The 3 written by the above brother should be changed to n, and n >；; When =3, A, B and C have no positive integer solutions. Wiles is not the only proof of this topic. He solved the most difficult part and finally solved this topic. At that time, his age was only 4 1, and his paper was more than 200 pages long. In short, this is a very difficult topic in number theory, which can be compared with twin prime numbers, Goldbach conjecture, Euler's most trivial law, whether there is an odd perfect number, whether there is an infinite even perfect number and so on.
The Final Proof of Fermat's Last Theorem
(Transferred from Science Times)
Since Fermat's last theorem was put forward 350 years ago, many excellent mathematicians have tried to prove this theorem in various ways, but they have never succeeded. Wiles, a British mathematician, sharpened his sword for ten years and finally solved this problem completely in 1995.
Wiles: Cautious Dragon Slayer
/kloc-in the 0 th and 7 th centuries, the French mathematician Fermat wrote a conjecture on the edge of a page of Diophantine's works: "Xn+Yn = Zn； when n >; There is no positive integer solution at 2. " Later people called this conjecture Fermat's last theorem. Fermat went on to write: "I have found a clever proof, but unfortunately the blank here is too small to write."
After Fermat's death, his son published Fermat's works, letters and Fermat's revision of complicated works together, but he didn't find the proof of Fermat's last theorem. Whether Fermat can really prove this conjecture is still a mystery.
For more than 300 years, many excellent mathematicians have tried to prove this theorem in various ways, but they have never succeeded. Until recently, wiles of England solved this problem. The historic change took place in1June 6 to June 23, 993. At that time, 40-year-old wiles was teaching in the mathematics department of Princeton University. Every day, he gave a speech at a mathematics conference attended by about 40 or 60 people in Cambridge University, England. The topic was "Modular Form, Elliptic Curve and Galois Representation". It is not obvious from the title that what he wants to talk about is Fermat's Last Theorem, but the last sentence of his speech is: "This shows that Fermat's Last Theorem is established and proved."
Wiles's proof has aroused great concern in the field of mathematics. Although his first draft had some flaws, it was later revised by wiles himself. 1on June 29th, 993, The New York Times published a report entitled "andrew wiles released mathematical satellites, and the 350-year problem has been solved".
The Final Proof of Fermat's Last Theorem
In order to find the solution of Fermat's Last Theorem, generations of mathematicians have been advancing wave after wave for more than three centuries, but their ambitions have not been rewarded. 1995, Professor andrew wiles of Princeton University in the United States proved Fermat's Last Theorem with 130 pages after eight years of independent struggle. Wiles became a hero in the whole mathematics field.
big problem
In physics, chemistry or biology, no problem can be described so simply and clearly, but it has been puzzling for a long time. Eric Temple Bell wrote in The Last Problem that the civilized world may have come to an end before Fermat's last theorem was solved. Proving Fermat's Last Theorem has become the most worthwhile thing in number theory.
Andrew wiles was born in Cambridge, England on 1953. His father is an engineering professor. Wiles was fascinated by mathematics when he was a teenager. In his later memories, he wrote: "I like to do topics at school. I took them home and wrote my own new topic. " But the best topic I found before was found in the library of our community. One day, wiles Jr. saw a book in the library of Milton Street. This book has only one question, but there is no answer. Wiles was attracted.
This is a big question written by E T bell. It narrates the history of Fermat's Last Theorem, which makes mathematicians afraid, and no one can solve it for more than 300 years. Wiles recalled the feeling when he was led to Fermat's Last Theorem more than 30 years later: "It seems so simple, but all the great mathematicians in history failed to solve it. There is a problem that I, a child of 10, can understand. From that moment on, I knew I would never give up. I must solve it. "
Wiles obtained a bachelor's degree in mathematics from Merton College, Oxford University on 1974, and then went to Clare College, Cambridge University to pursue a doctorate. Wiles didn't study Fermat's Last Theorem in the postgraduate stage. He said: "The possible problem with studying Fermat is that you spent many years and finally got nothing. My tutor john coates is studying the iwasawa theory of elliptic curves, and I started working with him. " Coates said: "I remember a colleague told me that he had a very good student who had just finished the third exam of Bachelor of Mathematics with excellent results, and he urged me to accept him as a student. I am honored to have a student like Andrew. Even from the requirements for graduate students, he has profound thoughts and knows very well that he will be a mathematician who will do great things. Of course, it is impossible for any graduate student to directly start learning Fermat's Last Theorem at that stage, even for a mathematician with deep qualifications. " Coates' responsibility is to find something for wiles that will at least make him interested in his study in the next three years. He said: "I think what a graduate tutor can do for a student is to push him in a fruitful direction." Of course, there is no guarantee that this will be a fruitful research direction, but in this process, one thing an older mathematician may do is to use his common sense and his intuition about good fields. Then how much a student can achieve in this direction is his own business. "
Coates decided that wiles should study the field called elliptic curve in mathematics. This decision became a turning point in wiles's career, and the study of elliptic equation was a tool for him to realize his dream.
Lonely warrior
1980 wiles received his doctorate from Cambridge University, and later went to Princeton University, where he became a professor. Under Coates' guidance, wiles probably knew more about elliptic equations than anyone else in the world. He has become a famous number theorist, but he clearly realizes that even with his extensive basic knowledge and mathematical literacy, the task of proving Fermat's Last Theorem is extremely arduous.
In the proof of wiles's Fermat's Last Theorem, the core is to prove the "Gushan-Zhicun conjecture", which has built a new bridge between two completely different fields of mathematics. "It was a late summer evening in 1986, and I was drinking iced tea at my friend's house. During the conversation, he casually told me that Ken Rebbert had proved the connection between the Taniyama-Zhicun conjecture and Fermat's Last Theorem. I feel very shocked. I remember that moment, the moment that changed the trajectory of my life, because it means that all I have to do to prove Fermat's last theorem is to prove the Gushan-Zhicun conjecture ... I know very well that I should go home and study the Gushan-Zhicun conjecture. " Wiles found a way to realize his childhood dream.
At the beginning of the 20th century, david hilbert, a great mathematician, was asked why he didn't try to prove Fermat's last theorem. He replied, "Before I start, I have to do in-depth research for three years. I don't have that much time to waste on things that may fail." Wiles knew that in order to find proof, he had to devote himself to this problem, but unlike Hilbert, he was willing to take the risk.
Wiles made an important decision: to conduct research completely independently and confidentially. He said: "I realized that anything related to Fermat's last theorem would attract too many people's interest." Unless your attention is not distracted by others, you really can't concentrate on yourself for many years, which will be impossible because there are too many people watching. " Wiles gave up all work that had nothing to do with proving Fermat's Last Theorem. Whenever possible, he goes home to work. In the attic study at home, he began the battle to prove Fermat's Last Theorem through the Taniyama-Zhicun conjecture.
It was a protracted war for seven years, during which only his wife knew that he was proving Fermat's last theorem.
Cheering and waiting
After seven years' efforts, wiles has completed the proof of Taniyama intellectual village's conjecture. As a result, he also proved Fermat's last theorem Now it's time to announce it to the world. At the end of June, 1993, the Newton Institute of Cambridge University will hold an important meeting. Wiles decided to take this opportunity to announce his work to an outstanding audience. Another main reason why he chose to announce at Newton College is that Cambridge is his hometown, where he once studied as a graduate student.
1On June 23rd, 993, Newton College held the most important mathematics lecture in the 20th century. 200 mathematicians attended the lecture, but only a quarter of them fully understood the meaning expressed by Greek letters and algebra on the blackboard. The rest came here to witness the truly meaningful moment they were looking forward to. The speaker is andrew wiles. Wiles recalled the scene at the last moment of the speech: "Although the news about the speech has been broken by the press, fortunately they didn't come to the speech. But someone in the audience photographed the scene at the end of the speech, and the director of the institute must have prepared a bottle of champagne in advance. When I read the proof, the meeting was particularly solemn. When I finished the proof of Fermat's Last Theorem, I said,' I think I'll stop here', and there was lasting applause at the venue. "
The New York Times shouted "I found it!" on the front page The ancient mathematical mystery was solved and the news that Fermat's Last Theorem was proved was reported. Overnight, wiles became the most famous mathematician and the only mathematician in the world. People magazine listed wiles and Princess Diana as "the 25 most attractive people of the year". The most creative compliment came from a large international clothing company, who invited this gentle genius to be the model of their new collection of men's wear.
When wiles became the center of media coverage, the work of carefully checking this certificate was also going on. The scientific procedure requires any mathematician to submit a complete manuscript to a prestigious publication, and then the editor of this publication sends it to a group of reviewers, whose duty is to check and prove line by line. Wiles gave his manuscript to the invention of mathematics. He waited anxiously for the judges' opinions and prayed for their blessings all summer. However, a flaw was found in the proof.
My mind is calm.
Because wiles's paper involves a lot of mathematical methods, editor Barry Mayhew decided not to appoint 2-3 reviewers as usual, but 6 reviewers. This 200-page certificate is divided into six chapters, one for each reviewer.
During this period, wiles interrupted his work to deal with the questions raised by the reviewers in the mail. He is sure that these problems will not cause him too much trouble. Nick Katz is in charge of reviewing Chapter 3,1August 23, 993. He found a small defect in the certificate. Mathematical absolutism requires wiles to prove beyond doubt that every step of his method works. Wiles thinks this is another minor problem, and the remedy may be nearby. However, more than six months later, the mistake has not been corrected, and wiles is facing a desperate situation. He is ready to admit defeat. He explained his situation to his colleague Peter Sack, who hinted that part of the difficulty was that he lacked a reliable person to discuss the problem with. After long consideration, wiles decided to invite richard taylor, a lecturer from Cambridge University, to work with him at Princeton.
Taylor 1994 1 10 arrived in Princeton in September, and there was still no result. They were ready to give up. Taylor encouraged them to hold on for another month. Wiles decided to have the last check-up at the end of September. On a Monday morning on September 19, 2009, wiles found the answer to the question. He described the moment: "Suddenly, I made an incredible discovery. This is the most important moment in my career, and I won't experience it again ... its beauty is so indescribable; It is so simple and beautiful. I stared at it for more than 20 minutes. I couldn't believe it. Then I walked around the department during the day and went back to the table to see if it was still there-it was still there. "
This is a teenager's dream and the culmination of eight years' hard work. Wiles finally proved his talent to the world. The world no longer doubts this proof. These two papers * * * total 130 pages, which are the most thoroughly checked mathematical manuscripts in history. They were published in1May 1995 in the Journal of Mathematics. Wiles once again appeared on the front page of The New York Times, with the title "Mathematicians say the classic mystery has been solved". John coates said: "In mathematical terms, this final proof can be compared with splitting atoms or discovering the structure of DNA. The proof of Fermat's last theorem is the victory of human intellectual activities. At the same time, we can't ignore that it has brought revolutionary changes to mathematics at once. For me, the beauty and charm of Andrew's achievement lies in that it is a huge step towards algebraic number theory. "
Fame and honor poured in. 1995 wiles won the Shawk Prize in Mathematics awarded by the Royal Swedish Society, and 1996 won the Wolff Prize, and was elected as a foreign academician of the American Academy of Sciences.
Wiles said, "... no other problem has the same meaning to me as Fermat's last theorem. I have such a rare privilege to realize my childhood dream when I am an adult ... That particularly long exploration has ended and my heart has returned to peace. "