After sorting out the paper proving the last step of the NS equation and throwing it on the Arxiv preprint website, Xu Chuan fell on the bed and fell asleep.
After the problem he had been thinking about was finally solved, it was an extremely comfortable sleep for him.
He didn't know how much time had passed, but when he woke up again, it was bright and bright outside.
Xu Chuan got up from the bed and stretched, opened the curtains and took a look at the Purple Mountain not far away. Even though it was winter, it was still lush and comfortable.
After taking a comfortable bath, he picked up his mobile phone from the bedside and checked the time.
November 17, 11:39.
It has been more than a month since I got the inspiration of microfluid in the classroom.
But the effort of more than a month was completely worth it.
Not only did he solve the difficult problem that he had been obsessed with in his previous life, he also created a new mathematical tool that built a new bridge between differential geometry, topology 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 difficult problems is like harvesting heavy fruits, and mathematical tools are the ladders or axes you use to harvest fruits.
Sometimes, a mathematical tool can not only be applied in a fixed field, it can also open up many other researches.
Just like the 'algebraic variety and group mapping tool' he created when solving Hodge's conjecture, it can not only be used for Hodge's conjecture.
It can be used to try many algebraic varieties, differential forms, polynomial equations, and even difficult problems in the direction of algebraic topology.
For example, it can be tried on questions such as the 'Bloch conjecture', which belongs to the same family of Hodge conjectures as the Hodge conjecture, and whether the Chow group is finite-dimensional.
This can bring more gains to mathematicians.
Touching his phone, Xu Chuan looked at the unread messages on his phone in the past few days, then stood up and touched a bag of bread and put it in his mouth.
Because he was studying the last step of the NS equation, he almost ignored all the calls and messages.
But now, he has time to deal with these missed calls and messages.
I took a rough look at my phone and found a lot of missed calls and messages sent to him, but the outbursts of messages to him were basically concentrated in the past ten hours or so.
Almost officially he uploaded the proof of the last step of the NS equation to the Arxiv preprint site.
After reading 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 dialed the number back.
But what surprised him was that Fefferman's phone was turned off and there was no call.
Xu Chuan didn't pay much attention. After all, it was noon now and it was late at night in the United States. He would just get a message back later. Fefferman would naturally call him if he saw it.
After briefly dealing with the missed calls and messages, he was just about to put down his phone and go back to sort out the manuscript papers in the study when the incoming call rang.
The caller was Fefferman.
"Xu, where are you now?" Fefferman on the other end asked impatiently as soon as the call was connected.
After being stunned for a moment, Xu Chuan replied: "Of course it's in China."
Fefferman: "."
"No, I'm asking you whether you are at home or at NTU, where exactly are you?"
Xu Chuan asked curiously: "I am at home now, have you come to China?"
Fefferman: "Yes, I have already arrived in Aurous Hill. I can be there in about half an hour to meet and chat."
After saying that, Fefferman hung up the phone in a hurry. Xu Chuan was stunned again when he looked at the phone with a black screen.
Is he asleep?
If I remember correctly, it shouldn't have been more than twelve hours since he uploaded the paper, right?
And from Princeton to Jinling, it takes at least 24 hours of flight, right?
Half an hour was not long, 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.
Good guy, there were five top figures in the mathematics circle standing at the door of his villa.
"Why are you all here?" After saying hello, Xu Chuan quickly welcomed the group of people into the villa and asked curiously.
Fefferman: "For the NS equations, of course!"
Hearing this, Xu Chuan glanced at the five people. Although the ns equation was indeed important, it was unlikely that so many top bosses would come here together.
On the side, Deligne explained with a smile: "There is a mathematics conference at the Ecole Normale Supérieure in Paris in mid-November, and I also sent you an invitation letter, but I was supposed to be studying the NS equation at the time, so I might have just ignored it."
"After you uploaded the paper to the arxiv website yesterday, we discussed it and came to your side together."
Xu Chuan suddenly nodded and said: "So that's it. I mean, why do so many of you suddenly gather together?"
Gowers smiled and said: "Speaking of which, this is the first time I met you. A few years ago, you wrote a paper proving the weak Weyl_Berry conjecture. I still remember it."
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."
This chapter is not finished yet, please click on the next page to continue reading the exciting content! "As for your questions, if it is convenient for you in the past few days, you can stay here. I live here, and you are always welcome to come and communicate."
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, it integrates differential equations, topological geometry and partial differential equations. 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 had Terence Tao made suggestions to him? Why didn't he know?
Opposite, 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 just gave it a name for expanded applications."
Xu Chuan looked ashamed, he is not bad at naming!
Aren’t the algebraic variety and group mapping tools great?
As for the expanded application of the Xu-Weyl-Berry theorem
Well, this can only mean that he is lazy!
Let me reiterate, his naming skills are really good!
But Fefferman was right when he said he created a new discipline.
He was indeed the first to apply the micro-element fluid 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 Perleman also used topology to solve the popular singularity 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 a discipline has been created.
As for how this subject can develop in the future, on the one hand, it depends on the potential of this mathematical tool, and on the other hand, it depends on Xu Chuan’s subsequent contributions and efforts to this subject.
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 discipline 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.
years of time.
Of course, if you want a subject to blossom fully, textbooks and other materials are definitely indispensable. But Xu Chuan currently does not have much time to write books and biographies.
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.
