The four-color conjecture was put forward by 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.
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Fermat's last theorem is one of the three major mathematical problems in the modern world.
The New York Times, a world-recognized newspaper, published a headline on June 24th, 1993.
About the news that the math problem has been solved, the news headline is "In the ancient math dilemma, someone finally called"
I found it. " The opening article of the first edition of The Times also attached a picture of long hair and wearing a medieval European robe.
Pictures of men. This ancient man was the French mathematician Pierre de Fermat.
Please refer to the appendix for the biography). Fermat is one of the most outstanding mathematicians in17th century, and he has made great achievements in many fields of mathematics.
Great contribution, because he is a professional lawyer, in order to commend his mathematical attainments, the world called him "amateur prince"
"Reputation, one day more than 360 years ago, Fermat was reading a book by the ancient Greek mathematician Diofendus.
When I was writing a math book, I suddenly wrote a seemingly simple theorem in the margin of the page.
Capacity is a problem about the positive integer solution of equation x2+y2 =z2. When n=2, it is called Pythagorean rule.
Li (also called Pythagorean Theorem in ancient China): x2+y2 =z2, where z represents the hypotenuse of a right angle, and X and Y are it.
The square of the hypotenuse of two strands, that is, a right triangle, is equal to the sum of the squares of its two strands. Of course, this equation has
Integer solutions (in fact, there are many), such as: x=3, y=4, z = 5；; x=6、y=8、z = 10； x=5、y= 12、z= 13…
Wait a minute.
Fermat claims that when n>2, there is no integer solution satisfying xn +yn = zn, such as the equation x3 +y3=z3.
Find an integer solution.
Fermat didn't explain the reason at that time, he just left this narrative, saying that he found the proof of this theorem wonderful.
Method, but there is not enough space on the page to write it down. The founder Fermat therefore left an eternal question, 300
Over the years, countless mathematicians have tried in vain to solve this problem. This Fermat, known as the century problem, is the most
The post-theorem has become a big worry in the field of mathematics, and it is eager to solve it quickly.
In the19th century, the Francis Institute of Mathematics in France provided a gold medal and two prizes in 18 15 and 1860.
Whoever solves this difficult problem will be given 300 francs, but unfortunately no one will get a reward. German mathematician Wolff
Skell (p？ Wolfskehl) provides100000 mark in 1908 to those who can prove the correctness of Fermat's last theorem.
The validity period is 100 year. At the same time, due to the Great Depression, this award has depreciated to 7500 marks, although
This 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 was correct when n was 286243- 1.
(Note 286243- 1 is astronomical, with about 25960 digits).
Nevertheless, mathematicians have not found a universal proof. However, this unsolved mathematical problem for more than 300 years has finally been solved.
Yes, this math problem was solved by British mathematician andrew wiles. In fact, Willis is
The development of abstract mathematics in the last 30 years of the 20th century proves this point.
In 1950s, Yutaka Taniyama, a Japanese mathematician, first put forward a conjecture about elliptic curvature, which was later recorded by another mathematician.
Muragoro carried it forward. At that time, no one thought that this conjecture had anything to do with Fermat's last theorem. In the 1980s, Germany
Frey, a mathematician in China, linked Yutaka Taniyama conjecture with Fermat's Last Theorem, and what Willis did was based on this connection.
Prove that one form of Yutaka Taniyama's conjecture is correct, so is Fermat's last theorem. This conclusion
Officially published by Willis1June 2, 9931at the seminar of Newton Institute of Mathematics, Cambridge University, USA. This newspaper
The report immediately shocked the whole mathematics field, and even the public outside the mathematics door wall paid infinite attention. But Willis's
The certificate was immediately found to have some defects, so it took Willis and his students another 14 months to correct it.
Correct it. 1September 1994 19 They finally handed over a complete and flawless scheme, and the nightmare of mathematics finally ended. 1997 6
In May, Willis won the Wolfskeil Prize from the University of G? ttingen. At that time,100000 FAK was about $2 million.
However, when Willis received it, it was only worth about $50,000, but Willis has gone down in history and will be immortal.
Prove Fermat's last theorem is correct
(that is, xn+yn = zn has no positive integer solution to n33)
Just prove that x4+ y4 = z4, xp+ yp = zp (P is an odd prime number) has no integer solution.
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Goldbach conjecture, one of the three major mathematical problems in the modern world.
Goldbach is a German middle school teacher and a famous mathematician. He was born in 1690, and was elected as an academician of Russian Academy of Sciences in 1725. 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.