Chapter 270 The Master Is Gone, How Should We Teach?

Chapter 270 The master is gone, how should we teach?

"Brother, I guess it's true...it's almost impossible to achieve results!"

"There may be a chance with Zhao Yi, but it would be... very difficult to research it in a short time!"

"We should remind Zhao Yi that he is still too young to do research!"

Several professors from the School of Science were discussing. They all knew that Zhao Yi was immersed in the proof of Goldbach's conjecture and had been studying the information carefully for several days. He seemed to be studying every time he saw him.

Many people are a little worried, but they cannot stop Zhao Yi from doing research and learning seriously.

The last sentence was said by Zhou Li. Zhou Li felt that Zhao Yi was still too young. “I think back when I was young, I just studied abroad as a teacher. I also wanted to produce results in research. Apart from attending classes, I spent most of my time on On research.”

"But what? How about it? My results were only released ten years later. If you think about a problem for a long time, it is easy to get into a dead end!"

Zhou Li lamented, "In particular, Goldbach's conjecture is too difficult. There has been no progress for decades. Mr. Chen Jingrun's results are extremely close to completing the proof."

"But everyone must have this step. Probably, he will know after he has experienced it."

"Zhao Yi has been going smoothly for more than a year, and the obstacles he encountered are normal, which is helpful for his growth."

Zhou Li's words received a lot of support.

Everyone thinks it makes sense.

It is impossible for anyone to have smooth research. The world's top research may be able to achieve it occasionally with a flash of inspiration, but no one has a flash of inspiration every day. It is normal to not produce results for several years or more than ten years. In the exploration of high-end mathematics On the other hand, achievement cannot be achieved by just doing research.

Zhao Yi is still young.

He must also go through the path taken by his predecessors in order to have more experience and deeper insights in research work.

Several people discussed not to disturb Zhao Yi, and there was no need to deliberately remind him, just let nature take its course.

Wednesday.

There was another advanced mathematics class for the biological science major. Hu Zhibin stepped into the classroom and found a surprise——

Zhao Yi is not here!

"Where's Zhao Yi? Why didn't you come to class?" Hu Zhibin asked with a frown. He was asking about Fan Lei. He knew that Fan Lei and Zhao Yi were always together and seemed to be very good friends.

Fan Lei said, "I don't know either. He lived in the staff dormitory yesterday and I didn't see him in the cafeteria this morning."

"Didn't you call him?"

"No."

Fan Lei shook his head, "He has been doing research recently, seems to be looking at prime numbers or something. He said we should not disturb him if we are fine."

"oh."

Hu Zhibin seemed to be treating other students who were not in class. The expression on his face seemed to be a little dissatisfied, but he felt unusually relaxed in his heart.

If a bottle of beer appeared in front of him, he would drink it down to celebrate.

"Very good!"

"Zhao Yi is not here! This feeling...yes, this is the feeling!"

"You can give lectures and say whatever you want..."

Hu Zhibin felt light and light all over, without any pressure at all.

When explaining series problems, he even started to talk about extracurricular knowledge and popularized a high-end conclusion to the students——

The sum of all natural numbers is ‘-1/12’.

"This is a classic proof of series calculation."

"But what's interesting is that when the sum of natural numbers is calculated using pure series methods, the conclusion is correct but the process is wrong."

"The earliest mathematician to prove that the sum of all natural numbers is '-1/12' was Euler, but his proof process was considered absurd at the time, incomprehensible, and not recognized."

"Later there was an Indian named Ramanujan. He did not receive formal higher education, but he was very obsessed with mathematics. He used the series method to prove Euler's conclusion."

"The proof is like this..."

Hu Zhibin was doing calculations on the blackboard. The process was indeed somewhat simple.

First introduce a series S, S=1-1+1-1+1-1+1, and then convert 1-S=S to get S=1/2.

Then introduce the series M, M=1-2+3-4+5-6+7, and calculate by dislocation substitution, 2M=S, M=1/4.

Finally, the sum N of all natural numbers is introduced, and N-M dislocation calculation is used to finally derive N=-1/12.

"Everyone has seen that from the proof process, there seems to be no problem, but in fact, when calculating the value of s from the beginning, it is wrong."

"S is a divergent series. In infinite series, only absolutely convergent series can rearrange the terms without changing the converged values. That is to say, for non-absolutely convergent infinite series, the sum cannot be changed arbitrarily order."

"And this is the Riemann series theorem, also called the Riemann rearrangement theorem."

Hu Zhibin's casual lectures were indeed very interesting. Even some of the sleeping classmates were attracted. It was the first time they discovered that Teacher Hu, who was advanced in mathematics, was so interesting when he taught mathematics, instead of always speaking in a rigid manner. Knowledge points in the book, exercises, etc.

Also attracted was Zhao Yi.

Zhao Yi knew the proof that the sum of natural numbers is -1/12, but he knew Riemann's proof, not Ramanujan's wrong proof.

Regarding the sum of all natural numbers, Euler had long proposed that the result was -1/12, but more than fifty years later, Riemann used strict complex analysis to prove its rationality.

However, judging from the results, it is still difficult to be accepted by people.

In the exploration of unknown areas of mathematics, many mathematicians are obsessed with studying mathematical theories to expand people's cognitive scope. For example, the conclusion of the sum of all natural numbers may seem impossible, but it can be proved that the theory can justify itself. .

Zhao Yi thought, "Maybe the final conclusion is wrong, but the difference between wrong and right depends on the theoretical system."

"Based on the current theoretical system generally accepted by mathematicians, this conclusion is correct."

"So, when studying high-dimensional complex functions, can we use the method of series substitution..."

Zhao Yi fell into thinking.

Hu Zhibin did not explain the Riemann proof method in detail. Many processes are incomprehensible to the mathematical level of undergraduates, and their knowledge is not yet so high-end.

In addition, even if you want to explain it seriously, one class time is far from enough.

These have nothing to do with the knowledge in class. Just give simple explanations so that students can understand the concept of series and wrong substitutions.

soon.

Hu Zhibin’s relaxing and interesting advanced mathematics class is over.

When he was packing his things, he saw a student walking towards the podium. There were many students in the corridor, but this student standing among them looked so outstanding and attractive that Hu Zhibin thought he was stunned. .

"Zhao...Zhao Yi? Didn't you come to class?"

"Are you here?" Zhao Yi pointed in the direction of the window, "I've been sitting there."

"But, during class..."

"Did you call me?" Zhao Yi was studying the information in his hand carefully just now, and spent learning coins to turn on the focus mode, and didn't notice what happened.

He sat at the very edge of the middle row, close to the window, and most students didn't notice.

Thinking about it, Hu Zhibin was indeed careless.

Before class, he subconsciously looked at the seat where Zhao Yi usually sat, and found that his friends Fan Lei and Li Renzhe were both there, but only Zhao Yi was not there, so he thought that Zhao Yi had not come.

He didn’t call anyone by name in this class either.

In fact, even if the roll call was called, Zhao Yi's name could not be called. He did not put Zhao Yi on the student list at all.

Anyway, the coincidence just happened.

Whether an ordinary student comes to class or not is not a big problem, but Hu Zhibin thought that because Zhao Yi didn't come, there would be no pressure during class, and he immediately relaxed.

Now think about it...

"I must have said something wrong, right? The students' reactions were quite good..." Hu Zhibin thought carefully under pressure.

Zhao Yi came over and said, "Teacher Hu."

"Just call me by my name."

"Okay, Teacher Hu, um... can you tell me again what you just proved about the sum of natural numbers?"

"Also, you know Riemann's proof, right? I want to hear it again."

"you do not know?"

"I know, but I just thought of something and I feel like I forgot it. Anyway..." Zhao Yi frowned in explanation.

After hearing this, Hu Zhibin breathed a sigh of relief. As long as it was not a matter of course selection, he said simply, "Okay, come to the office with me and I will explain it to you."

He was quite excited when he thought about it.

This is Zhao Yi's request that he give him a lecture. After this semester is over, when he goes to teach the next class of students, he can brag and say, "I was asked by Zhao Yi to teach him..."

Hu Zhibin felt a little dizzy thinking about it.

…

In the office.

Hu Zhibin explained to Zhao Yi the method of solving the sum of natural numbers very seriously. He probably did special research and knew this aspect very well, and the content he taught was much more than what was taught in class.

For example, he talked about two ways to prove errors.

One is Ramanujan’s dislocation series substitution method;

Another method is to introduce a function, the function f(x)=1+(x+x^2+x^3+x^4), and then factor it to get f(x)=1/(1 -x), we get 1+x+x^2+x^3+x^4=1/(1-x), and then substitute x=-1, we get 1-1+1-1+1-1 +1=1/2.

The conclusion of the latter method is the beginning of the former method, and the mistake lies in the fact that the development of the series does not diverge.

After talking about the two wrong methods, Hu Zhibin explained Riemann's complex analysis proof method in detail.

Zhao Yi knew about Riemann's negative analysis proof method. He saw it from some information and even performed the calculation. However, after hearing the detailed explanation from others, he still felt a little different.

In fact, for mathematics, the process is very rigorous, but everyone's ideas, ideas and understanding are different.

It's like a simple calculation problem, multiply 25 by 25. Many people know the result without calculation because they have memorized the result. Some people just substitute the formula, 2*3*100+25, and some people simply Just multiply the equations in your head.

In short, everyone thinks differently, and their understanding of the same complex question will be different.

While listening to Hu Zhibin's explanation, Zhao Yi found that his understanding of series was deeper.

He found that series is a very interesting thing. Whether he is doing complex calculations, exploring the theoretical field of mathematics, or doing infinite extension substitutions of functions, even if he is trying to understand the Riemann Hypothesis, series cannot be avoided. content.

And use the simple and crude multiplication of prime centerline symmetric numbers to analyze the result factors to prove Goldbach's conjecture, and use series to conduct overall analysis...

It seems to be a passage?

Zhao Yi seemed to be listening to Hu Zhibin's explanation attentively, but his mind had already turned to the proof of Goldbach's conjecture.

By the time Hu Zhibin finished explaining everything, half an hour had passed. He saw Zhao Yi frowning and asked, "Zhao Yi, is there anything you don't understand?"

Zhao Yi pursed his lips and thought for a moment before reacting, "Oh, I was thinking about other issues. I'm sorry, there's nothing I don't understand. Thank you, Teacher Hu, this has been a great help to me."

Hu Zhibin pulled the corners of his mouth hard.

If the person standing in front of him was an ordinary student, he would want to pick up the book and slap it on the other person's mouth.

Did he talk carefully for half an hour?

The results of it?

other side. It doesn’t matter if you don’t listen carefully, you just bluntly say that you are thinking about other issues.

Fortunately, the last sentence gave me comfort, "Is there any help? Just help."

Hu Zhibin knew they were polite words, so what he said could be related to Ge Guess?

That’s weird!

impossible!

Even though it was just a kind word, it still sounded very comforting.

Zhao Yi didn’t say anything in detail about how to help, but Hu Zhibin would naturally think of Goldbach’s conjecture. When he saw Zhao Yi’s appearance, he still advised him, “Brother, it won’t take a few days to prove it. If you don’t have an idea, don’t keep thinking. I think if I do other things and relax, I might be inspired.”

"Oh, thank you."

Zhao Yi thanked Hu Zhibin and walked out of the office.

What he said about ‘helping’ is true.

After listening to Hu Zhibin's explanation, he thought about how to analyze the problem of high-dimensional complex functions.

…

When Hu Zhibin returned to the office, he couldn't help but talk about his explanation of the sum of natural numbers to Zhao Yi.

He and several people in the office, including Professor Zhou Li, said ostentatiously, "Zhao Yi specifically asked me about this topic, and I happened to know everything."

"When I was doing my master's thesis, that was five years ago. At that time, I summarized several methods for summing natural numbers. Some of them were correct and some were wrong. I still remember them clearly to this day."

"Zhao Yi just said that my explanation was of great help to him."

Although Hu Zhibin didn't believe this, it didn't stop him from saying it in a showy way.

Gao Yihua happened to be walking by the door. When he heard it, he walked in immediately and said, "I heard you shouting in the corridor, Lao Hu, do you still want to be shameless?"

"What are you talking about!" Hu Zhibin hated people who made trouble the most.

Everyone in the office laughed.

"Let me tell you, Zhao Yihui doesn't know the sum of natural numbers? Isn't this a joke? I remember that his three-dimensional tremor waveform diagram proof contains part of it, and I have studied it."

"The sum of natural numbers and the Riemann function are closely related..."

Gao Yihua didn't give Hu Zhibin any face, he spoke very professionally.

Of course Hu Zhibin understood this truth, and he knew that others also understood it, but why didn't others say it directly?

Isn’t it okay to let people brag?

Hu Zhibin was so angry that he immediately retorted, "Anyway, I'm better than you anyway. Don't say you're giving lectures to Zhao Yi. Zhao Yi deliberately doesn't want to listen to your lectures."

Gao Yihua laughed and said, "Speaking of it, Zhao Yi really didn't miss a single lesson in my class!"

This was originally a very depressing thing, but in the current situation, it seemed a bit proud to say it?

Gao Yihua felt something was wrong. He shook his head, said nothing more, and walked away with a victorious smile.

In fact, Gao Yihua knew that Hu Zhibin was not bragging. If Hu Zhibin could tell that Zhao Yi asked him for advice, there must be something wrong. As for the specific reason why Zhao Yi did this, he had to ask Zhao Yi himself.

Gao Yihua really hoped that Zhaoyi would also ask him questions. This possibility was much greater than asking Hu Zhibin.

Although Zhao Yi is also very accomplished in physics, he found new particles using computer physics methods while participating in a quantum physics team's research trip to Switzerland.

This achievement is of quasi-Nobel level.

But compared to mathematics, Zhao Yi's achievements in physics are very limited. First, his achievements in discovering new particles are difficult to compare with Zhao Yi's achievements in mathematics.

The three-dimensional tremor waveform diagram is Fields-level, and the Fields Medal is the Nobel in mathematics.

In addition, Zhao Yi uses computer physics methods, which are still based on computer algorithms. A large part of it is attributed to computer achievements. His physics level is still not recognized by the world's top physicists.

This aspect can also be seen in ordinary times.

Not to mention the extremely profound quantum physics and cosmic physics, even the physics knowledge in ordinary textbooks, Zhao Yi did not know. Occasionally, he would listen very carefully in class.

He was not pretending, but he was really listening to the class carefully.

Zhao Yi's level in physics is definitely not as good as mathematics. He usually listens to a lot of things in class, so the likelihood of coming to him to ask questions is much higher than that of Hu Zhibin.

There is a physics class that day.

Gao Yihua walked into the classroom with a little expectation. He looked carefully at the students in the audience and suddenly realized that something was wrong.

"Where is Zhao Yi?" He immediately found the reason.

A classmate raised his hand.

Fan Lei.

Gao Yihua also knew Fan Lei, and he knew that Fan Lei was Zhao Yi's good friend.

Fan Lei said loudly, "Teacher Gao, Zhao Yi asked me to ask for leave. He won't come to class today. Also, he may not come to class this week."

"..."

Gao Yihua, who was expecting Zhao Yi to come to class for the first time, was a little confused.

what happened?

Did that guy Hu Zhibin really get it right?

Zhao Yi didn't even come to the class.

If this matter reaches Hu Zhibin's ears, he doesn't know how he will laugh.

Gao Yihua took a deep breath, but there was nothing he could do. He found that he was too obsessed with the verbal dispute with Hu Zhibin.

Isn't it a good thing that Zhao Yi didn't come to class?

This is something that should be celebrated!

easy!

comfortable!

Gao Yihua put his hands on the podium and looked at the students in the audience. He suddenly felt a little uncomfortable. He was used to having a master listening to the lectures.

As a result, the master is gone...how should I teach?