Four-color conjecture, Goldbach conjecture, Fermat's last theorem four-color conjecture, one of the three major mathematical problems in the modern world, comes from Britain. 1852, when Francis guthrie, who graduated from London University, came to a scientific research institute to do map coloring, he found an interesting phenomenon: "It seems that every map can be colored with four colors, which makes countries with the same border painted with different colors." Can this conclusion be strictly proved by mathematical methods? He and his younger brother, Grace, who is in college, are determined to give it a try. The manuscript papers used by the two brothers to prove this problem have been piled up, but the research work has not progressed. 1852, 10 year123 October, his younger brother asked his teacher, the famous mathematician de Morgan, for proof of this problem. Morgan couldn't find a solution to this problem, so he wrote to his good friend, Sir Hamilton, a famous mathematician, for advice. Hamilton demonstrated the four-color problem after receiving Morgan's letter. But until the death of 1865 Hamilton, this problem was not solved. 1872, Kelly, the most famous mathematician in Britain at that time, formally put forward this question to the London Mathematical Society, so the four-color conjecture became a concern of the world mathematical community. Many first-class mathematicians in the world have participated in the great battle of four-color conjecture. During the two years from 1878 to 1880, Kemp and Taylor, two famous lawyers and mathematicians, respectively submitted papers to prove the four-color conjecture and announced that they had proved the four-color theorem. Everyone thought that the four-color conjecture was solved from now on. 1 1 years later, that is, 1890, the mathematician Hurwood pointed out that Kemp's proof and his accurate calculation were wrong. Soon, Taylor's proof was also denied. Later, more and more mathematicians racked their brains for this, but found nothing. Therefore, people began to realize that this seemingly simple topic is actually a difficult problem comparable to Fermat's conjecture: the efforts of previous mathematicians paved the way for later mathematicians to uncover the mystery of the four-color conjecture. Since the 20th century, scientists have basically proved the four-color conjecture according to Kemp's idea. 19 13 years, boekhoff introduced some new skills on the basis of Kemp, and American mathematician Franklin proved in 1939 that maps in 22 countries can be colored in four colors. 1950 someone has been promoted from 22 countries to 35 countries. 1960 proves that maps below 39 countries can be colored with only four colors; And then push it to 50 countries. It seems that this progress is still very slow. After the emergence of electronic computers, the process of proving the four-color conjecture has been greatly accelerated due to the rapid improvement of calculation speed and the emergence of man-machine dialogue. 1976, American mathematicians Appel and Harken spent 1200 hours on two different computers at the University of Illinois in the United States, made 1000 billion judgments, and finally completed the proof of the four-color theorem. The computer proof of the four-color conjecture has caused a sensation in the world. It not only solved a problem that lasted for more than 100 years, but also may become the starting point of a series of new ideas in the history of mathematics. However, many mathematicians are not satisfied with the achievements made by computers, and they are still looking for a simple and clear written proof method. Fermat's Last Theorem, one of the three major mathematical problems in the modern world: The New York Times, an authoritative newspaper recognized by the world, published a news that a mathematical problem was solved on the front page of June 24th, 1993. The headline of the news is "In the ancient mathematical dilemma, someone finally shouted' I found it'". The opening article of the first edition of The Times is accompanied by a photo of a man with long hair and wearing a medieval European robe. This ancient man was the French mathematician Pierre de Fermat. Fermat is one of the most outstanding mathematicians in17th century. He has made great contributions in many fields of mathematics because he is a professional lawyer. In recognition of his achievements in mathematics, the world called him "Prince of Amateur Mathematics". One day more than 360 years ago, Fermat was reading a math book by Diofendos, an ancient Greek mathematician, when he suddenly had a whim in the margin of the page. Write down a seemingly simple theorem. The content of this theorem is about the positive integer solution of an equation x2+y2 =z2. When n=2, it is the well-known Pythagorean Theorem (also called Pythagorean Theorem in ancient China): x2+y2 =z2, where z represents the hypotenuse of a right triangle, and x and y are its two branches, that is, the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two branches. Of course, this equation has an integer solution. x=6、y=8、z = 10； X=5, y= 12, z= 13… and so on. Fermat claims that when n>2, there is no integer solution satisfying xn +yn = zn, such as the equation x3 +y3=z3. At that time, Fermat did not explain why. He just left this narrative, saying that he found a wonderful way to prove this theorem, but there was not enough space on the page to write it down. Fermat, the initiator, thus left an eternal problem. For more than 300 years, countless mathematicians have tried in vain to solve this problem. This Fermat's last theorem, known as the century's difficult problem, has become a big worry in mathematics and is extremely eager to solve it. 19th century, Francis Institute of Mathematics in France provided a gold medal and 300 francs to anyone who solved this problem twice in 18 15 and 1860. Unfortunately, no one can receive the prize. German mathematician Wolfskeil (p? Wolfskehl) provides 100000 marks in 1908 to those who can prove the correctness of Fermat's last theorem, and the validity period is100 years. In the meantime, due to the Great Depression, the bonus amount has been devalued to 7500 marks, but it still attracts many "math idiots". After the development of computers in the 20th century, many mathematicians can prove that this theorem holds when n is large. 1983, the computer expert Sloansky ran the computer for 5782 seconds, which proved that Fermat's last theorem is correct when n is the 86243 power of 2-1 (Note 2: 86243 power-1 is an astronomical number with about 25960 digits). Nevertheless, mathematicians have not found a universal proof. However, this 300-year-old math unsolved case has finally been solved. Andrew wiles, an English mathematician, solved this mathematical problem. In fact, Willis used the achievements of the development of abstract mathematics in the last 30 years of the twentieth century to prove it. In 1950s, Yutaka Taniyama, a Japanese mathematician, first put forward a conjecture about elliptic curvature, and later another mathematician Goro Shimamura developed this conjecture. At that time, no one thought that this conjecture had anything to do with Fermat's last theorem. In 1980s, German mathematician Frey linked Yutai Taniyama's conjecture with Fermat's last theorem. What Willis did was to prove that one form of Yutai Taniyama's conjecture was correct according to this connection, and then deduced Fermat's last theorem. This conclusion was officially published by Willis at the seminar of Newton Institute of Mathematics, Cambridge University, USA on June 2 1, 1993. This report immediately shocked the whole mathematics field, and even the public outside the mathematics door paid infinite attention. However, Willis' proof was immediately found to have some defects, so it took Willis and his students 14 months to correct it. 1September 1994 19 They finally handed over a complete and flawless scheme, and the nightmare of mathematics finally ended. 1In June, 1997, Willis won the Wolfskeil Prize at the University of G? ttingen. At that time,1100,000 grams was about $2 million, and when Willis received it, it was only worth about $50,000, but Willis has been recorded in the history books and will be immortal. Goldbach conjecture: Goldbach is a German middle school teacher and a famous mathematician. Born in 1690, 1725 was elected as an academician of the Academy of Sciences in Petersburg, Russia. 1742, Goldbach found in teaching that every even number not less than 6 is the sum of two prime numbers (numbers that can only be divisible by themselves). For example, 6 = 3+3, 12 = 5+7 and so on. 1742 On June 7th, Goldbach wrote to tell the great Italian mathematician Euler this problem and asked him to help prove it. In his reply to him on June 30th, Euler said that he thought this conjecture was correct, but he could not prove it. Describing such a simple problem, even a top mathematician like Euler can't prove it. This conjecture has attracted the attention of many mathematicians. They began to check even numbers until they reached 330 million, which showed that the guess was correct. But for a larger number, the guess should be correct, but it can't be proved. Euler died without proof. Since then, this famous mathematical problem has attracted the attention of thousands of mathematicians all over the world. 200 years have passed and no one has proved it. Goldbach conjecture has therefore become an unattainable "pearl" in the crown of mathematics. It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Bujue proved by an ancient screening method, and reached the conclusion that every even number with larger ratio can be expressed as (99). This method of narrowing the encirclement is very effective, so scientists gradually reduced the number of prime factors in each number from (99) until each number is a prime number, thus proving "Goldbach". 1924, mathematician Rad mahar proved (7+7); 1932, mathematician eissmann proved (6+6); In 1938, mathematician Buchstaber proved (55), and in 1940, he proved (4+4). 1956, mathematician vinogradov proved (3+3); In 1958, China mathematician Wang Yuan proved (23). Subsequently, Chen Jingrun, a young mathematician in China, also devoted himself to the study of Goldbach's conjecture. After 10 years of hard research, we finally made a major breakthrough on the basis of previous studies and took the lead in proving it (L 12). At this point, Goldbach conjecture is only the last step (1+ 1). Chen Jingrun's paper was published in 1973 Science Bulletin of China Academy of SciencesNo. 17. This achievement has attracted the attention of the international mathematics community, which has made China's number theory research leap to the leading position in the world. Chen Jingrun's related theory is called "Chen Theorem". 1in late March, 996, when Chen Jingrun was about to take off the jewel in the crown of mathematics, "when he was only a few feet away from the brilliant peak of Goldbach's conjecture (1+ 1), he fell down exhausted ..." Behind him, more people would climb this peak.