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Chapter 29: Four-color conjecture

Kong Jidao looked at Liu Meng with a smile, narrowed his eyes, and said proudly: "Of course it was adopted, but you should not be too happy too early. Tomorrow, all members of the school's degree evaluation and positioning member will hold a meeting for the last consultation on the hiring of you as a researcher. You must also participate at that time, so it is best to prepare."

"This..., will time be a little hasty? I will only tell me today when I participate tomorrow?" Even if the genius is like Liu Meng, he knows that this level will definitely not be easy tomorrow. Teacher Kong trusts himself too much. He actually only prepares for himself one night. Can't he notify him early?

Kong Jidao waved his hand and said indifferently: "It's not a big deal. Let's go back with me tonight. I have been telling the school that we are studying mathematics together and are studying the Goldbach conjecture, one of the three major mathematical conjectures in the world. Do you know these three major conjectures?"

Liu Meng nodded and shook his head again. He had indeed heard of it, but he didn't know the details.

"All right, I'll talk to you." Kong Jidao smiled happily. For those who love mathematics, there is nothing more interesting than talking about these gossips in the mathematics world.

"The so-called three major conjectures are the Fermat Conjecture, the Four Color Conjecture and the Goldbach Conjecture. The proof of the Fermat Conjecture was completed by the British mathematician Andrew Wiles in 1994, so it was called the Fermat's Grand Theorem; the proof of the Four Color Conjecture was completed by American mathematicians Appell and Haken in 1976 with the help of computers; only the Goldbach Conjecture has not been solved yet, and the best result is obtained by Chinese mathematician Chen Jingrun in 1966. The common points of these three problems are that the topic is simple and easy to understand, and the connotation is extremely profound. It has troubled generations of mathematicians."

"There are many people who have been going on for it all their lives, and they pursue it without regrets. It is much more enthusiastic than pursuing the beloved girl." Kong Jidao said of math gossip, and his originally gray face suddenly became excited, especially when he said this, the spirit on his face was very high. Perhaps he was also a member of this huge army, so he was alone.

Liu Meng was happy to see him speak, although he knew some of it. He still pretended not to know at all, and followed his words: "What do these three guesses say in detail?"

"Okay, then I'll talk about the following steps. Let's talk about these four-color conjectures. In layman's terms, each plan map can be dyed with only four colors, and no two adjacent areas have the same color."

"In 1852, when Gusri, who graduated from the University of London, came to a scientific research unit to do map coloring work, he found that each map could be colored in only four colors. Can this phenomenon be strictly proved mathematically? He and his younger brother who was studying in college were determined to give it a try. However, the manuscript paper had been piled up, but the research work had not made any progress."

"On October 23, 1852, his younger brother consulted his teacher, the famous mathematician De Morgan, and Morgan could not find a way to solve this problem, so he wrote to his friend, Sir Hamilton, for advice, but the problem could not be solved until Hamilton died in 1865."

When Liu Meng heard the big joy, he said that the so-called "Regression Method" means contradictory. It is like a fool holding a spear and a shield, claiming that his spear is the sharpest in the world and can pierce all shields. He also claims that his shield is the strongest and can protect the sharpest spear. The essence of Regression Method is to use your sharpest spear to attack your strongest shield and get contradictory conclusions.

It's the inference of a neurotic.

"But Kemp's proof clarifies two important concepts and provides a way to solve the problem later. The first concept is configuration. He proves that in each map there are at least one country with two, three, four or five neighbors, and there is no map with six or more neighbors in each country, that is, a group of configurations composed of two neighbors, three neighbors, four or five neighbors is inevitable, and each map contains at least one of these four configurations."

"Another concept proposed by Kemp is remitability. The use of the word remitability comes from Kemp's argument. He proved that as long as one country has four neighbors in the five-color map, there will be a five-color map with a decrease in the number of countries. Since the introduction of the concept of configuration and the remitability, some standard methods have been gradually developed to check configurations to determine whether they are remitable. Being able to seek inevitable groups of remitable configurations is an important basis for proving the four-color problem. However, to prove that large configurations are remitable, a large number of details are required, which is quite complicated."

Although Kong Jidao tried his best to speak briefly, he still unconsciously introduced some more professional concepts in mathematics, which were concepts. Even if he had never been exposed to them, Liu Meng still understood them at first. However, as Kong Jidao held lectures on the second floor of the convenience cafeteria, he attracted several students from other colleges to eavesdrop.

These students may not know Kong Jidao, but none of them do not know Liu Meng. The Basics Department of Bingcheng University of Technology is known as the transition from high school to university. Here, although the students have entered the university, they still maintain their high school study habits. There is still a fixed study room in each class. Similarly, everyone is very serious about their studies. For the best, Liu Meng still admires the best and unconsciously wants to get to know Liu Meng.

When Kong Jidao heard from his mouth that Liu Meng was about to be hired as a researcher by the school, he opened his mouth wide in shock. When Kong Jidao talked about gossip in the mathematics world, as a top student, he naturally attracted attention.

At this moment, when Kong Jidao became more and more professional, he couldn't help but frown, but he still maintained a lot of interest. He just felt that the four-color guess was still very close to life. Isn't it just drawing a map? What are the tricks?

At this moment, several classmates whispered, and roughly guessed that the old man sitting with the god-level academic master Liu Meng was Teacher Kong Jidao. The classmate who knew the truth couldn't help but glared at Kong Jidao fiercely, seeing that he was so murderous.

There were many classmates present, and the girl was dedicated to Teacher Kong Jidao. It was really light and unfamiliar. When she took action, she didn't know how many classmates' golden bodies were broken, making life a little more complete from now on.

Kong Jidao opened his mouth and said, "People found that the four-color problem was unexpectedly difficult. Many people once published proofs or counterexamples of the four-color problem, but they were proved to be wrong. Later, more and more mathematicians racked their brains on it, but they got nothing. So people began to realize that this seemingly easy problem is actually a difficult problem comparable to the Fermat conjecture."

"Since the 20th century, scientists' proof of the four-color conjecture was basically carried out according to Kemp's idea. In 1913, the famous American mathematician, Berkhoff of Harvard University, used Kemp's idea and combined his new idea to prove that some large configurations were sub-constrained. Later, American mathematician Franklin proved in 1939 that maps below 22 countries could be colored with four colors. In 1950, Winn advanced from 22 countries to 35 countries. In 1960, some people proved that maps below 39 countries could be colored with only four colors; then advanced to 50 countries. This quantitative advancement speed is really slow."

After taking a sip of beer and moistening his throat, Kong Jidao continued: "That simple question has stumped everyone on this planet. It was not until the advent of electronic computers that made critical progress. Due to the rapid increase in calculation speed, the process of proof of the four-color conjecture was greatly accelerated. In June 1976, on two different electronic computers at the University of Illinois in the United States, it took 1,200 hours to make a judgment of 10 billion yuan. As a result, no map needed five colors, and finally proved the four-color theorem, which caused a sensation in the world."

"This is a big event that has attracted many mathematicians and mathematicians over the past hundred years. When the two mathematicians published their research results, the local post office stamped all the emails sent on that day with four colors and enough special postmarks to celebrate the solution of this problem. It is said that the letters for this day are quite popular in the collection market, and every mathematician enthusiast wants to buy a retention."

"Is there any practical application of this theorem?" Compared to Kong Jidao's pure love for mathematics, Liu Meng was more practical, and he preferred to consider application, and asked curiously. Is this theorem just like studying "Dream of Red Mansions"? It's just an interest, and that's not a pain in the idleness.

It also added: "Although any plan map can be colored with only four colors, the application of this theorem is quite limited, because in reality, maps often have enclaves, that is, two non-connected areas belong to the same country. When making maps, we still require these two areas to be painted with the same color. In this case, using only four colors will cause many inconvenience."

Kong Jidao replied: "You are right. In fact, maps that use four colors to color are rare, and these maps often require at least three colors to dye. In addition, even if the maps can be dyed with only four colors, more colors will be used for the sake of distinction to indicate the differences between different regions."

Seeing that Liu Meng was very dissatisfied with this four-color conjecture, Kong Jidao said again: "The problem itself may not have much practical significance, but in order to solve this conjecture, mathematicians have racked their brains for more than a century, and the concepts and methods introduced have stimulated the growth and development of topology and graph theory."

"In the process of research on the four-color problems, many new mathematical theories emerged and many mathematical calculation techniques have been developed. For example, turning the coloring problem of maps into graph theory problems has enriched the content of graph theory. Not only that, the four-color problem has played a driving role in effectively designing various schedules and computer coding programs." (To be continued...)
Chapter completed!
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