Chapter 113 Junior Brother, Tell Me
"Sure enough, to prove and solve every difficult mathematical problem, in addition to requiring the prover to have a high understanding of mathematics, talent, logical thinking, and extraordinary self-confidence are all indispensable."

Tang Shihong took a deep breath to calm his excitement. His emotions were quite complicated at this moment.

Through Xu Yuan, he finally understood why most of the people who solve difficult problems in mathematics are young people.

Take himself for example, as he grew older, his contribution was more on students' education, and his academic achievements were less and less.

In addition to the fact that their thinking is becoming increasingly rigid and not as good as that of young people, they are more afraid to try to solve those difficult mathematical problems.

Afraid of investing too much sunk costs.

I remember that he was not very supportive when Xu Yuan chose the Monge-Ampere equation as the topic of his graduation thesis.

I think this topic is still a bit difficult for Xu Yuan.

You should proceed step by step and take your time.

But the final result was that Xu Yuan successfully proved the overall smoothness of the free boundary of the Monge-Ampere equation.

It has promoted the progress of academic research on partial differential equations.

He was somewhat thankful for this, fortunately Xu Yuan did not listen to his suggestion to change the topic.

Otherwise it will be a loss to the entire mathematics community.

In his opinion, Xu Yuan was able to solve this difficult problem not only because of his enviable mathematical talent, but also because he had full confidence in himself and was able to devote himself wholeheartedly to research in the face of difficulties.

When Tang Shihong was confused, Xu Yuan's voice suddenly sounded in his ears.

“The problem of the smoothness of the solution to the Monge-Ampere equation took me a lot of time to study the proof method.”

"Especially in the case of uniform convexity, many ideas don't work."

“You can only abandon the original method and start over.”

"Finally, I thought of using physical methods to prove mathematical properties, and luckily I completed the final proof."

"Your mathematical talent and thinking are the best I've ever seen. The fact that you can come up with this method shows that your knowledge is flexible and diverse, and you are not just a bookworm trapped in a template." Tang Shihong couldn't let go of the manuscripts and was not stingy with his praise: "I want to formally congratulate you for successfully breaking the existing understanding of the Monge-Ampere equation in the academic community."

After saying this, he walked towards Xu Yuan and handed over the manuscript reluctantly.

"And you should write a detailed paper as soon as possible. Its content is fully qualified to be published in the Annals of Mathematics."

Xu Yuan also saw through Tang Shihong's thoughts at this time, and the corners of his mouth immediately rose and he responded with a smile.

"Then I'll start writing when I get back. Once I finish the paper, I'll give these manuscripts to you, Professor Tang, as a souvenir."

"Really?"

Tang Shihong's face lit up when he heard this: "You can't go back on your word."

"When you become a world-famous mathematician, these manuscripts will be of great collection value."

"If that day really comes, I'll write more for you." Xu Yuan took over the conversation half-jokingly.

"Once your paper is published in the Annals of Mathematics, you will be truly famous in the mathematics community." Tang Shihong suddenly said in a very serious manner.

Previously, Xu Yuan solved the Carmichael number spacing problem in the field of number theory. Although he was called a mathematical genius, it was only a false reputation.

In addition, number theory is a field with a low threshold, so many people would think that he is just a lucky guy.

But a year later, he published a paper in the Annals of Mathematics again, and his research also spanned from number theory to the field of partial differential equations, which was enough to prove his level and talent in mathematics.

His name will also be well known in the mathematics community and he will become a mathematical genius no less than Terence Tao.

As soon as he finished speaking, he added: "It's getting late today, you should go back and rest."

Hearing this, Xu Yuan no longer hesitated. He said hello and turned to leave the office.

Tang Shihong stared at Xu Yuan's back until he disappeared from his sight. Then he prepared to pack up, lock the door and go home, muttering something thoughtfully.

"It seems that we need to find more talents for the graduation defense after the new year, otherwise it will become this kid's personal report meeting."

The whole person is still immersed in joy, and the excitement in his heart has not completely subsided.

He knew that he would probably suffer from insomnia tonight.

But he was only happy about it.

It can be said that discovering Xu Yuan and letting him enter the Department of Mathematics at Qinghua University was the best decision he made in his life.

Although only a little over a year has passed, I am already looking forward to Xu Yuan's future achievements.

If he could really become a world-renowned master of mathematics, then he, as a teacher, might also appear in the history of the development of mathematics. This honor would be much higher than that of Professor Qinghua.

……

From the moment Xu Yuan decided on the topic of his graduation thesis, his main goal was to thoroughly prove the smoothness of the Monge-Ampere equation.

Now I can focus on my graduation defense, so I am not in a hurry to submit my paper to the Annals of Mathematics.

After returning to the dormitory, he saw Li Zhenya and the others lying on the bed. He didn't waste any more time. After washing up, he took off his clothes and went to bed to rest.

The next day.

Xu Yuan got up early as usual.

Coming back from a morning run at the playground.

Wake up a few people in the dormitory and go to the cafeteria to have breakfast.

Li Zhenya and his classmates all had classes in the morning, so they didn't dare to be negligent. They hurried to the classroom with the buns without finishing them.

After Xu Yuan separated from them, he went to the discussion room alone.

Since I need to write a paper for submission, I must use the computer in the discussion room.

I won't be going to the library for some time.

Fortunately, he had already completed all the steps of the proof process, so it wouldn't take too long to write it into a paper, and he was very experienced in writing mathematics papers. He quickly came to the discussion room, turned on the computer, put his hands on the keyboard, and typed out the title and abstract in a blink of an eye.

【Proof of overall smoothness of Monge-Ampere equation under natural boundary conditions】

【Abstract：The smoothness of the solution of Monge-Ampere equation is studied. By removing the two conditions of regional uniform convexity and smoothness of the cryptographic function through several methods, the overall smoothness under natural boundaries is proved...】

In the following time, Xu Yuan was immersed in it, and his hands were playing the piano faster and faster.

There is almost no pause in between.

And he didn't even look at the manuscript in his backpack.

All the calculations from last night were in my mind, I just needed to transfer them to the computer.

The format of the paper is the same as last time, still in both Chinese and English, and there is nothing wrong with it.

In the entire discussion room, the only thing that was placed on the upper left corner of the table was a cute calf-shaped clock, which was specially brought by Chen Yuran. For this reason, Xu Yuan basically never checked the time on his computer or mobile phone.

With the ticking sound of the hands, time is slowly passing by.

Until about ten o'clock.

There was a sudden knock on the door outside the discussion room.

This caused Xu Yuan to break away from the deep learning state and temporarily stop what he was doing.

In order to ensure that he would not be disturbed, Xu Yuan would lock the door of the discussion room when he was immersed in a discussion.

If Chen Yuran wanted to come over, she would call in advance.

Therefore, when he suddenly heard someone knocking on the door, Xu Yuan was quite confused.

"Could it be Li Zhenya, Liu Yang and the others?"

As soon as a guess emerged in his mind, he immediately denied it. After all, they were in class at the moment and would definitely not come to him.

His thought stayed here, and he was about to ask, but he heard a familiar voice coming from outside.

"Junior brother."

"It's me, Lu Chunming."

"Are you occupied?"

Upon learning that it was his class counselor and senior student coming, Xu Yuan quickly stood up and walked over to open the door.

"coming."

The moment the door opened, Lu Chunming's familiar face came into view.

"Senior, please come in."

The next second he warmly invited the other person in.

Lu Chunming was holding a document in his hand, and seemed a little embarrassed, perhaps because he had never been here before.

"Didn't I disturb you, my junior brother?"

"I just stopped to stretch my body. If you have anything to say, just tell me directly." Xu Yuan responded in a very worldly-wise manner.

After hearing this, Lu Chunming stopped keeping the secret. He glanced at the computer screen from the corner of his eye, swallowed his saliva, and asked:

"Junior, have you finished your graduation thesis?"

"It was just proved yesterday." Xu Yuan nodded and answered truthfully.

As soon as he finished saying this, Lu Chunming's expression looked like he was constipated, and he began to complain with a grim look on his face.

"You don't know, junior brother. Today, when I took my thesis to my supervisor, he scolded me. He said that not only was your thesis already completed, but it could also be published in the Annals of Mathematics, but mine still hasn't satisfied your supervisor."

When Xu Yuan heard this, he immediately understood what Lu Chunming had gone through, and couldn't help but take over the conversation and asked back.

"Brother, you haven't finished your thesis yet?"

Lu Chunming was instantly embarrassed: "That one is almost finished."

The next second he quickly changed the subject.

"By the way, Junior Brother, have you really thoroughly proved the problem of the overall smoothness of the solution to the Monge-Ampere equation?"

"I was lucky to find a suitable method." Xu Yuan said modestly to take care of Lu Chunming's feelings.

Unexpectedly, Lu Chunming immediately raised his hand and said, "You don't need to comfort my junior brother. Now your mathematical talent and level are much higher than mine."

When Lu Chunming talked about this, he was naturally very envious.

He couldn't even satisfy his supervisor with a graduate thesis, while Xu Yuan completed his graduation thesis in just a few months.

And I was able to publish my graduation thesis in the Annals of Mathematics.

He remembered that when Xu Yuan just chose to study the Monge-Ampere equation, he thought Xu Yuan would give up and change the topic. Unexpectedly, Xu Yuan completed the whole proof without much difficulty.

It seemed that his previous worries were completely unnecessary.

Having published two papers in the Annals of Mathematics during his undergraduate studies is an achievement that can only be described as astonishing.

It is hard to imagine what kind of shock Xu Yuan will bring to the mathematics community in his future as a doctoral student or as a professor.

Having never been in contact with the international mathematics community, he couldn't even imagine it.

However, although Lu Chunming was envious, he did not forget the main reason why he came here today.

After a little hesitation, he said:
"Actually, I came here today because I want you to help me with my guidance, so that I can quickly hand in my work to my instructor."

As soon as he finished speaking, he handed over the printed paper in his hand. It can be seen that he came here sincerely to seek advice and hoped that Xu Yuan could give him some guidance on his paper.

(End of this chapter)