Junior high school students have studied Pythagorean theorem in plane geometry. According to this theorem, the lengths of three sides of a right triangle satisfy this equation. People will definitely ask: Is there a positive integer solution for x3+y3=z3 and x4+y4=z4? Generally speaking, xn+yn=zn(n is an integer greater than 2) has a positive integer solution? The French mathematician Fermat (160 1 ~ 1665) first put forward this problem.
In A.D. 1637, Fermat came to the following conclusion after repeated research: For the equation xn+yn=zn, where n is an integer greater than 2, there is no positive integer solution. This conclusion is called Fermat's Last Theorem. It is called "Theorem" because Fermat claims that he has been able to prove this conclusion. He wrote in the form of a note in the blank of a book: "I found this amazing proof, but the pages are too narrow to write." However, since then, people have searched Fermat's works and failed to find the "proof" mentioned in the notes.
In order to solve the mystery of annotation, mathematicians and amateur mathematicians have studied this problem. However, after more than 100 years of research, this problem has not been solved. 1850 and 1853, the French academy of sciences offered a reward of 2000 francs twice, but both were disappointed. 1908, the German Academy of G? ttingen offered a reward of100000 mark to find the "mystery" of Fermat's last theorem.
The honor and high reward of scientific discovery attracted a large number of amateur mathematicians to study this problem. There are also many people who claim to be "proved", but after the "review" by authoritative mathematicians, these "proofs" have been denied one by one. Unable to bear the annoyance of peer review, G? ttingen College reduced its bonus to 75,000 marks on the one hand, and sent a large number of "certifiers" on the other hand on the grounds that it only accepted published articles. However, the result of this has produced side effects: thousands of so-called "proof of Fermat's last theorem" and tens of thousands of articles of the same nature have appeared in society. Of course, this is just a tributary in the long history of proving Fermat's last theorem. What should be fully affirmed is the long-term efforts and achievements of some outstanding mathematicians:
Euler proved that n = 3,4;
1823, French mathematician Legendre proved that n=5;
1840, French mathematicians Lame and Leberg proved that n=7;
1849, the German mathematician Cuomo proved the case of n = 3 ~ 100 (except 37, 59 and 67), but there were some mistakes.
1976, American mathematicians proved 2 < n < 1000000.
Of course, these numbers also include their multiples. 1983, Falitings, a 29-year-old lecturer at Uppertal University in the former Federal Republic of Germany, proved the "Mo Deer conjecture" in mathematics. A direct corollary of this conjecture is that for any fixed positive integer n (n(n>3), xn+yn=zn has at most finite coprime positive integer solutions.
Then, Heath-Brown proved that Fermat's Last Theorem holds for "almost all" n.
On March 1988, 10, The Boston Globe reported that Japanese mathematician Miyaoka proved Fermat's Last Theorem in the former Federal Republic of Germany. However, only one month later, American Science News and other newspapers reported that famous mathematicians, after examining Miyaoka's manuscript, said that it proved that there were problems in details.
1On June 23rd, 993, a shocking news spread all over the world-the 350-year-old unsolved Fermat's Last Theorem was finally solved by the 40-year-old British mathematician andrew wiles.
Wiles now works in Princeton University. He is a world-class expert in number theory. 1June 2, 9931~ 23 gave a three-day lecture on "Galois Representation of Elliptic Curves and Modules" at isaac newton Institute of Mathematics, Cambridge University, UK. At first, no one could see that he had the intention to discuss Fermat's last theorem. On the last day, at the end of his speech, wiles concluded that he had proved a conjecture put forward by Japanese scholar Yutaka Taniyama. The experts present immediately realized that this meant that wiles had proved Fermat's Last Theorem.
People raised their cameras to capture this history. Then there was prolonged applause. Thousands of congratulatory phone calls and emails rained in, and the world's major newspapers rushed to report the news.
Is wiles's proof correct? This requires detailed study by mathematicians. However, international number theory authorities Bombieri, Rebett, Meige and Adlerman are optimistic about this. This is because wiles's research style has always been rigorous and meticulous, and his reasoning is based on the achievements of many mathematicians in the past 30 years, which is reliable.
Now it seems that Fermat's original "annotation", if not a joke, then his "proof" must be problematic. Because at that time, it was impossible to prove this theorem only with mathematical knowledge. However, whether joking or making mistakes, Fermat's "annotation" has established historical merits after all, because he blew the marching number to conquer Fermat's last theorem.