Chapter 116 Deligne's Exclamation
"You should know my standards. If it is a paper that has no value, it is better to take it away as soon as possible. I don't want to see this paper in the shredder ten minutes later."

Deligne turned his gaze to Holt and spoke in a deep voice, without directly taking the paper.

With his authority and status in the mathematics community.

I don’t know how many people usually want to ask him to read their papers.

If he read every article, he probably wouldn't even have time to study mathematics.

Therefore, I naturally would not agree easily.

If it weren't for Holt's position as the editor-in-chief of the editorial board of the Annals of Mathematics, and the fact that he had previously taken a paper that proved the Carmichael number spacing problem and had quite interested him, the other party wouldn't even have had the chance to enter the living room and sit down for a cup of coffee.

Holt had a lot of dealings with Deligne, and when he heard this he knew that Deligne had given in.

Then he quickly added: "This paper is about the study of the Monge-Ampere equation for optimal transport. The authors thoroughly prove the overall smoothness of the solution to the equation."

"Monge-Ampere equation?"

Deligne was stunned for a moment when he heard this equation, and then he sighed: "It's been a long time since I saw any research on the Monge-Ampere equation."

After saying that, he took the initiative to pick up the paper.

But as soon as he looked over, he immediately frowned and had to ask Holt again.

“Why is there no author’s name on it?”

"Professor Deligne, you might as well take a look at the contents of this paper first. I will tell you the author of the paper later." Holt gave such an answer to Deligne's question, which was obviously intentional.

It's a coincidence.

As the editor-in-chief of the editorial board, he accidentally saw a familiar author's information while screening papers. It was Xu Yuan, a college student who independently proved the problem of the intervals between infinite Carmichael numbers last year. Naturally, he was curious to see that the other party had submitted a new manuscript again.

I was especially surprised after seeing the title and abstract of the paper.

The first reaction that popped into my mind was disbelief.

It is hard to imagine that such a young person who has just entered university can, after solving difficult problems in number theory, move on to partial differential equations in such a short period of time.

He even proved the smoothness of the solution to Monge-Ampere's equation.

He didn't know how strong the mathematical talent must be to be able to do this. He was afraid that even Terence Tao, the mathematical genius known as the Mozart of the mathematical world, couldn't do it.

In order to confirm whether the paper had truly completed the proof, he did not bother to review it and immediately invited several professors in this field to verify it.

The end result was that the paper was highly praised by them.

It is believed that it breaks the existing understanding of the Monge-Ampere equation in the mathematical community for many years.

Although the facts were right in front of him, Holt still couldn't imagine it, so he came to Professor Deligne to confirm.

Mainly, the proof of the Carmichael number interval problem paper was highly praised by Professor Pomerance, and Professor Deligne also verified it and praised the author of the paper, Xu Yuan.

However, he kept it a little suspense here and deliberately concealed the name of the author of the paper.

Deligne expressed his dissatisfaction with Holt's somewhat perfunctory answer with his eyes without any hesitation, but due to the attraction brought by Monge-Ampere's equation, he still read the paper.

At first his expression wasn't particularly focused.

Later on, he became more and more solemn, always maintaining the same posture.

I even forgot to drink the coffee in the cup.

Holt, who was sitting opposite him, also remained silent, fearing that he would disturb Deligne's thoughts.

So, even though it was a living room for two people, the only sound was the ticking of the old pendulum clock on the wall, which made the atmosphere seem a little weird.

About twenty minutes passed.

Deligne suddenly stood up and walked straight to the study, closing the door without saying a word.

It was like he was the only one in the room.

Holt felt relieved when he saw this scene. He knew that according to Deligne's habit, this meant that he was completely attracted by the content of the paper and could not wait to do some calculations to verify the proof process in the paper.

At this time, he was finally able to move his body.

In the study, Deligne took out a piece of scratch paper and began to check his calculations. As a large number of mathematical formulas filled up the paper, he became more and more surprised.

First of all, the whole paper has very clear ideas and its logic is impeccable.

The key point is that the author actually used physical methods to prove mathematical problems, which was quite clever and fluent. What surprised him was that he always felt a sense of familiarity from the format characteristics of the paper.

More than another hour passed.

Deligne looked at the final verification result on the draft paper, was silent for a long time before he came back to his senses and slowly uttered a word.

"sharp."

Without any hesitation, he quickly stood up and opened the study door with the printed manuscript of the thesis.

Holt, who was waiting in the living room and was getting a little bored, immediately went over and asked, "What do you think, Professor Deligne? Does this paper really prove the global smoothness of the solutions to Monge-Ampere's equation?" He was looking forward to Deligne's answer.

"That's right." Deligne nodded in confirmation. "The authors of the paper cleverly used physical methods to prove the problem, completely eliminating the two necessary conditions for the overall smoothness of the Monge-Ampere equation."

"For many years, experts in the relevant field have almost all believed that these two conditions are indispensable, but this article has broken the existing cognition."

"This is a great progress in the study of the Monge-Ampere equation, which is equivalent to expanding the scope of the Monge-Ampere equation theory to a wider range of fields." At this point, Deligne looked at Holt and said, "Now you can tell me the author of the paper."

After getting Professor Deligne's personal confirmation, Holt naturally no longer had any doubts in his mind.

Although I still find it hard to believe, the only option left is to accept the facts before my eyes.

His thought stopped here. Naturally, he would not continue to hide anything, and immediately told Deligne the author of the paper.

"Professor Deligne."

“You are not unfamiliar with the author of this paper.”

"The other party is the same person who proved the gap problem between infinite Carmichael numbers. He is Xu Yuan, a student from the School of Mathematics at Qinghua University."

"According to the time, he is a sophomore."

After quickly explaining the situation of the author of the paper, Holt fell silent and just watched Deligne's reaction.

"This is really shocking news."

When Deligne learned that the author of the paper was an acquaintance, his eyes fell on the printed manuscript in his hand again, and he did not hide his surprise and surprise at the moment.

"It's incredible that he made the leap from number theory to partial differential equations in just one year, and solved the problem of smoothness of solutions to Monge-Ampere equations, even though he was just a freshman in college."

“No wonder I felt a sense of familiarity from this paper.”

"genius."

“He’s definitely a true math genius.”

"I would like to use the Gauss of mathematics to evaluate this paper and its author, and hope to have the opportunity to communicate with them."

Holt listened to everything Deligne said and was surprised that Deligne gave such a high evaluation to the other party. He could describe him as the Gauss of the mathematics world, which showed his expectations for this young Chinese scholar.

You know, Gauss has always enjoyed the reputation of the Prince of Mathematics.

"The other party is indeed a rare mathematical genius." Holt took over the conversation and echoed.

Hearing this, Deligne walked to the sofa next to him and sat down, still praising Xu Yuan: "I really don't know what kind of teacher and family can cultivate such a genius. Maybe he will bring surprises to the mathematics world."

Xu Yuan's age and educational background are not so bad, but the main problem is the gap between number theory and partial differential equations.

It is normal to rely on one's own talents to learn number theory and solve difficult problems, but after all, everyone has limited time. It is already very rare to be able to thoroughly understand number theory at this stage. It is really hard to imagine how one can understand partial differential equations to this extent.

It can be said that if Xu Yuan had solved the same difficult number theory problem this time, they would definitely not have had such a big reaction.

Seeing that his goal had been achieved, Holt did not stay any longer. After all, there were still many things waiting for him to deal with on the editorial board.

"Professor Deligne, thank you very much for your help today."

"Mr. Holt, you don't have to say that. I also want to thank you for letting me see such an excellent paper." Upon hearing this, Deligne waved his hand and replied with a smile.

Afterwards, Deligne personally sent Holt out.

After thoroughly confirming the value of this paper, Holt only needed to notify the author that the paper had been included and arrange for it to be published in the latest journal according to the procedures of the Annals of Mathematics.

Unfortunately, Deligne’s wish to communicate with Xu Yuan face to face could not be fulfilled for the time being.

Because after the Spring Festival, Xu Yuan packed his bags and set out on the journey back to school again.

-

On the train, Xu Yuan was sitting by the window, holding a differential geometry textbook in his hand and reading it with great interest. Whenever he came across new content, he would become particularly interested, which could be considered as learning for graduate courses in advance.

He studied differential geometry a lot during the winter vacation.

When he encounters something he doesn't understand, he will take the initiative to call Tang Shihong for advice.

Tang Shihong was very happy to see this situation. After all, compared with partial differential equations, differential geometry was the area he was best at.

After more than half a month of self-study during the winter vacation, it is no exaggeration to say that if he were to guide his senior brother Lu Chunming's paper again, he is confident that the quality of the paper can be raised to a higher level.

Although it is no longer needed now.

In addition, he also learned about the graduation defense from Tang Shihong. The department decided to hold the defense in March.

It can also be said to be the most special defense since the founding of Qinghua School.

However, Xu Yuan didn't have any worries in his heart, and he didn't even feel nervous at all.

The fact that he did not check the paper proving the global smoothness of the solution to the Monge-Ampere equation during the winter vacation was enough to explain the problem. On the contrary, he was very much looking forward to the graduation defense, which would bring a perfect end to his undergraduate career.

……

(End of this chapter)