The top student must be diligent.

Chapter 275 Amazing Method

In the following period of time, Xiao Yi started directly from the modular form and combined the content of the geometric Langlands program to formally begin the study of the Riemann hypothesis.

Ok……

Of course, strictly speaking, he was actually more focused on further expanding the analysis of the elliptical recurve that had been developed.

Let's see how far we can extend this new approach by exploiting modular forms and combining it with the geometric Langlands program.

As for actually starting the research on the Riemann hypothesis, there is no need to rush. As the saying goes, sharpening the knife does not delay the chopping of wood. Only by sharpening the knife called theory can we better chop the wood called the Riemann hypothesis.

However, this is destined to be a long-term thing.

Since it involves the Riemann hypothesis, it is naturally not easy to solve.

……

The day passed quickly.

Xiao Yi's research gradually got into shape.

On the other hand, the video of his class yesterday has also been uploaded to the Internet.

Every class he teaches is recorded and uploaded to major video websites.

Now he mainly teaches two classes, number theory for freshmen in the last semester and real analysis for sophomores in the second semester.

His class recordings receive a lot of praise every semester.

Many students who study on their own will come to watch his two classes, and quite a number of students preparing for postgraduate entrance examinations have already regarded his videos as the best tutorials for self-studying number theory and real analysis. Even graduate students will come to study specifically, whether it is to consolidate basic knowledge or to learn his thinking from him, it is very helpful. In addition to students, many teachers also come to learn his teaching style, and then in their own classes, they will imitate his rhythm or even copy it completely.

Basically, after a few years, the average number of views of his recorded videos has reached over 500,000.

As a professional mathematics, this amount of playback is quite high. Of course, considering that China has never had such a top mathematician before, and he even won the Fields Medal in Mathematics, it is normal to have such a high number of playbacks.

Moreover, as new students enroll every year, or begin to study related courses, and new students begin to enter the postgraduate entrance examination review stage, it can be predicted that the number of views will gradually increase, and it will not be impossible to exceed one million by then.

In addition, since the quality of his recordings is very good, quite a number of people have left messages expressing their hope that he could teach more classes, preferably teaching every class in the mathematics major and recording them all.

In this way, they don’t have to search for various online courses on the Internet and then have no idea whether the quality of the online courses is good.

In response to such a request, Xiao Yi could only say that if there was a chance, he would definitely do it next time.

Having said that, as soon as his video was released yesterday, it immediately attracted quite a lot of mathematics students and teachers to study it. In particular, yesterday's video involved the distribution of prime numbers, an important problem in the field of number theory, so the number of views increased rapidly. On the second day, the number of views reached nearly 100,000.

But on the next day, the number of views suddenly started to increase again, directly increasing by 50,000.

The main reason lies in the analysis of elliptic inverse curves that Xiao Yi demonstrated during his lecture.

Undoubtedly, this new method immediately attracted the attention of quite a lot of people who watched the video.

And first of all, it was discovered among those graduate students.

……

Princeton University.

"Chen, can you tell me more about Professor Xiao's story?"

Sitting in the laboratory, Chen Muhua was swimming in a swimsuit, and then he heard a voice coming from the side.

Turning around, he saw that it was a classmate of his and also a doctoral student under the same supervisor, named Sanjay Khan, an Indian.

And he was a high caste, a Kshatriya.

When Chen Muhua first came here, he was asked a lot of questions by people because his previous mentor was Xiao Yi. Of course, they all wanted to know from him what kind of person Xiao Yi was.

Of course, he was also very happy to speak. In the first month, he spoke not every day, but almost every hour. At that time, when his classmates occasionally didn't hear him speak, they would laugh and tease him: "You haven't talked about your mentor Xiao Yi for a minute."

A month later, he realized that his classmates were probably used to hearing it, and he couldn't bring it up all the time, or he would bring bad luck to his tutor.

So he didn't talk about it again after that.

As a result, after a while, the classmates around him found that he stopped talking and were a little uncomfortable. Moreover, those who studied mathematics would never stop being interested in Xiao Yi, a genius who was hailed as the smartest genius in history, so they started asking about it from time to time.

Sanjay Khan is one of them, and the most enthusiastic one among them.

Chen Muhua rolled his eyes: "It's you."

Then he said, "Wait a minute, I'm going to watch a video now."

"Hmm? What video is it?" Sanjay asked curiously.

"You might be interested." Chen Muhua opened a link sent from the group and said, "It's about Professor Xiao."

Sanjay's eyes lit up: "Then I am indeed interested."

Then he dragged a chair over and sat next to Chen Muhua, ready to watch it with him.

Soon, the video was opened, and Xiao Yi's figure appeared in it.

As for the scene, it is obviously set in a classroom.

This is the recording of Xiao Yi’s class, and the video inside is from yesterday’s class.

Chen Muhua was very curious, because this video was sent to him by Liang Qiushi, and he was given a time node for the video, saying that after this time node, what their professor Xiao said was very important.

So he decided to take a look.

Soon, I jumped directly to this video node.

And this time point is exactly the point when Xiao Yi began to demonstrate the analytical method of elliptic inverse curve.

Chen Muhua himself studies algebraic geometry and the Langlands program, so he is not unfamiliar with these contents. After seeing the method demonstrated by Xiao Yi, his eyes immediately widened.

There is actually such a method?
Can analytical extension be demonstrated in this way?
Elliptic curves...

Elliptic curves...

As someone who had some knowledge of Langlands geometry, he was of course well aware of how much help it would bring if the elliptic curve method could be used to explain analytical continuation.

Then he continued to look down, and after actually seeing how this method was used, his eyes lit up even brighter.

Although his ability can only be said to be relatively outstanding among mathematics doctoral students, it can be seen how great the impact of such a method is.

Especially the information reflected in this process is particularly important.

He could see that by using this new analytical extension, the information of the original analytical function after extension could be displayed in a more detailed and comprehensive way, which would be very helpful for processing and using this information in the research process.

Thinking of this, he felt great amazement in his eyes.

Professor Xiao will always be Professor Xiao.

At this moment, Sanjay next to him was a little anxious: "Chen, what on earth did Professor Xiao say? I don't understand Chinese! But it looks like it should be something about elliptic curves, right?"

Chen Muhua smiled and said, "Yes, it is indeed related to elliptic curves, and it is very important. I remember that you study number theory, right?"

"Yes." Sanjay nodded. As they all had the same mentor, their research fields were basically not too different.

"Then let me explain to you what Professor Xiao is talking about. You will be surprised after listening to it!"

Then, he began to tell Sanjay about the method Xiao Yi mentioned in the video.

Of course, he acted more as a translator, telling Sanjay exactly what Xiao Yi said in the video.

However, as he spoke, Sanjay gradually realized how awesome this method was, and he immediately exclaimed in their laboratory, attracting the attention of everyone else.

Sanjay immediately told everyone present the news.

So in the end, Chen Muhua had to start introducing Xiao Yi's new method to everyone present. The main reason was that although analytic continuation could be used in number theory, this method strictly speaking still belonged to the field of complex analysis, so almost everyone present knew what analytic continuation was.

Now that they know there is a completely new method of analysis and extension, especially since this method was invented by Xiao Yi, they are of course very curious.

So, Chen Muhua began to act as a teacher, standing in front of the blackboard and introducing this new method to them. For a moment, the whole laboratory was filled with amazement.

……

In the corridor outside the laboratory.

Two professors are walking towards this side.

Suddenly, the sound of screams in the laboratory caught their attention.

"Haha, Manuel, your lab is quite lively."

Andrei Okunkov said to Manuel Bhargava with a smile.

Manuel frowned.

Manuel Bhargava, the mentor of Chen Muhua and his classmates, heard that his students were not studying well and were making so much noise, so he immediately decided to go in and teach them a lesson.

So when he reached the door of the laboratory, he suddenly opened the door and shouted, "What are you doing? My laboratory is definitely not for you to have a party. There is only one theme here, and that is learning. If you want to have a party, the campus or the bar are completely sufficient for you to do so."

The students in the laboratory suddenly became quiet.

Manuel turned his head and looked at Chen Muhua standing on the podium. He frowned and was about to say something when he saw what was written on the blackboard, which made him stunned.

There were no scribbles on the blackboard, at least not anything indescribable drawn on it, but rather rows of neat formulas, and these formulas looked particularly familiar to him.

Elliptic curve.

He himself studied number theory and elliptic curves, and he won the Fields Medal for his achievements in this area.

Yes, he is also a Fields Medal winner, having won the award in 2014.

As for Andrei Okunkov, who follows him, he is also a Fields Medal winner.

When Okunkov heard Manuel suddenly stop moving, he followed in. When he saw what was on the blackboard, he was stunned for a moment, and then he started to look at it like Manuel.

So, the students present were trembling with fear because they had just been scolded by the professor, while the two big guys who won the Fields Medal were particularly quiet.

It was not until a moment later that Manuel finally came back to his senses and looked at Chen Muhua again: "Did you write this?"

"Ah... yes, it's me, professor." Chen Muhua responded quickly.

"You figured that out?"

"Uh..." Chen Muhua shook his head repeatedly: "No, this is Professor Xiao Yi's achievement."

"Oh!" Manuel nodded. "That makes sense."

Chen Muhua did not refute this, because such a method was indeed not something he could come up with.

Okunkov next to him raised his eyebrows: "So, this is a new method invented by Professor Xiao?"

He also turned to Chen Muhua and asked, "You should be Professor Xiao's student, right? Could it be that Professor Xiao has written a new paper?"

Chen Muhua explained: "No, this method... was actually proposed by Professor Xiao in his class. I have his video here!"

Then, he showed the video of Xiao Yi to the two big guys in front of him.

However, because it was in Chinese, the two big guys couldn’t understand it.

So naturally, Chen Muhua took on the duties of a translator.

Manuel and Okunkov also sat down and listened to Chen Muhua's story.

Soon, with Chen Muhua's explanation, they understood what was in front of them.

"It's amazing... This new method can actually be used to demonstrate the extension of analysis in this way."

Manuel nodded and expressed his emotion.

Okunkov next to him was also full of praise: "This method is a huge improvement for analytical extension. With the information revealed by this method, many problems can be simplified."

"Yes." Manuel nodded, and then he said with a little surprise: "Did Professor Xiao really come up with this method in class?"

Okunkov said: "I think it is very likely. Otherwise, the current form is still a little too rough, and there should be many places that can be improved."

"Indeed it is……"

Manuel began to think, from which aspects could he start to improve?

After a moment, he was stunned: "Perhaps... this method can be used to study the Riemann hypothesis? You know, if we combine it with the modular form, using Taniyama Shimura's theorem..."

When Okunkov heard Manuel say this, he was also stunned: "It seems... it is indeed feasible!"

The two Fields Medal winners' eyes lit up at the same time, and then they immediately began to discuss the topic.

It seemed as if their voices were the only sounds left in the entire laboratory.

Meanwhile, many of Manuel's students were listening to the discussion between the two big men, and for a moment they all looked confused and impressed, especially because this method could actually be used to study the Riemann hypothesis!
They all looked at Chen Muhua immediately.

Chen Muhua was also surprised.

He doesn’t know either!

But then again, maybe his former mentor has really started researching the Riemann hypothesis?
"I really envy your country, China, for having such a great genius."

At this time, Sanjay next to him suddenly said.

Chen Muhua was stunned and smiled: "Yes, maybe this is our national destiny."

Then he asked, “But I remember there are many Indian scientists, right? Are there any who have won the Nobel Prize or the Fields Medal?

Sanjay shook his head and said, "In fact, we don't have many scientists, and those truly outstanding scientists have gone abroad. Even if they have achieved results, most of them will choose to stay abroad in the end and cannot bring much change to us in India. But Professor Xiao is different. Not only has he stayed in China, but he has also brought so many changes to China. He can even complete major technologies such as nuclear fusion. I can't imagine the possibility of such a thing happening in India."

Chen Muhua was stunned, then smiled.

Such a question...

It is also often mentioned in China.

But fortunately, among their Chinese talents who have gone abroad, there are still quite a few who are willing to come back.

As for those who leave China and never return, why should we care about them?
He asked, "What about you? Are you going back to India after graduation?"

"Of course." Sanjay said, "I must go back. There is a girl waiting for me. I also want to go back to be a teacher and educate our Indian children."

Chen Muhua wants to say that if the caste system is not changed, India’s development may always face problems.

But in the end, he still didn't say such words, but just said: "You will succeed."

"Thank you. What about you? Will you return home after graduation?" Sanjay asked.

Chen Muhua said without thinking: "Of course!"

Sanjay smiled and said, “Do you have a girl waiting for you too?”

"That's not the case." Chen Muhua said, "It's just because that's my hometown."

Happy National Day everyone

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(End of this chapter)