Speaking of Gauss, Kong Jidao didn't like it very much, glanced at his mouth and said: "Gauss has fellow mathematicians who evaluate him, saying that this person hates him to death, every time he proves a theorem, he will walk through the forest like that old fox, and will use his big tail to sweep the traces behind it clean, you can see that he proved so beautifully, but his way of thinking, he will never tell you! This is very bad, his way of thinking will give others a lot of enlightenment, but it is a proof step, and the usability value is much lower." ”

The other is that Gauss has not done anything to promote the future generations, but it is not conducive to the growth of others, and when others want to ask him for advice, he either ignores it at all, or is cold. Abel sent his results to Gauss to see, and asked Gauss to throw them away, and Galois did not forget to send a copy of what Galois wrote before his death, and it is estimated that Gauss did not read it, and Pollot's research on non-Euclidean geometry, wanting to get his support, said that he had studied it a long time ago, and Polio was disheartened. ”

Abel and Galois, two pathetic mathematicians, both of whom were the founders of group theory, made similar contributions and suffered the same experience, and can only be said to be jealous of geniuses, and I will talk about these two men in more detail later, because the group theory they created was crucial to the solution of Fermat's theorem. ”

It is said that Gauss thinks too highly of himself, and most of the other mathematicians are dismissive, the only exception is because of Fermat's theorem, and the offspring he gave support and affirmation is a woman, a French girl named Germain, hehe, but don't think of Gauss so unbearable, when you meet a beautiful woman, your attitude will change. ”

"Originally, Germain was not interested in mathematics. The thing that changed her life was born one day, when she was casually flipping through her father's library, and she came across a chapter about the life of Archimedes written in The History of Mathematics, which led to her fantasies. His description of Archimedes' various manifestations is undoubtedly interesting. But what particularly fascinates Germain is the plot that revolves around the death of Archimedes. ”

"Archimedes lived in Syracuse, studying mathematics in relative peace, but when he was almost 8o years old, the peace was destroyed by the invasion of the Roman army. Legend says that during the Roman invasion, Archimedes was so engrossed in studying a geometric figure in the sand that he neglected to answer a Roman soldier's question. As a result, he was stabbed to death with a spear. ”

Germain came to the conclusion that if one would be so obsessed with the geometry of a result that would lead him to death. Then mathematics must be the most fascinating subject in the world. She immediately began to teach herself the basics of number theory and calculus, and soon worked late into the night, studying the works of Euler and Newton. Her sudden interest in such a subject, which was not suitable for women, worried her parents. ”

Her father confiscated her candles and clothes. And move anything that can keep her warm to stop her from continuing her studies. Germain's countermeasure was to use hidden candles and wrap himself in sheets. The winter night was so cold that the ink froze in the inkwell, but Germain insisted on looking at it despite it. She was so determined that her parents eventually became compassionate. Agree with her to continue her studies. ”

Kong Jidao said here. Looking around at the more and more students who were listening to the lecture, he reprimanded: "Compared to Germain, look at you children, the classrooms and dormitories are heated, spacious and bright, how do you study? If I am still asked to take out the exam papers this semester, it must be more difficult than last time, and it is shameful to study just to cope with the exam." It is a waste of intelligence and resources. ”

After speaking, Kong Jidao was huffing. Very angry. "We have medalists in the Olympiad every year, but no one has been able to achieve as outstanding achievements as Tao Zhexuan or Perelman, and some have even stayed away from mathematics. ”

"In China, many secondary and secondary school students see the Olympiad as a shortcut to university and devote a lot of time to training. If you are only taking the Olympiad to get into a good university, this goal is too short-sighted. Many parents want their children to become Jackie Chan, push their children too quickly, and learn that from primary school, wasting too much interest and spirit of exploration. ”

"Mathematical research is not the same as the environment required for the Olympiad, which is like a sprint race under predictable conditions, while mathematical research is a marathon under unpredictable conditions in real life, which requires more patience and a willingness to study small problems before tackling big problems. ”

In 1972, Klein wrote a well-known book on the history of mathematics called "Ancient and Modern Mathematical Thought", and he actually said in the preface that in order not to let the material of this book be aimlessly extravagant, we automatically ignore the mathematics of some nationalities. ”

I didn't expect Mr. Kong to be so cynical, Liu Meng persuaded and said: "Mr. Kong, this is not formed overnight, it is not easy to change the overall environment, we can only do our best first, or tell us the story of Germain and Gauss first, it is said that German has never married in his life, I don't know if it has anything to do with Gauss?"

Liu Meng had a feeling that Mr. Kong seemed to be sharper and less peaceful than before.

After Kong Jidao leaked his brain, he calmed down, and when he heard Liu Meng say this, he teased: "You kid can really gossip, but Germain has said a famous saying, say don't look at me not married, I have been engaged a long time ago, I am married to the truth! This is a pursuit, this is a state of life." ”

Liu Meng looked at the look on Kong Jidao's face, and had a strange feeling, how could it seem that Mr. Kong was talking about himself, who said that people were not married, they had already married mathematics.

Kong Jidao was a little hairy by Liu Meng, and continued: "The real difficulty of Fermat's theorem is that if you solve any single number, no matter how much you solve, it is useless, because there is a devil in mathematics, called infinity, that is, no matter how few you prove, then add 1? Is that number still valid? Just in the recent history of mathematics, there has been such a thing, in a very large number suddenly proves that a certain formula is not true, so the whole formula is overturned, such a thing is not uncommon in the history of mathematics. So if Fermat's theorem is proved one by one, when will it be a head?"

"In 1794, the Polytechnic School was born in Paris. It was established as an excellent school for the training of mathematicians and scientists for the country. It could have been an ideal place for Germain to showcase her mathematical talents, but it was a male-only academy. Her naturally shy personality made her afraid to meet the school's management, so she secretly studied at the school under the guise of LeBron, a former male student of the school. ”

"The administration of the school did not know that the real Mr. LeBlanc had left Paris, so they continued to print lecture materials and exercises for him. Germain managed to obtain the materials originally given to LeBron, and turned in the answers to the exercises every week under her new pseudonym. Everything went smoothly as planned, until two months later, when the instructor of the course, the famous Lagrange, could no longer ignore the talent shown in LeBron's work-solving. ”

"Not only is LeBron's solution ingenious, but it shows a profound change in a student who was previously known for his terrible math abilities. Lagrange, one of the finest mathematicians of the 19th century, asked the changed student to meet him, and Germain was forced to reveal her true identity. Lagrange was shocked and he was so excited to meet the young schoolgirl and be her mentor and friend. Germain finally had a teacher who could motivate her and who could be honest with him about her talents and ambitions. ”

Germain became more and more confident, moving from solving exercises in her coursework to studying unexplored areas of mathematics. Of particular importance was her interest in number theory, which made it inevitable for her to know Fermat's theorem. She studied this issue for several years, and finally reached the stage where she was confident that she had made an important breakthrough. She needed to discuss her idea with a male mathematician and decided to go straight to the best mathematician. So she went to consult Gauss, the world's most prominent number theorist at that time. ”

Germain adopted a new tactic, in which she described to Gauss what was called a general approach to the problem. In other words, her immediate goal is not to prove a particular case, but to arrive at a solution that suits many situations at once. It is to find a unified scheme that, once proved, can be proved by all numbers, and all Germain actually came up with a completely new idea of proving Fermat's theorem. ”

When Germain wrote to Gauss, she was just over 2o years old. Although she already had a bit of a reputation in Paris, she was still afraid that the big man wouldn't take her seriously because of her gender. In order to protect herself, Germain once again used her pseudonym, and the letter was signed by LeBron. Gauss, not knowing the true identity of his correspondent, tried to comfort Germain by writing back: I am glad that arithmetic has found such a talented friend as you. ”

Had it not been for Emperor Napoleon, Germain's contribution might have been forever wrongly attributed to the mysterious LeBron. In 18o6 Napoleon invaded Prussia, and the French army stormed German cities one by one. Fearing that fate befell Archimedes would also take the life of Gauss, another of her admirers, Germain wrote a letter to her friend, General Joseph, who was then in charge of commanding the advancing army. ”

She begged him to guarantee Gauss's safety, and as a result, the general gave the German mathematician special care and explained to him that it was Mademoiselle Germain who saved his life. Gauss was grateful and surprised, because he had never heard of Sophie Germain. (To be continued......)

PS: Gauss is indeed a genius, and geniuses always have a temper.

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