Seeing that some book friends reacted that there were too many things to talk about mathematics, this is also something that can't be helped, Liu Meng is best at mathematics, if you don't explain it clearly here, you can't feel his achievements later.

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Kong Jidao said to Liu Meng: "Just when you were presenting the paper on the Sitapan conjecture, Wiles saw it, and praised you vigorously at the annual meeting of mathematicians. ”

As soon as they heard this, the classmates looked at Liu Meng one after another, with envious eyes, and also said that Fermat's theorem was solved by so many cattle people in books, and in the end it was Wiles who solved it, and Wiles praised Liu Meng, and it seemed that Liu Meng was suddenly associated with the cattle Lagrange, Newton, Gauss, Euler, etc. in the books of "Advanced Mathematics", and they couldn't help but be in awe.

After more than 3oo years of stumbling and stopping, Fermat's theorem finally came to the end of its relay race, and the gang was handed over to a professor in the Department of Mathematics at Princeton University in the United States, whose name was Wiles. This Wiles is not an American, he is British, when he was young, when he was 1o years old, he once encountered Fermat's theorem, but at that time, everyone can imagine that the little boy was weak, so he let it go later. ”

But this fate made him have a strong interest in mathematics, so he later became a professional mathematician, but his field of study has nothing to do with Fermat's theorem, he studies a kind of science called elliptic curves, what is elliptic curves? and Fermat's theorem are two completely different branches of mathematics, you may be surprised. How to solve Fermat's theorem, it seems to be a layman, yes. In fact, many of the top problems of human beings are often solved by this characteristic. ”

"First, it is often the people of the past generations who have paved the way for its final solution, but this step is often paved, but no one has shown its value for many years, and after many years, someone suddenly has a flash of inspiration. Blessing the soul and transforming the previous achievements into their own glory. ”

"The second characteristic is that it is often a layman who has crossed over. Crookedly, this is called planting flowers with intention, unintentionally planting willows and willows, and finally solving this problem. ”

"Between Fermat's theorem and Wiles. These two characteristics are very typical. ”

"Pave the first steps for Wiles. In fact, a man who lived nearly 2oo years ago, and a Frenchman, his name was Galois, 12 years old, he entered the Lycée Louis Royale, his grades were very good, his passion for mathematics exploded, and he could no longer raise any interest in other subjects. The school described Galois as peculiar, weird, original, and closed. ”

"In 1827. At the age of 16, Galois confidently applied to his dream university, the comprehensive engineering school, but was discredited by his incompetent examiner. Year 1829. Galois presented the results of his solution to the algebraic equations to the French Academy of Sciences, which was reviewed by Cauchy, who lost the article and the abstract. ”

To make matters worse, when Galois was about to apply for the Polytechnic University for the second time, his father committed suicide because he was maliciously slandered during the election. The unjust death of his upright father affected his failure in the exam, and also led his political outlook and outlook on life to become more extreme. ”

Galois entered the École Normale Supérieure and the following year he again wrote three papers on the results of equation theory to win the mathematics prize of the Academy of Sciences that year, but after the article was sent to Fourier, it was dusted by Fourier's death, and Galois could only watch the prize fall into the hands of Abel and Jacobi. ”

A series of blows and encounters, as if Heaven was jealous of his talent, Gradually, Galois became a radical republican. In our words today, he is an angry young man, because of the political views and many people have fierce friction, but this person also has a very cute characteristic of the French, that is, the pursuit of beautiful women, he hooked up with all kinds of girls, and finally hooked up with a girl, and ended up in trouble. ”

"This girl's fiancé was a famous gunman in France at that time, and this gunman said, 'Do you dare to move my woman?' According to the customs of the time, you can't refuse, or according to your own sense of honor, you can't refuse this duel, but the other party is the best gunman, and you will definitely die. The so-called dueling arena is actually your death penalty field. ”

"So, Galois is very crazy, Galois is not a professional mathematician, he has only been studying mathematics for five years, but he is indeed a genius, he has a new idea brewing in his head, so he will go to the execution ground the next day, the first night, he wrote a manuscript, this manuscript, extremely important. ”

"On the eve of his death, he spent the whole night anxiously writing his last words of science, writing as much as he could before he died, and writing as much as possible of the great things of his rich mind. From time to time, he interrupted and wrote in the margins of the paper: I don't have time, I don't have time. Then he scribbled down an extremely scribbled outline. ”

"In the early morning of May 3o, 1832, near Lake Glassell in Paris, lay an unconscious young man, and the passing peasant, judging from the gunshot wounds, was seriously wounded after a duel, and carried the unknown young man to the hospital. At ten o'clock the next morning, the poor young man died, and the youngest and most creative mind in the history of mathematics stopped thinking. ”

"Galois's death delayed the exhibition of mathematics for decades, and the two founders of group theory were full of pathetic romanticism, Abel died of poverty and Galois died of stupidity. In all the history of science, there is no more comprehensive example of the triumph of utter stupidity over irrepressible genius than Galois's excessively short life. ”

His friend complied with Galois's last wish and sent his mathematical papers to Gauss and Jacoby, but they were all lost, and many years later, until 1843, it was another mathematician, Liu Wei, who appeared in this manuscript, and then was astonished to express the whole idea of this manuscript to him in a coherent way, and later, this idea became a very important theoretical branch in the history of mathematics, called group theory. ”

"What is group theory? That is, sometimes to solve a mathematical problem, you don't try to solve it in a package, or solve it individually, it often doesn't work, you often have to take a domino method, that is, I push down the first one, then crush the second one by the way, and then a string can solve it. It is exactly the same as the characteristics of Fermat's theorem mentioned earlier, and this key seems to be able to open another lock. ”

Speaking of Galois, Kong Jidao still couldn't help sighing, in the history of mathematics exhibitions, only Galois is the most sentimental, this is a too talented teenager, but he has encountered too many ups and downs, with a touch of sadness, said.

"After all, Galois was a mathematical genius, but he was unlucky, and the reason why he was so radical in politics was also caused by his depression and nowhere to vent in mathematics. Of course, Galois's tragedy also has its own shortcomings, that is, the writing is too concise, young people are prone to impetuousness, geniuses are even more young and frivolous, and their thoughts are already very advanced, and they are not clearly expressed, how can those predecessors take it seriously?"

Speaking of which, you can see that Fermat's theorem seems to be a human intellectual game, but it is a relay race of highly intelligent people in the world, and it is completed in a historical span of more than 3oo years and in a collaborative scene around the world. ”

"These two little devils, one is called Yutaka Taniyama and the other is Goro Shimura, what are the achievements of Yutaka Taniyama and Goro Shimura? They put forward a conjecture, that is, between the two branches of mathematics, one is called elliptic curves and the other is called modular forms, there is a one-to-one correspondence between zài, what is the one-to-one correspondence?"

"It's like the Pythagorean theorem, which is an algebraic formula, but it also corresponds to the geometry of a right triangle, which is called a one-to-one correspondence. To put it bluntly, solving this formula, although it solves an algebra problem, it also solves a geometry problem. ”

So once this conjecture was put in front of Wiles as a mathematical achievement, it suddenly dawned on him that it was possible to prove Fermat's theorem indirectly through the independent field of mathematics called the elliptic curve, which had plagued mankind for hundreds of years, through the independent field of mathematics called guò modeling, and as a bridge to the field called elliptic curves, which he was very familiar with in his own career. ”

You see, the whole mind suddenly opened up, and Wiles knew that his life had a great opportunity to gamble, and if he won the bet, he would become the most famous mathematician in history, and if he didn't win, his life would be bleak. He decided to bet. ”

"The way he gambled was also interesting, and he decided to play alone. Mathematicians are a little intrigued with each other, because mathematicians are different from scientists in other fields, and they have some external conditions in other fields, but mathematicians rely on pure ideas, otherwise there would not be the incident of Lame and Cauchy delivering secret letters mentioned above. ”

The female classmate who had been listening to the lecture was still immersed in the tragedy of Galois, and then she came back to her senses and shouted: "Galois is so pitiful, this Cauchy is too shameless, and Gauss is too unkind, I have decided not to study Gauss's research results again." ”

The classmates looked at her like idiots, Gauss's achievements in "Advanced Mathematics" are many, not to mention anything else, almost all the series are Gauss's achievements, if you don't learn his achievements, don't you wait to fail the course......!

ps: It's a bit of a thousand and one nights.,Friends who don't like to watch it are temporarily ridiculed.,It's estimated that there are about two chapters.。

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