Volume 1: Student Life Chapter 308: An opportunity to analyze number theory!
Zhang Zhongyuan really wanted to ignore this hand, but he saw that many classmates simply ignored the three minutes he gave them and instead looked back at Chen Zhou first.
There's nothing we can do about it. We can't just let people hold it up, right?
So, under the expectant gazes of his classmates, Zhang Zhongyuan called on Chen Zhou, "Chen Zhou, you come and answer."
Chen Zhou stood up with a smile on his face.
"Think of the Klein quaternion group as a form of quaternion permutation. S4 is a group of order 24, and Klein is a group of order 4."
"So, from Lagrange's theorem we know that the quotient group s4/Klein is an order 6 group. There are only two order 6 groups in the sense of isomorphism, one is the order 6 cyclic group and the other is s3."
"Here we list all the elements in s4/Klein, or we can write it in the form of left cosets. If we look at the representative elements of those cosets, we can see that s4/Klein obviously cannot form a cyclic group of order 6, so s4/Klein must be isomorphic to s3."
"At this point, the answer to this question has come out."
Chen Zhou spoke in a steady tone, fully explaining the ideas and methods for proving this problem.
Zhang Zhongyuan looked at Chen Zhou, seeming to want to say something but stopping himself.
Some of the students below had already started to check their calculations, while others were looking at Chen Zhou with admiration.
A boss is a boss. As soon as the question comes out , the answer comes out without any thinking.
However, many students who checked the calculations found that Chen Zhou had overlooked a problem.
That is, there is one step missing to prove that the Klein quaternion group is a normal subgroup.
They set out to prove this part.
Zhang Zhongyuan looked at the speed at which the students wrote, which was much faster than in his usual classes. He couldn't help but sigh in his heart.
Looking at Zhang Zhongyuan who had been silent, Chen Zhou thought about it and felt that his idea should be correct, right?
But then he realized that he had omitted something, and added: "By the way, the proof that the Klein quaternion group is a normal subgroup is too simple, so I didn't mention it."
Upon hearing Chen Zhou's voice, the students who were trying to prove that the Klein four-group is a normal subgroup were startled and stopped holding their pens.
Their faces were full of bitter smiles.
Seeing this scene, Zhang Zhongyuan finally couldn't help but said: "Okay, sit down first, let's take a look at this question..."
In the second half of the class, Zhang Zhongyuan looked at the time from time to time. He felt that this was the most "difficult" class he had ever taught.
It wasn't because of any special reason, it was just because he was too familiar with Chen Zhou. This kid hadn't been to class for such a long time, and suddenly coming to class made him a little...uncomfortable...
"Okay, that's all for today's class. Remember to do your exercises when you go back."
As Zhang Zhongyuan said this, the "Abstract Algebra" class came to an end.
Chen Zhou was not in a hurry to leave. He noticed that Zhang Zhongyuan was looking at him.
If he understood correctly, it should mean, don't leave after class.
Seeing that Chen Zhou did not leave, the students in the classroom also slowed down their pace.
When Chen Zhou returned from MIT, they had only seen him on the news broadcast and on the Internet.
Now that the real person has appeared, we must watch him carefully and absorb the aura of this top student.
Who knows, maybe I won’t fail in the upcoming final exam?
Even a face-to-face meeting is fine!
They still remember vividly the widespread failure of senior high school students.
But it's obvious that Zhang Zhongyuan is unhappy. He has something else to talk to Chen Zhou about. Why are you guys joining in the fun?
"What? Don't you want to leave get out of class? How about we continue..."
Zhang Zhongyuan paused unconsciously when he said this. Seeing the excited classmates, he immediately changed his words and said, "How about we assign more homework and everyone can do it here?"
Hearing this, a classmate quickly said, "No, Professor Zhang, aren't you packing your things? You have too much stuff to bring, so leave right away!"
Then, Zhang Zhongyuan saw a strange scene.
These students did not go out through the main gate, but walked to Chen Zhou and said, "Boss, please go easy on me next time" or "Boss, you are so handsome!".
Then he left the classroom through the back door.
Chen Zhou was a little amused and helpless about this.
After everyone had left, Chen Zhou stood up and walked towards Zhang Zhongyuan.
Zhang Zhongyuan looked at Chen Zhou and asked, "How was your trip to MIT? Did you gain a lot?"
Chen Zhou shook his head. "It's not a very fruitful experience. I spent most of my time researching Cramer's conjecture. I didn't even have time to attend the seminar."
Zhang Zhongyuan immediately laughed and scolded, "You are so good at taking advantage of me, kid. Will those reports have a big impact on you whether you listen to them or not? Can they help you solve the Kramer conjecture?"
"Hehe." Chen Zhou laughed, "That's not the case. There are still many lectures by bigwigs. Like Professor Faltings, Professor Deligne..."
"Stop, stop it!" Zhang Zhongyuan felt that he shouldn't bring up this topic.
After a pause, he asked again, "Have you completed the paper on Cramer's conjecture?"
Chen Zhou nodded: "I have submitted it to the Annals of Mathematics."
"That's fine. This is another research that shocked the mathematics world." Zhang Zhongyuan glanced at Chen Zhou and added, "Compared to those mathematicians who didn't go to the lecture in person."
Seeing Zhang Zhongyuan like this, Chen Zhou smiled. How come he was a little different from the Professor Zhang he was familiar with?
"I heard that you rejected Princeton's invitation? And it was Professor Faltings' personal invitation." Zhang Zhongyuan asked the question in his mind.
"Well." Chen Zhou thought for a moment and explained, "Since Yanda has already made the contact, there is no need for me to change these. Besides, mathematical research depends mainly on the individual. It doesn't mean that you can do good research just because you are in Princeton."
Hearing this, Zhang Zhongyuan couldn't help but be amazed. Is this kid so conscious?
As expected, someone who can come up with two world-class mathematical conjectures in a row is different and has the style I had back then.
But then, he heard Chen Zhou continue, "Besides, you don't have to go to Princeton to communicate with these great mathematicians. You can communicate through email or phone."
"And if you go to Princeton, I guess the communication method will be the same. I don't believe they will just stay there and wait for you to find them. Maybe it will be faster than sending an email."
Zhang Zhongyuan: “…”
After a moment of silence, Zhang Zhongyuan said, "Since you have made up your mind, I won't say much. Just like me when I was young, you have always had your own ideas and are able to do them. I believe you can find your own way."
"Uh... Professor, I'll just take it as you praising me..." Chen Zhou said with a smile.
Zhang Zhongyuan glared at Chen Zhou: "Of course!"
After separating from Zhang Zhongyuan, Chen Zhou went straight to find Yang Yiyi for lunch .
Chen Zhou's purpose of attending this class was, on the one hand, to relax, and on the other hand, to "consolidate" his knowledge.
You may get different results through different learning methods.
Knowledge needs to be reviewed.
Reviewing the past to learn new things is not just empty talk.
At the same time, Chen Zhou also wanted to see what different feelings he would have when learning mathematics knowledge after his mathematics level reached Level 6.
The result did not disappoint him. He could always gain different contents from the small details.
Take that proof question for example , he could think of at least three methods.
In the process of proof, he can also think of various different mathematical knowledge.
This is a reflection of knowledge proficiency.
The Annals of Mathematics is published every two months, with no more than a hundred articles published each year.
Logically speaking, the last issue of the Annals of Mathematics in 2015 should be published in late December at the earliest.
However, to Chen Zhou's surprise, he had only submitted the paper about a week ago.
The latest issue of the Annals of Mathematics has been published.
And his paper [Proof of Cramer's conjecture using distributional deconstruction] is published in the latest issue of the Annals of Mathematics.
And it is the first article in this issue of the journal.
At the end of the paper, there is a line of reviewers' comments on the paper.
[This is not only a proof of Cramer's conjecture, but also the key to the prime number gap problem. If we want to talk about its importance, it is this: this is an opportunity to analyze number theory! ]
