Genius of the Rules-Style System

Many famous mathematical conjectures in the world start from special case arguments. The so-called "special case argument" is an argument for numbers or areas with special values. The same is true for Fermat's conjecture at the beginning.

The content of Fermat's conjecture is very simple--

When the integer n is greater than 2, the equation x raised to the nth power + y raised to the n power equals z raised to the n power has no positive integer solution.

The equation also contains four unknowns. x, y, and z are fixed unknowns. The special case argument generally targets the power value n.

The famous Swiss mathematician Euler was the first person to demonstrate Fermat's conjecture. In a letter to Goldbach, he said that he had proved Fermat's conjecture when n=3. Thirteen years later, his proof was published. In the book "Algebra Guide", the method is the "infinite descent method" and the unique factorization theorem in the form of a number system. This method has also been cited many times by later generations.

In 1816, the Paris Academy of Sciences simplified Fermat's conjecture to the case where n is an odd prime number (all prime numbers except 2). In other words, as long as it can be proven that n takes on an odd prime number, it can be proved that Fermat's conjecture is true. .

Later, many mathematicians participated in the proof of Fermat's conjecture and completed the special cases 'n=3', 'n=5', and 'n=7'. Kummer even used the change of 'ideal prime number' to prove ' For all prime exponents n less than 100, Fermat's last theorem holds'.

This was the most significant breakthrough in Fermat's conjecture in the nineteenth century.

For the next 150 years, there was no further breakthrough in Fermat's conjecture, until the British mathematician Wiles announced that he had proved Fermat's conjecture.

At the International Congress of Mathematicians, Zhao Yi explained the logical errors in Wiles' proof process by linking the Riemann Hypothesis to the logic of Wiles' proof.

Fermat's conjecture has now become an unsolved mystery.

Zhao Yi had thought about Fermat's conjecture for a long time before and found that it was very difficult to conduct a direct overall proof like Wiles, and it was also difficult to advance to all prime numbers by making a special case argument for n.

For example, continuing to move forward, it is proved that when n=101, Fermat's conjecture is true.

This is indeed an improvement, but a very small one.

Proving for n=101 can only explain the situation of 101, and there are infinite values ​​of n, so Fermat's conjecture cannot be proved.

"If you are making a special case argument and making separate arguments, why not choose variables x and y?"

"x and y are indeed random numbers, but they also have merits."

Zhao Yi looked at the Fermat conjecture formula on the manuscript paper and thought carefully, "If it can be proved that x and y are both odd prime numbers, maybe it can be extended to all numbers."

“First we still have to prove the process.”

He started to write after thinking, "Suppose x and y are both odd prime numbers..."

Prime numbers are magical numbers.

All numbers can be seen as evolving based on prime numbers. For example, even numbers can be seen as the sum of two prime numbers, which is now Goldbach's theorem.

At the same time, any odd number that is large enough can be written in the form of "3 + even number", which can also be regarded as the sum of three prime numbers.

"As long as it is proven that x and y have odd prime numbers, it may be possible to generalize to all numbers."

"As for the special case of 2, it is easy to discuss."

"After completing this proof, Fermat's conjecture can be simplified..."

…

Although there are ideas to simplify Fermat's conjecture, sometimes the ideas that suddenly arise are not necessarily correct, let alone proven.

Zhao Yi consumed a lot of brain cells and found that the more he thought about the problem, the more complicated it became. He somewhat understood why Wiles's paper was so complicated that it had more than a hundred pages of proofs and wanted to really think about it in depth.

Fermat's conjecture is really, really complicated if you think about it in depth.

He felt that when he returned to normal life, he still had time to think about it, and he could not delay his life because of research.

The second week is here.

The course "Overview of Particle Boundary Theory" is scheduled on Tuesday evening in the large classroom of the Faculty of Science Building.

Zhao Yi felt a little nervous that day and was a little absent-minded in class in the afternoon. He was always thinking about the lecture. He also made small corrections to the prepared lesson plan with Qian Hong.

After dinner, he returned to the dormitory and took a short rest. He looked at the time and saw that there was still half an hour left. He also took out the lesson plan and looked at it again. It felt a bit like facing an exam.

Fan Lei's reminder came from the side, "Zhao Yi, it's almost time, get ready!"

"right!"

Li Renzhe followed, "Today is a big day, didn't you say you still want to wear a suit?"

"Put it on and see!"

Zhao Yi usually wears sportswear, no different from other students. Even when giving speeches, most of them are dressed in casual clothes. This is the first time he wears a suit. He mainly considers distinguishing himself from the students. After all, he is the first As a teacher for the first time, it is better to dress appropriately.

At the urging of Li Renzhe and Fan Lei, Zhao Yi changed into a suit. It was just a casual suit, but he still looked very stylish by styling the clothes.

Zhao Yi looked in the mirror and was very satisfied with his appearance.

After getting dressed, they went out together and strolled to class.

On the road.

Zhao Yi was dressed in a suit, but he was a little more low-key than usual. Some people who knew him didn't even notice him from a distance, but they made several girls passing by turn their heads neatly.

"It turns out that's Zhao Yi!"

"I looked carefully and saw that he was dressed very stylishly today! By the way, he seems to be going to class. I noticed that his class is tonight!"

"The two ordinary-looking ones next to him are his roommates..."

The discussion among the girls was quite loud, and Zhao Yi and others heard it from a distance.

Zhao Yi felt very relieved.

Fan Lei didn't care.

Li Renzhe glanced away depressedly and said dissatisfied, "You still say we are ordinary? It's just that I'm not wearing a suit, otherwise I would definitely be more handsome than Zhao Yi!"

"When the time comes, the girls will look at Zhao Yi first, but when they see me next to them, they won't be able to move their eyes away..."

"Snapped!"

Fan Lei slapped the back of Li Renzhe's head hard, "I noticed, Lao Li, why are you becoming more and more shameless? After you started dating Huang Wenqian..."

"what are you doing!"

Li Renzhe was startled and muttered. He raised his fist and wanted to fight back, but Zhao Yi stopped him, "Let's go quickly. Stop making trouble."

"Look, Zhao Yi doesn't even care if I say this, you're talking nonsense!" Li Renzhe continued to walk forward while saying to Fan Lei.

Fan Lei rolled his eyes and said nothing.

Zhao Yi walked with a smile on his face, as if he really didn't care about what he just said, but his speed became slower and slower. When walking through the basketball court, he also suggested watching the basketball, "Look at that tall guy, he's playing How nice!”

"You can't even make this shot!"

"How stupid!"

Zhao Yi seemed to be immersed in the fun of watching the ball.

Fan Lei and Li Renzhe looked at the time and quickly urged, "Zhao Yi, it's almost there. There are still five minutes left. Let's go quickly. It doesn't matter that we are students. Today is your first time in class."

"All right."

Zhao Yi sighed and continued walking, but they all reached the downstairs of the science school classroom, and they would have arrived if they walked a few minutes slower.

When he reached the door of the classroom, he looked at the time and found that there were still two minutes left.

"stop!"

Zhao Yi motioned for Fan Lei to go in first, leaving Li Renzhe alone, and took him to the window next to him. He sighed softly and said, "Old Li, to be honest, I'm a little nervous."

"Can you share your experience with me? Just talk about it... with Huang Wenqian, the kind that is a bit disgusting, but you still do it for the sake of sex... Anyway, that's the kind of thing, how do you persist?"

"ah?"

Li Renzhe thought for a long time before he figured it out.

What Zhao Yi said was a bit 'unpalatable', as if he and Huang Wenqian were not really in love... Ahem, no matter what, Zhao Yi was talking to him from the bottom of his heart, so he had to say a few words carefully, just in case he could be helped. Woolen cloth?

He spoke, "That's right, just think about it and go ahead with it...anyway, that's it."

"I don't know what to say either."

"But what are you afraid of? This is your first time in class. Everyone knows that without experience, even if you don't teach well..."

"alright!"

Zhao Yi looked down at his watch and found that it was past the class time. He immediately interrupted Li Renzhe and said with a smile on his face, "You can go in, let's not be late. This is my first time as a teacher, so I can't be accused of favoritism. Cheating, even if you are my roommate..."

"If you're late, I can't pretend I didn't see you." There was a guilty tone in the last words.

Li Renzhe nodded to show that he understood.

The two entered the classroom together.

Zhao Yi walked up to the podium with a smile on his face, his steps were steady, his expression was relaxed, and there was no trace of nervousness at all. He greeted everyone and introduced himself, "My name is Zhao Yi, Zhao Qian Sun Li's Zhao , game, game of chess.”

"Life and human beings are about making progress in constant games and competitions. I hope that every student can become a winner in the game of life!"

"Hulala-"

There was a burst of applause from the audience.

After the applause subsided a little, Zhao Yi talked about the issue of the course, "This is my first time as a teacher and my first time giving a lecture. You all want to get credits, so I will talk about the score issue first."

""Overview of Particle Boundary Theory" is a novel mathematical physics course. There is no textbook for the time being. However, after this class, each student will be given the content materials for the next class. Finally, excerpts from all the materials will be Take some as exam content.”

"Examination marks account for 70% of the total score, and regular marks account for 30%."

"I don't leave homework for this course. Everyone just needs to understand the content, especially those who are not students of the School of Science. They can understand the theory of science and expand their horizons and knowledge. That's all."

"The usual score is roll call in class. There are ten classes in total. I will call roll twice. The usual score for both times is a perfect score."

"Today is the first time."

"By the way, I would like to remind you that recording lateness and absenteeism is very troublesome. I also hope that the course assistant, Teacher Qian Hongqian, can make the work easier." Zhao Yi said and pointed to Qian Hong next to the first row, as if all I'm thinking about her.

Qian Hong quickly stood up and turned around to say hello to everyone.

"correct!"

After Zhao Yi finished speaking, he gave a special reminder, "Not only is being late the same as being absent from class, being late for a minute or a few seconds is also being late."

"I remember all the students who were late just now."

"Let's start the roll call!"

"Uh-huh!"

The moment Zhao Yi finished speaking, many people looked at Li Renzhe. Because it was Zhao Yi's first class, most of the students came early and saw Li Renzhe and Zhao Yi entering the door at the same time. I was on time for class, but I was definitely late.

Li Renzhe also realized it, but the panic in his heart was immediately calmed down, and he muttered to the student who turned his head, "What are you looking at! Zhao Yi and I are in the same dormitory, can he deduct points from me?"

"Oh~"

The students in the front row said nothing.

Think about it too.

Li Renzhe is Zhao Yi's roommate. Entering the classroom with Zhao Yi must not be considered late.

but……

It seemed like Li Renzhe was the only one who was late just now?