Rule department scholar

Finally, the sum N of all natural numbers is introduced, and NM's dislocation calculation is used to finally deduce N=-1/12.

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

"S is a divergent series. In infinite series, only absolutely convergent series can rearrange the terms without changing the converged value, that is, for non-absolutely convergent infinite series, the summation cannot be changed arbitrarily order."

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

Hu Zhibin's casual lectures are indeed very interesting, and even some of the sleeping classmates are attracted. It is the first time for them to discover that Mr. Hu, who is a high-level math teacher, is so interesting when he talks about mathematics, and he doesn't always talk about it in a rigid way. The knowledge points in the book, doing exercises, etc.

Zhao Yi was also attracted.

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

Regarding the sum of all natural numbers, Euler proposed early that the result was -1/12, but more than 50 years later, Riemann proved its rationality by using strict complex analysis.

However, the result is still difficult to be accepted by people.

In the exploration of the unknown areas of mathematics, many mathematicians are obsessed with studying mathematical theories to expand people's cognition, such as the conclusion of the sum of all natural numbers. It seems that the result is impossible, but it can be proved that the theory can justify itself. .

Zhao Yi thought, "Maybe the final conclusion is still wrong, but wrong and right depend on the theoretical system."

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

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

Zhao Yi was lost in thought.

Hu Zhibin did not explain the Riemann proof method in detail. As far as the mathematics level of undergraduates is concerned, many processes are incomprehensible, and their knowledge has not yet reached such a high-end level.

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

These have nothing to do with the knowledge in the class. Simply explain and let students understand the concept of series and the wrong substitution.

soon.

Hu Zhibin's relaxed and interesting advanced mathematics class is over.

When he was packing up his things, he saw a student walking towards the podium. There were many students in the aisle, but this student stood in the middle of it and looked so outstanding and attractive that Hu Zhibin was taken aback. up.

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

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

"But, during class..."

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

He sat on the far side of the middle row, some near the windows, and most of the students didn't notice.

Hu Zhibin was really careless after thinking about it.

Before class, he subconsciously looked at the seat where Zhao Yi often sat, and found that his friends Fan Lei and Li Renzhe were there, but Zhao Yi was not there, so he thought that Zhao Yi hadn't come.

He also didn't call the class.

In fact, Zhao Yi's name couldn't be called even if he called the roll call. He didn't put Zhao Yi in the student list at all.

Anyway, it happened by coincidence.

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

Now think about it...

"There shouldn't be anything wrong with what I said, right? The reactions of the students are pretty good..." Hu Zhibin began to think carefully under pressure.

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

"Just call me by name."

"Okay, Mr. Hu, that... can you tell me again, the content of proving the sum of natural numbers just now?"

"Also, do you know Riemann's proof? I want to listen to it too."

"You do not know?"

"I know, but what I thought of just now, I feel like I forgot, anyway..." Zhao Yi frowned and explained.

Hu Zhibin heaved a sigh of relief after hearing this, as long as it wasn't a matter of choosing a course, he said straightforwardly, "Okay, come with me to the office, and I'll explain it to you."

He was quite moved when he thought about it.

This is Zhao Yi asking himself to give him a lecture. After this semester is over, he will go to lead the next class of students. He can brag and say, "I was asked by Zhao Yi..."

Hu Zhibin was a little lost thinking about it.

……

in the office.

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

For example, he talked about two ways of proving mistakes.

One is Ramanujan's dislocation series substitution method;

另外一种是引入函数的方法，函数f(x)=1+(x+x^2+x^3+x^4......)，随后进行因式分解，得出f(x)=1/(1-x)，得出1+x+x^2+x^3+x^4......=1/(1-x)，再代入x=-1，得出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 is that the development of the series still does not diverge.

After talking about 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 materials and even performed calculations. However, he felt a little different after hearing the detailed explanation from other people.

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

It’s like a simple calculation problem, multiplying 25 by 25, many people know the result without calculation, because they have already memorized the result, some people use the substitution formula, 2x3x100+25, and some people simply do it in their heads Multiply by columns.

In short, everyone's way of thinking is different, and the understanding of the same complex topic will also be different.

In the process of listening to Hu Zhibin's explanation, Zhao Yi found that he had a deeper understanding of series.

He found that series is really a very interesting thing, whether it is doing complicated calculations, exploring the theoretical field of mathematics, or doing infinite extension and substitution of functions, even if it is to understand the Riemann Hypothesis, series cannot be avoided content.

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

Seems like a path too?

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

When Hu Zhibin finished all the explanations, half an hour had passed. Seeing Zhao Yi frowning, he asked, "Zhao Yi, is there anything you don't understand?"

Zhao Yi pursed his lips and thought for a while before reacting, "Oh, I was thinking about other issues, sorry, there is nothing I don't understand, thank you, Teacher Hu, this is of great help to me."

Hu Zhibin tugged at the corner of his mouth.

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

But he talked hard for half an hour?

The results of it?

other side.It doesn't matter if you don't listen carefully, and you can also bluntly say that you are thinking about other issues.

Fortunately, the last sentence gave me comfort, "Is it helpful? It's good to be helpful."

Hu Zhibin knew it was a polite word, could what he said be related to Brother Guess?

No wonder!

impossible!

Even though it was just a polite word, it still sounds very comfortable.

Zhao Yi didn't say anything in detail to help, but Hu Zhibin would naturally think of Goldbach's conjecture. Seeing Zhao Yi's appearance, he persuaded him, "Guess, it won't take a few days to prove it. If you don't have an idea, don't keep your head down." Think, do other things, relax, maybe there will be inspiration.”

"Oh, thank you."

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

It was true when he said 'helpful'.

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 talking about how he explained the sum of natural numbers to Zhao Yi.

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

"When I was doing my master's thesis, it was five years ago. At that time, I summed up several methods of summing natural numbers. Some were correct and some were wrong. I still remember it clearly."

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

Although Hu Zhibin didn't believe this sentence, it didn't prevent him from saying it in a showy manner.

Gao Yihua happened to pass by the door, and immediately walked in and said, "I heard you yelling in the corridor, old Hu, how can you be ashamed to be a human being?"

"What are you talking about!" Hu Zhibin hated people who disrupted the stage the most.

Everyone in the office laughed.

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

"The summation of natural numbers is closely related to the Riemann function..."

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

Of course Hu Zhibin understands this truth, he knows that other people also understand, but why don't others directly say it?

Isn't it okay to let people brag!

Hu Zhibin was so angry that he immediately snapped back, "Anyway, I'm better than you, don't say that you are giving lectures to Zhao Yi, because Zhao Yi is deliberately unwilling to listen to your lectures."

Gao Yihua laughed and said, "To be honest, Zhao Yi never missed a single lesson in my class!"

This was originally a very depressing thing, but it seems a little proud to say it on this occasion?

Gao Yihua felt something was wrong, he shook his head, said nothing, and walked away with a triumphant smile.

In fact, Gao Yihua knew that Hu Zhibin was not bragging. Hu Zhibin could say that Zhao Yi asked him for advice. There must be something. As for why Zhao Yi did this, he had to ask Zhao Yi himself.

Gao Yihua really wanted to ask himself the same question as he wanted, which was much more likely than asking Hu Zhibin.

Although Zhao Yi is also very accomplished in physics, when he participated in the quantum physics team's research in Switzerland, he found new particles by means of computer physics.

This achievement is quasi-Nobel.

However, compared with mathematics, Zhao Yi's achievements in physics are very limited. One is the achievement of discovering new particles, which is difficult to compare with Zhao Yi's achievements in mathematics.

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

In addition, Zhao Yi adopted the method of computer physics, which is still based on computer algorithms, and 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 incomparably profound quantum physics and cosmic physics, even the physics knowledge in ordinary textbooks, Zhao Yi still has some knowledge, and occasionally he listens very carefully in class.

It's not pretending, it's just really listening to the class seriously.

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

There is 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 found something was wrong.

"Where's Zhao Yi?" He immediately found the reason.

A classmate raised his hand.

Fan Lei.

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

Fan Lei said loudly, "Mr. Gao, Zhao Yi asked me to ask for leave. He won't come to class today, and maybe he won't come to class this week."

"..."

Gao Yihua, who was looking forward to Zhao Yi's class for the first time, was a little confused.

what happened?

Did Hu Zhibin really hit the mark?

Zhao Yi didn't even come to class.

If this matter got to Hu Zhibin's ears, he didn't know how he would 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.