Chapter 322: Creating a New Discipline!

On the other side, China, Jinling.

After finishing the paper proving the last step of the NS equation and posting it on the Arxiv preprint website, Xu Chuan fell asleep on the bed.

After the problem he had been thinking about was finally solved, he had a very comfortable sleep.

He didn't know how much time had passed, but when he woke up again, it was bright outside.

Xu Chuan got up from the bed and stretched, opened the curtains and looked at the Purple Mountain not far away. Even though it was winter, it was still lush and green, which made people feel comfortable.

After taking a comfortable bath, he picked up his mobile phone from the bed and checked the time.

November 17th, 11:39.

It has been more than a month since he got the inspiration of microfluid in the classroom.

But the efforts of more than a month are completely worth it.

He not only solved the problem that he had been thinking about in his previous life, but also made a new mathematical tool, which built a new bridge between differential geometry, topological structure and partial differential equations.

For the mathematics community, the emergence of a new mathematical tool is often more important than the solution of a difficult problem.

For mathematics, solving a difficult problem is like harvesting heavy fruits, and mathematical tools are the ladder or axe you use to harvest the fruits.

Sometimes, a mathematical tool can not only be applied in a fixed field, but also open up many other research.

Just like the "algebraic cluster and group mapping tool" he created when solving the Hodge conjecture before, it can not only be used for the Hodge conjecture.

Many algebraic clusters and differential forms and polynomial equations, and even difficult problems in the direction of algebraic topology, can be used to try.

For example, the "Bloch conjecture" and "whether the Chow group is finite-dimensional", which belong to the same family of Hodge conjectures as the Hodge conjecture, can be tried.

This can bring more gains to mathematicians.

Touching his mobile phone, Xu Chuan looked at the unread messages on his mobile phone in recent days, and got up and touched a bag of bread and held it in his mouth.

Because he was studying the last step of the NS equation before, he almost ignored all the calls and messages.

Now, he has time to deal with these missed calls and messages.

He roughly browsed his phone and found that there were many missed calls and messages sent to him, but the burst of messages to him was basically concentrated in the past ten hours or so.

It was almost the day after he officially uploaded the proof of the last step of the NS equation to the Arxiv preprint website.

After looking at the messages, Xu Chuan found that the person who called and sent him the most messages was Professor Fefferman of Princeton.

After thinking about it, he called back.

But to his surprise, Fefferman's phone was turned off and he couldn't get through.

Xu Chuan didn't care too much. After all, it was noon now, and it was late at night in the United States. He would just reply to the message later, and Fefferman would call him naturally when he saw it.

After simply dealing with these missed calls and messages, he was about to put down his phone and go back to organize the manuscripts in the study when the ringtone rang.

It was Fefferman who called.

"Xu, where are you now?" Fefferman asked impatiently as soon as the call was connected.

After a pause, Xu Chuan replied: "Of course I'm in China."

Fefferman: "."

"No, I'm asking if you're at home or in Nanjing University, where exactly are you."

Xu Chuan asked curiously: "I'm at home now, are you in China?"

Fefferman: "Yes, I'm already in Jinling, I'll be there in about half an hour, let's meet and talk."

After that, Fefferman hung up the phone in a hurry, and Xu Chuan stared at the black screen of the phone and was stunned again.

Is he half asleep?

If I remember correctly, it should have taken him less than twelve hours to upload the paper to now?

And it takes at least twenty-four hours to fly from Princeton to Jinling, right?

Half an hour is not a long time, and soon, a hurried doorbell rang in the villa, and at the same time, Fefferman called again.

Xu Chuan didn't answer the phone, got up and walked out of the villa, and then was startled by the person standing in front of him.

Fefferman, Deligne, Faltings, Gowers, Mori Shigefumi

Wow, there were five top math guys standing at the door of his villa.

"Why are you all here?" After greeting them, Xu Chuan quickly welcomed the group into the villa and asked curiously.

Feferman: "Of course it's for the NS equation!"

Hearing this, Xu Chuan glanced at the five people. Although the NS equation is indeed important, it's not necessary for so many top guys to come here together.

On the side, Deligne smiled and explained: "There was a math conference at the École Normale Supérieure in Paris in mid-November, and you were also invited. But you should have been studying the NS equation at the time, so you may have ignored it directly."

"After you uploaded your paper to the arxiv website yesterday, we discussed it and came to your place together."

Xu Chuan nodded suddenly and said, "So that's how it is. I mean, how come so many of you suddenly gathered together."

Goers smiled and said, "Speaking of which, this is the first time I met you. A few years ago, I still remember the paper you wrote about the proof of the weak Weyl_Berry conjecture."

Xu Chuan smiled and said: "Many times I thought we could meet, but we ended up missing it."

He and Gowers have a deep relationship, but unfortunately they have never met each other. This is the first time today.

After the group chatted in the living room for a while, Fefferman asked: "Xu, when are you going to give a report on solving the NS equation? I think everyone has a lot of questions."

Xu Chuan thought for a while and said: "At least part of the time should be set aside for others to get familiar with the paper, right? How about opening it on December 1st? About half a month should be enough for most people to get familiar with it."

"As for your questions, if it's convenient for you in the past few days, you can stay here. I live here and welcome everyone to come and communicate at any time."

Fefferman thought for a while and nodded: "That's okay. I'd like to hear you introduce the mathematical tool in detail. Based on micro-element fluids, differential equations, topological geometry and partial differential equations are integrated. Strictly speaking, This is no longer a mathematical tool, it is a completely new subject!”

After a pause, he continued: "I think you should seriously consider Tao's suggestion and give this tool a good name."

Hearing this, Xu Chuan looked at Fefferman with confusion and curiosity in his eyes. When did Terence Tao give him advice? How come he doesn't know.

On the opposite side, Shigebumi Mori, the current director of the International Mathematical Union, explained with a smile: "Maybe you don't surf the Internet? Tao complained on his blog yesterday, saying that your naming skills are too poor."

"For example, for your previous tool results for computational astronomy and physics, you directly gave it a name for expanded applications."

Xu Chuan looked ashamed. He was not bad at naming, right?

Aren’t the algebraic variety and group mapping tools great?

As for the expanded application of the Xu-Weyl-Berry theorem

Well, this just means he is lazy!

Once again, his naming skills are really good!

But Fefferman was right when he said he had created a new discipline.

He was indeed the first to apply micro-element fluids defined in mathematical physics to spaces and topological structures with local Euclidean space properties to study partial differential equations in such detail.

Although as early as the 19th century, Hamilton had used manifolds to solve the Poincaré conjecture, and later Perelman also used topology to solve the popular singularity problem when proving the Poincaré conjecture in three-dimensional space. question.

But he was the first to completely integrate the three to form a whole.

It is not a big problem to say that I have created a discipline.

As for how this discipline can develop in the future, it depends on the potential of this mathematical tool on the one hand, and on the other hand, it depends on Xu Chuan’s subsequent contributions and efforts to this discipline.

Just like his ancestor, the "God of Mathematics" Mr. Grothendieck, the modern abstract theoretical system of algebraic geometry he founded can be said to be the most popular field in mathematics today.

But at the beginning, this set of subjects did not receive much attention from the mathematics community at that time.

It was not until 1967 that he and Professor Jean Dieudonné co-wrote the first eight volumes of "Fundamentals of Algebraic Geometry", which gradually promoted algebraic geometry to the entire mathematical community.

After that, he trained many mathematicians, the most famous of whom are Pierre Deligne and Michel Reynaud. He also gathered a powerful school that dominated the entire mathematics world for more than ten years. time.

Of course, if you want a subject to flourish fully, textbooks and the like are definitely indispensable. But Xu Chuan currently doesn't have much time to write a book or biography.

Perhaps after the controllable nuclear fusion project is completed, he will consider compiling the theories and methods he has developed, such as the expanded application of the Xu-Weyl-Berry theorem, such as algebraic varieties and group mapping tools, into textbooks.

Therefore, in comparison, he is still a long way from his ancestor Grothendieck.

But at least a seed has been planted, and all that's left is to take care of it and wait for it to grow into a towering tree.