Kong Jidao looked at Liu Meng with a smile, his eyes narrowed, and he said proudly: "Of course it is adopted, but don't be too happy too early, tomorrow morning all the members of the school's degree evaluation and positioning members will hold a meeting to hold a final consultation on the matter of hiring you as a researcher, and you will also participate in it at that time, it is best to prepare." ”

"This ...... Won't the time be a little rushed? Participate tomorrow, and only tell me today?" "Even if a genius is like Liu Meng, he also knows that tomorrow's level will definitely be difficult, and Mr. Kong believes in himself too much, so he only prepares for himself one night, can't he notify him early!

Kong Jidao waved his hand and said indifferently: "Don't worry, come back with me tonight, I have been telling the school that the two of us are studying mathematics together, and we are studying Goldbach's conjecture, one of the world's three major mathematical conjectures, these three conjectures, you kid know?"

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

"Come on, then I'll tell you. Kong Jidao smiled very happily, for people who love mathematics, there is nothing more interesting than the gossip in the mathematics world like Shen Kan.

The so-called three conjectures are the Fermat conjecture, the four-color conjecture and the Goldbach conjecture. The proof of Fermat's conjecture was completed in 1994 by the British mathematician Andrew Wiles, and was called Fermat's theorem; the proof of the four-color conjecture was completed by the American mathematicians Appel and Haken with the help of a computer in 1976; only the Goldbach conjecture has not yet been solved, and the best result was obtained by the Chinese mathematician Mr. Chen Jingrun in 1966. What these three questions have in common is that the questions are simple and easy to understand, and the content is extremely profound. has plagued generations of mathematicians. ”

"There are many people who have spent their lives for this, and they are all pursuing without regrets. It's much more enthusiastic than pursuing the girl you love. Kong Jidao talked about mathematical gossip, and his dead gray face suddenly became excited, especially when he said this, the look on his face was very high, probably he himself was also a member of this behemoth army, so that he was alone.

Liu Meng was happy to see what he said, although he had some understanding in it. Still pretending not to know at all, he followed his words and said, "What exactly do these three conjectures say?"

"Okay, then I'll talk about the order of solution. Let's start with the four-color conjecture, which is commonly known as the fact that each flat map can be colored with only four colors, and no two adjacent areas are the same color. ”

"In 1852, when Guthrie, a graduate of the University of London, came to work in a scientific research institute to work on map coloring. Each map can now be colored in just four colors. Can this be mathematically rigorously proven? He and his brother, who was in college, decided to give it a try. However, there was a huge pile of manuscript paper, and there was no progress in the research work. ”

On 23 January 1852, his brother consulted his teacher, the famous mathematician de Morgan, about the proof of the problem, but Morgan could not find a solution to the problem, so he wrote to his friend, the famous mathematician Sir Hamilton, for advice, but the problem was not solved until Hamilton's death in 1865. ”

In 1872, Kelly, Britain's most famous mathematician at the time, formally raised the question to the London Mathematical Society. As a result, the four-color conjecture has become a concern of the world's mathematical community, and many first-class mathematicians in the world have participated in the four-color conjecture. From now on. The question was passed down among some people, when the problem of tripartite angles and the squaring of circles had become notorious in society, and the plague of four colors had quietly spread. ”

Kong Jidao said that these things in the history of the mathematics exhibition are really like a treasure, and even every time node can be accurately said, I have to make Liu Meng admire, how much do you love mathematics to reach this point, if you use these energy to love a woman, the birthday, hand-holding anniversary, kissing anniversary, bed anniversary, bed anniversary, etc., all accurately recorded, how kind of move does that woman have to be?

Mathematicians are selfless and have modeled the species of women for analysis, and probably in their minds, mathematics is the sexiest woman.

After that, the four-color conjecture progressed slowly until 188o, when the famous lawyer and mathematician Kemp and Taylor respectively submitted papers proving the four-color conjecture, announcing the proof of the four-color theorem. Everyone thought that the four-color conjecture would be solved, but Kemp didn't prove the four-color problem. ”

Eleven years later, in 189o, at the age of 29 at Oxford, Herwood pointed out Kemp's holes in his proof with his own precise calculations. He pointed out that Kemp's argument that there is no such thing as a very small five-color map with one country and five neighbors is flawed. Soon Taylor's proof was also denied. People now actually prove a weaker proposition, the five-color theorem. That is, to color the map, five colors are enough. ”

However, to the comfort of mathematicians, Herwood did not completely dismiss the value of Kemp's paper, and using Kempming's method, Herwood proved the weaker five-color theorem. This is tantamount to a slap in the face of Kemp and a praising of him, which is generally more derogatory than positive. I wonder what the poor lawyer Kemp is feeling?"

As he spoke, Kong Jidao's face was flushed with excitement, and there was a little bit of gossip, probably thinking about what kind of mood Kemp, the unlucky guy would be?

"It's in the nature of mathematicians to get to the bottom of it. On the one hand, five colors are sufficient, and on the other hand, there are indeed examples where three colors are not enough. So are four colors enough? It's like a gold digger who knows that there are a lot of gold mines somewhere, but only digs up a piece of silver, and you think he's willing to go back like that?"

In the final analysis, it is the nature of mathematicians, Liu Meng absolutely agrees with this, as can be seen in the last time he participated in the mathematics annual meeting, this is an extremely stubborn group, stubborn to a certain extent, that is, careful eyes, eyes can not rub a little sand, in the pursuit of mathematics, this spirit is worthy of affirmation, but, unfortunately, most people substitute this trait into life.

Kemp proves this by the fallacy, to the effect that if there is a five-color map. If a country has fewer than six neighboring countries, a map with a small number of countries will be stored and the map with a small number of countries will remain five-colored. In this way, there will be no very small number of countries on the five-color map, and there will be no zài five-color map. So Kemp thinks he's proven the four-color problem, but then people realize he's wrong. ”

When Liu Meng heard the great joy, the so-called fallacy method is not a self-contradiction, just 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 against the sharpest spear, and the essence of the fallacy is to attack your strongest shield with your sharpest spear. Reach contradictory conclusions.

It is the inference of neuropathy.

But Kemp's proof illuminates two important concepts that provide a way to solve the problem later. The first concept is configuration. He proved that in every map there is at least one country with two, three, four or five neighbors, and that every country does not exist with a map of six or more neighbors, that is. by two neighboring countries. A set of three, four, or five neighbors is inevitable, and each map contains at least one of these four configurations. ”

Another concept Kemp brings up is reducibility. The use of the word Keoff comes from Kemp's argument. He proved that as long as one country has four neighbors in a five-color map, there will be a five-color map with fewer countries. Since the introduction of the concept of reducibility and reducibility, some standard methods of examining configurations to determine whether they are reducible have been gradually developed, and the inevitable group of reducible configurations can be sought, which is an important basis for proving the four-color problem. But to prove that a large configuration is reducible, a large amount of detail needs to be checked, which is quite complicated. ”

Although Kong Jidao tried to say it as plain as possible. Or unconsciously will introduce some mathematically more specialized concepts, these concepts. Even if he hadn't been in contact, Liu Meng still understood it as soon as he heard it, but as Kong Jidao gave a lecture 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 there is no one who does not know Liu Meng, the basic department of Bingcheng University of Technology is known as the transition between high school and university, here, although the students have entered the university, but still maintain the study habits of high school, there is still a fixed study room in each class, the same, everyone is also very serious about learning, for the most excellent, Liu Meng, or worship in his heart, unconsciously want to know Liu Meng.

And when he heard from Kong Jidao's mouth that Liu Meng was about to be hired as a researcher by the school, he opened his mouth in shock, and when he heard Kong Jidao talk about gossip in the mathematics world, as a scholar, he naturally attracted attention.

At this moment, when I heard Kong Jidao talk more and more professionally, I couldn't help frowning, but I still maintained a considerable interest, I just felt that this four-color conjecture was still very close to life, isn't it just drawing a map, what is the doorway.

At this moment, several classmates whispered, and they roughly guessed that the old man who was sitting and chatting with Liu Meng, a god-level academic bully, was Teacher Kong Jidao, and the classmates who knew the truth couldn't help but glared at Kong Jidao fiercely, seeing that they had the heart to kill people like that.

There were many classmates present whose virginity was dedicated to Mr. Kong Jidao, who was really light and not close to women, but he didn't know how many classmates' non-golden bodies were broken, which made life a little bit complete from then on.

Kong Jidao opened the chatterbox, and said spittle, extremely excited, "People are unexpectedly difficult to solve the four-color problem, and there have been many people who have expressed proof or counter-examples of the four-color problem, but they have all been proven to be wrong. Later, more and more mathematicians racked their brains about it, but found nothing. As a result, people began to realize that this seemingly easy problem was actually a difficult problem comparable to Fermat's conjecture. ”

"Since the beginning of the 2o century, scientists have basically followed Kemp's ideas in proving the four-color conjecture. In 1913, the famous American mathematician Berkhoff of Harvard University used Kemp's ideas and combined them with his new ideas to prove that some large configurations were reducible. Later, in 1939, the American mathematician Benjamin Franklin proved that maps of less than 22 countries could be colored in four colors. In 195o, Wynn advanced from 22 to 35 countries. In 196o, it was proved that maps with less than 39 countries could be colored in only four colors, and then it was advanced to 5o. This quantitative progress is really slow. ”

After taking a sip of beer and moistening his throat, Kong Jidao continued: "It's just such a simple question, but it stumped everyone on this planet, and it wasn't until the advent of electronic computers that there was a critical progress, and due to the rapid improvement of the calculus, the process of proving 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 12oo hours to make 1oo00 million judgments, and the result was that none of the maps needed five colors, and finally proved the four-color theorem, which caused a sensation in the world. ”

This was a major event that attracted many mathematicians and math enthusiasts for more than 100 years, and when the two mathematicians presented their research results, the local post office stamped all the mail that day with a special postmark of four colors to celebrate the solution of the problem. It is said that the letters of this day are quite sought-after in the collector's market, and every math enthusiast wants to buy one for keep. ”

"Is there any practical application of this theorem?" Compared with Kong Jidao's pure love of mathematics, Liu Meng was more practical, inclined to consider the application, and asked curiously. Is it the same as studying "Dream of Red Mansions", just an interest, isn't it a pain to be idle?

He adds: "Although any flat map can be colored with only four colors, the application of this theorem is quite limited, because in real world maps often have enclaves, i.e. two disconnected areas belong to the same country, and we still require the two areas to be painted the same color when making a map, in which case using only four colors would cause a lot of inconvenience." ”

Kong Jidao replied: "You are right, in practice, it is rare to use four colors to color maps, and these maps often only need at least three colors to color. In addition, even if the map can be colored with only four colors, more colors will be used to indicate the differences between different regions. ”

Seeing that Liu Meng was very dissatisfied with this four-color conjecture, Kong Jidao said: "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 studying the four-color problem, many new mathematical theories have been produced, and many mathematical calculation skills have also been developed. For example, the problem of map coloring is transformed into a graph theory problem, which enriches the content of graph theory. Not only that, but the four-color problem has played a role in the effective design of various schedules as well as the coding programs of computers. (To be continued......)

PS: I've wanted to write this for a long time, but in fact, the three major conjectures in mathematics are very interesting.

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