others to correct the priority of the loss results, Perelman said:" if I'm wrong but someone use my work gives the right to prove that I will be very happy. I never want to be the Poincare conjecture of unique crackers. "Tiangang in MIT received Perelman's e-mail, immediately aware of its importance. He began to read and with his colleagues discuss the article. November 19, geometers Kapovitch e-mail asking whether Perelman: "I have understood correctly: you outline in Hamilton's already can do enough steps so that you can solve the geometry of guess?," Perelman on the second day to answer only one sentence: "this is correct. " Tiangang wrote to Perelman invited him to MIT for speech. Princeton and colleagues at Stony Brook, also issued a similar invitation. Perelman all accepted, and in April 2003, began in the United States do tours. Mathematicians and the media have put this as a great event. He was disappointed that Hamilton had not participated in the meeting. Perelman tells us, "I was Hamilton's disciples, although haven't got his endorsement. " When Colombia University JohnMorgan invited him to his speech, he agreed, because he hoped that there could see Hamilton. Lectures will be held on a Sunday morning, Hamilton was late, and in the meeting's discussions and there is no reference to any lunch. "My impression is that he read my article in part one. " Perelman said. To July of 2003, has been published in online Perelman had his twoArticle. Mathematicians began his proven hard to test, and description. In the United States at least two groups of experts undertook this task: tiangang (qiuchengtong opponent) and Morgan; University of Michigan's two experts. Clay gave to them the Institute and funded, and plan to put the Tin and Morgan's work published in book form. This book provides, in addition to the mathematicians Perelman logical proof of, or access to Clement Perelman million dollars bonus on the basis of the Institute. 10 September 2004, in Saint-Petersburg Perelman back more than a year later, he received tiangang issued a long email, in which it wrote: "I think we have to understand your article, it is completely correct. " Perelman no reply. He explained to us, "people need time to adapt to the famous question is no longer a suspect fact. .... It is important that I'm not going to affect the process. "In the spring of 2003, convened by Sun Yat-sen University of Zhu Xi Qiuchengtong calm one of his students, the University of the Caspian Sea, assume the CAO huaidong Perelman's proof of interpretation. Hill also arranged Zhu in 2005-06 school year access Harvard University, in a discussion in class about Perelman's proof and continue to write them together with Cao. 13 April 2006, the Asian mathematics Magazine Editorial Board of 31 mathematician receives qiuchengtong and another joint editor of e-mail to inform them in 3 days on the Hill is going in the magazine of Zhu Xi and Cao huaidong article comments, entitled "Ricky stream of Hamilton-Perelman theory: Poincare and geometry of conjecture". E-mail messages are not included in this article, the assessment report or summary. At least one member of the Editorial Board asked to see this article, only to be told to get. April 16, Cao received a mound of messages tell his story has been accepted, a summary of which was published in the magazine's Web site. A month later, Zhu and Cao article title in the Asian Journal of mathematics on the Web page is changed to "the Poincare conjecture and geometry of a full proof: rich stream of the Hamilton-Perelman theory of application". Summary has also been modified, new saying, "this proof should look as a rich stream of the Hamilton-Perelman theory of the highest achievements". Zhu and Cao article said that they had to "study based on its new approach insteadof Perelman's several key steps, because we cannot understand his original reasoning, but the reasoning on the geometry of the completion of the programme is important. " Familiar with Perelman proof of mathematicians do not agree with Mr CAO for Poincare conjecture and make important new contributions. Morgan said: "Perelman have done that, the proof is complete and correct. I don't see them doing different things. "Two authors arrived at the St. Petersburg after experienced a zigzag didn't see Perelman. Perelman repeatedly said that he had quit the mathematical community, no longer thinks he is a professional mathematician. He mentioned some years ago he same partners on how to evaluate an author of a work of dispute. He said he had scholars lax ethics was very depressed. "Don't violate ethical standards were regarded as heterogeneous," he said, "but people like me are isolated. " When asked whether he had read the article Cao and Zhu, he replied" I don't know what they do. Apparently did not fully understand those Zhu, reasoning and do it again. "As for qiuchengtong, Perelman said," I can't say I was violated. It was also doing worse than this. Of course, how many mathematicians are honest, but they almost all peacemaker. They tolerate those who are not honest. "Get fields Prize prospects forced him and his career a clean break. " As long as I am not famous, I still have the choice," Perelman explained that, "or do some scandal,"-----for lack of a sense of a fuss about mathematics-----"or does not do so without being as a pet. Now, I became very famous, I can no longer do pets without talking. This is why I want to quit. "When asked, he rejected the fields Prize, withdrew from the field, does that mean he ruled out the impact of any potential for the mathematical community, he replied" I'm not a politician. "Perelman refuses to answer whether he would reject Clemente Institute of million dollar bonus. " Before issuing bonus I don't make decisions," he said. Gromov says he can understand the logic of Perelman. "You have to do the great work you must have a pure heart. You can only think of mathematics. Other everything belongs to human weakness. "Although people will put his refusal to accept the fields prize as an arrogant, Gromov said his principle worthy of admiration. " Ideal scientists outside except science doesn't care about other things. He wanted to live in that ideal. Although he failed to do, but he wants to do. "The significance of the Poincare conjecture Poincare conjecture of significance, proof of the conjecture, condensed China six scientists contribution, which is in three dimensions on the merits of the first challenges, but also a belong to the basic algebraic topology with meaningful proposition will help humanity to better study of three-dimensional space, its results will increase people's awareness of the convection-nature, to physics and engineering will have a profound impact, even for people with a mathematical language for the description of an impact for Aerospace. Other challenges of resolving the situation Poincare conjecture we look at and similarly course as "world 's largest challenges" of math of solving of advertising: sucstressed' life-time Riemann hypothesis: many people, did not split true hoping 's Mir conjecture: when Yang - these guys are so difficult, and few: people do P and NP life-time: when in the porch and aubject to wear Swinerton - hopefully mention ya Chinese: Neville Earl - Stokes equations: far from solved sucstressed