Kong Jidao was very satisfied with this girl's question, and continued with a smile.

"In the 15oo years after the current pair of affinity numbers 22o and 284, there are many mathematicians in the world who are committed to exploring affinity numbers. ”

"Mathematicians still haven't found a second pair of affinity numbers. In the sixteenth century, it was already believed that there was only one pair of affinity numbers in the natural number. Some boring people even add superstition or mystery to the affinity, and make up a lot of myths. It is also advertised that this pair of affinity numbers plays an important role in magic, spells, astrology and divination, which are all nonsense and a great trick in the world. ”

More than 25oo years after the birth of the first pair of affinities, the wheel of history turned to the seventeenth century, and in 1636, Fermat found the second pairs of affinities 17296 and 18416, rekindling the torch of searching for affinities and finding light in the darkness. Two years later, on March 31, 1638, Descartes, the father of analytic geometry, also announced the discovery of a third pair of affinities 9437o56 and 9363584. In the space of two years, Fermat and Descartes broke the silence of more than 2,000 years and stirred up a wave of re-searching for affinity numbers in the mathematical community. ”

"In the years after the seventeenth century, many mathematicians threw themselves into the search for new affinity numbers, and they tried to use inspiration and boring calculations to create a new big 6. However, the unforgiving facts make them realize that they have fallen into a mathematical labyrinth. The splendor of Fermat and Descartes is impossible. ”

Just when the mathematicians were really desperate, there was another thunderclap on the ground. In 1747, the genius Swiss mathematician Euler announced to the world that he had found a 3o pair of affinity numbers. Later, it was extended to 6o pairs, which not only listed the number table of affinity numbers, but also published the entire operation process. Euler is worthy of being the first genius of the mathematical world, and human mathematical thinking has solved the problem that has stopped people for more than 25oo years, and the case is amazing. ”

Of course, no matter how great a person is, there are times when he makes mistakes and misses. Another 12o years passed, and in 1867, there was a 16-year-old middle school student in Italy who loved to use his brain and was diligent in calculations. It turned out that the mathematician Euler had made a mistake that made a pair of smaller affinities 1184 and 121o slip out of his eyelids. This dramatic moment has fascinated mathematicians. ”

Kong Jidao said that he looked at Liu Meng with satisfaction here, and said loudly: "Therefore, mathematics is never the older you get, the more powerful you are. Opposite. The greatest achievements are created by young people, and many times, the young lads are far better than us old guys, and the old guys are at most adding bricks and tiles. ”

"A mathematician, if he hasn't achieved anything by the time he is thirty years old, is basically like this in his life. So, unlike the Nobel Prize, the Fields Medal, the highest award in mathematics, is only given to people under the age of 4o. Relaxed to 4o years old, all kinds of accidents have been taken into account. Of course. There are exceptions, and Wiles, the final solver of Fermat's theorem, is the accident of the unexpected. He was really not good enough when he was young, he was still working hard in his thirties, but he became famous in one fell swoop at the age of forty, and we will tell his story in detail later. ”

As soon as these words came out, the surrounding students couldn't help but look at Liu Meng, and at this moment they all felt that Liu Meng was a rare genius in the mathematical world.

It was still the little girl who asked curiously: "Having said so much, what is Fermat's great theorem? Isn't it called Fermat's last theorem, it is said that even the peerless genius Euler and the prince of mathematics Gauss are stumped." ”

Kong Jidao nodded, but he was impressed by this little girl, and said very proudly: "To understand the origin of Fermat's theorem, we must first talk about the source of number theory, that is, the Diophantus diagram with the same name as Euclidean, Euclid wrote a book "Geometry Original", became a generation of masters of geometry, and Diophantan wrote a book "Arithmetic", which became the pioneering work of number theory and a classic. ”

In 1621, Fermat finally bought this book in Paris, and when he returned home, he read it when he had time, and conducted an in-depth study of the indefinite equations in the book, and limited the study of indefinite equations to integers, thus really starting the mathematical branch of number theory. ”

"It's the same as Wang Chongyang who practiced the "Nine Yin True Scripture" and created the Quanzhen Sect. Kong Jidao's spare time is to read martial arts, and in his heart, the world of mathematics is not a river and lake.

"Everyone knows the Pythagorean theorem, that is, the sum of the squares of the two right-angled sides of a triangle is equal to the sum of the squares of the hypotenuse, the most classic is the Pythagorean four mysteries, when Fermat read "Arithmetic", he once wrote next to the proposition in volume 11, No. 8: It is impossible to divide a cubic number into the sum of two cubic numbers, or a power of four into the sum of two powers of four, or to divide a power higher than the second into the sum of two powers of the same power. I am sure that a wonderful proof has been developed on this point, but unfortunately the blank space here is too small to write. ”

When Kong Jidao said this, he couldn't help laughing, "It's just a paragraph written casually, after the death of the old guy Fermat, his son sorted out the relics and found them, and since then this passage has troubled human sages for 358 years. ”

The girl who was sitting not far away was completely fascinated by what she heard, and said hurriedly: "Didn't Fermat claim to have manifested a wonderful method of proof? Why has it been bothered for so long, has it been lost?"

Kong Jidao touched his chin and pretended to be mysterious: "In my opinion, I'm afraid Fermat is bragging, and he hasn't found a wonderful proof at all, or maybe this is just a short thought he made while reading the book, and it is not thorough and detailed, and he himself doesn't know the difficulty of this conjecture." ”

"Cut, the great mathematician is still bragging?" the girl was straightforward.

Kong Jidao glared and shouted: "Mathematicians are not people, are they people, they have seven emotions and six desires, monks still eat meat, and Taoist priests still marry wives." ”

The frightened little girl stuck out her tongue.

After Fermat's death, he left behind a large number of mathematical puzzles, but with the progress of human mathematical technology, they were gradually solved, except for the great theorem named after him, which has never been answered. Of course, in this process, it is not without bits and pieces of progress, for example, his contemporaries are thinking, didn't you Fermat himself brag, saying that I have a concise and wonderful proof method, but I can't write it here, so I won't write it, well, you can't write it here, maybe one day when you live, you have itchy hands for a while, write it down there?"

After a pause, Kong Jidao took a sip of beer and said.

So after he died, many people rummaged through his manuscripts to see if he had left any traces. Looking around, there is really something to gain, everyone now, Fermat once proved this formula before his death, that is, when this 2 becomes 4, Fermat's great theorem is true. In other words, it has been proven that the power of the 4th of any positive integer, plus the power of the 4th of any positive integer, cannot be expressed as the power of any positive integer. Well, with such a good start, we will arch down little by little. ”

Then, the cruel reality told us that Fermat's theorem was not so easy, until 17o6, a great mathematician named Euler was born, who was an unborn genius who once left the famous Euler's formula. ”

Euler made a slight modification to Fermat's method, proving 3, don't underestimate 3 and 4, although it is only these two numbers, but if you prove 3, you can prove the 9th power, and if you prove the 4th power, you can prove the 16th power, so in the group of positive integers, there are actually many numbers that have been solved by these two people. ”

"The rings of time continue to roll downward, and Gauss, the king of mathematics, comes into play. He was born in the 18th century, but the mainstream of life was in the 19th century, and he died in 1855. He solved countless mathematical problems in his life, and he was most proud of the drawing of a regular seventeen-sided ruler, which is strange to you to hear, what does it mean? If you are only given two tools, one is a compass and the other is a ruler without a scale, can you draw a regular seventeen-sided shape with these two things?"

"You know, the regular seventeen-sided ruler gauge drawing is a famous mathematical problem, from the ancient Greek time to Archimedes stumped, in modern times, Newton did not solve, Gauss Tianzong talent, the mathematics teacher assigned him three problems that night, the first two problems were easily solved, this problem is a little more difficult, people also used one night, to solve, he solved when he solved it did not know that Newton had not been solved. ”

Gauss's work influenced every area of mathematics, but it is strange that he never wrote about Fermat's theorem. In one letter, he even exuded contempt for the issue. Gauss's friend, the German astronomer Olbers, wrote to him to persuade him to run for the prize of the Paris Academy of Sciences for the solution of Fermat's theorem. ”

Two weeks later, Gauss wrote back: "I thank you very much for telling me about the prize in Paris." But I think Fermat's theorem as an isolated proposition is of little interest to me, because I could easily write down many such propositions that one can neither prove nor deny them. ”

Perhaps Gauss had tried this question in the past and failed, and his answer to Olbers was just an example of intellectual sour grapes. In fact, if there is any bit of progress in Fermat's theorem, Gauss will come over attentively to see what is going on? (To be continued......)

PS: I've wanted to write this paragraph for a long time, but I didn't expect it to be so hard to write, to keep it interesting, and to make things clear.

Tips: The new domain name "biquge.info" has been launched by Biquge, and the original domain name is about to be discontinued. Please tell each other, thank you!