The news that Lin's conjecture was proved spread throughout the world.
Although this matter has not yet been recognized by everyone, verifying whether the proof of a conjecture is correct is definitely not as simple as publishing a paper on arxiv. However, in the past few days, no one in the mathematics community has been able to pass it.
A top mathematician said there were problems with this proof, so everyone assumed that the conjecture had really been proven.
As for other people’s questions, they are basically problems with the “obvious” parts, as well as some problems caused by insufficient knowledge reserves.
As a result, everyone is looking forward to this period of time passing quickly and letting the real big names in algebraic geometry give the final answer, such as Pierre Deligne and Faltings, these two
The world of algebraic geometry is famous and capable. Such achievements related to algebraic geometry must be recognized by these two people. Of course, there are many talents in algebraic geometry. Apart from these two, other big guys
There are also many of them. After all, every time a Fields Medal is awarded, there is one who studies algebraic geometry.
Of course, in addition to this, everyone is also looking forward to Lin Xiao holding an academic report again and publicly answering people's questions.
However, for the time being, there is no news that Lin Xiao will hold a report to answer people's questions.
This makes people confused.
What is Lin Xiao doing?
…
"That's it for today's class. See you next semester."
After giving the last mathematics class of the semester to the graduate students, although all the mathematics graduate students from Peking University present are considered to be the leading talents in the Chinese mathematics community, they cannot help but stare at the mathematical symbols on the blackboard in a daze.
After all, those were all written by Lin Xiao.
What's more, this is still number theory.
As we all know, number theory is a game for geniuses. If you are not a genius, don't try to invest in the research of number theory. Otherwise, you will only sigh and regret it in the end.
Just like there are countless people trying to solve Goldbach's conjecture, from top scientists to civilian scientists. As a result, mathematicians only know how to turn around after hitting a wall, while civilian scientists are amusing themselves without knowing it.
.
Of course, this pearl in the world of number theory has been picked off by Lin Xiao, and it has nothing to do with them.
The pearl is number theory, and ordinary number theory problems are also number theory. When taking Lin Xiao's class, for these graduate students, there are only three things: confused, confused, and really confused.
However, although they were at a loss, they reviewed when they needed to review. Compared with the last time they saw Lin Xiao this semester, and the news some time ago, they had many, many more things they wanted to ask him.
"Professor, professor! Have you really proved your Lin's conjecture?"
Lin Xiao: "Just read my paper."
"But some of us can't understand it!"
"Then go and supplement your knowledge so that you can understand."
"But we need to understand it first to know what knowledge we still lack."
"Then go read my paper."
"But we can't understand it!"
Lin Xiao: "...You put this card on my BUG?"
There was laughter in the classroom.
Lin Xiao shook his head and said, "Okay, let's pass your exam first and then we'll talk about other things later."
"Don't let me know that you copied other people's work during the exam!"
"Definitely not!"
There was a sound of reassurance in the classroom.
Lin Xiao rolled his eyes.
The final exams for graduate students are not as strict as those for undergraduates, so there are cases where students copy each other during the exams.
Although Lin Xiao has never experienced it, she has heard of it.
Of course, he didn't invigilate the exam, so it wasn't his turn to take care of it, so he didn't say anything more.
After leaving the classroom, he returned to his office. At this moment, several professors from the School of Mathematics, including Xu Ji, and the dean of their school, Zhao Qi, appeared.
Seeing these people coming in, Lin Xiao couldn't help but asked in confusion: "What's the matter?"
"Haha, Professor Lin, I want to discuss something with you."
Zhao Qi rubbed his hands and said with a smile.
"Well, it's fine as long as Dean Zhao says so." Lin Xiao said.
"It's like this, Professor Lin, didn't you prove your Lin's conjecture? Now there are a lot of calls in the mathematics community, hoping that you can give an academic report, so I just want to ask you, when do you plan to give it?
?The related matters will then be taken care of by our college and school. If you tell us about it here, we can make preparations in advance."
Zhao Qi said with a smile.
As soon as Lin Xiao heard this, he knew what he meant.
After all, this kind of thing is a good thing for their college and school, and Zhao Qi, as the dean, of course has such a responsibility to carry forward their college.
Lin Xiao proved Goldbach's conjecture last time. When there was a report meeting, there was originally such an opportunity, but there were too many people who wanted to come. Their Beijing University did not have the diamond, so they could not take the porcelain job.
The city government could not find a hall that could accommodate 10,000 people at the last moment. The Great Hall of the People had to be reserved some time in advance, so it had no choice but to ask the state to issue an order to vacate the 10,000-person auditorium in the Great Hall of the People.
So it had nothing to do with them. Although everyone knew that Lin Xiao was a student of their Beijing University at the time, the report meeting was held elsewhere. People naturally remembered Lin Xiaohua's identity as a Chinese, not their identity as a Beijing University student.
.
Of course, Goldbach's conjecture is a thing of the past. Now Lin Xiao has figured out Lin's conjecture again, and because its status in the mathematics community is not low, there are quite a lot of people paying attention to it. As the dean,
Zhao Qi, of course, did not want to lose such an opportunity.
However, Lin Xiao just shook his head and said, "Dean Zhao, I have no such plan yet."
Zhao Qi was stunned and couldn't help but ask: "Professor Lin, why is this?"
Lin Xiao said: "Because I am also responsible for the X-ray project, there are actually people on the Internet who have speculated that I have proven whether Lin's conjecture is to build a lithography machine. Although it seems a bit impossible, it is actually possible, and it
This is indeed my purpose.”
"Now that Lin's conjecture has been proven, I should continue to devote my attention to the X-ray project."
After hearing Lin Xiao's words, several people present were stunned.
Lin Xiao proved Lin's conjecture, just for the X-ray project?
Although using "just" to describe it makes it seem that the X-ray project is unimportant, in the eyes of mathematicians, the fact is almost like this.
After all, they are not like Lin Xiao, who not only studies mathematics, but also studies on these lithography machines. In their view, mathematical truths are of course much more important than these application technologies.
For a moment, they couldn't help but look at each other.
Xu Ji felt very curious: "Lin Xiao, is this theorem you have now really useful for lithography machine technology?"
Lin Xiao smiled and said: "Of course it works, otherwise why would I solve it?"
"Also, maybe after a while, you will know how to use my Lin's theorem."
Hearing what Lin Xiao said, several people didn't know what to say. Zhao Qi could only say: "Professor Lin, so be it. However, if you have time, you must give a lecture in our school."
ah!"
"Of course it's no problem." Lin Xiao said with a smile: "Maybe it won't be long before I have time to make this report."
"Okay!" Zhao Qi just took Lin Xiao's polite words as a courtesy and responded without saying anything more.
Instead, Xu Ji asked: "You are not planning to give this report at this year's International Congress of Mathematicians, are you?"
"We don't rule out this possibility," Lin Xiao said.
But the conversation between the two still stunned Zhao Qi and several others.
International Congress of Mathematicians?
They didn't know that Lin Xiao had received the invitation, only Xu Ji knew.
So Zhao Qi couldn't help but said in surprise: "Professor Lin, have you received an invitation to give a report at the International Congress of Mathematicians?"
Lin Xiao nodded and said modestly: "Well, it's just a one-hour report, so it's probably a little better than last time."
Zhao Qi, several other professors: "..."
Better than last time?
That’s it?
Are you leaving this with us in Versailles?
Wasn’t it a special one-hour report last time?!
Moreover, because the one-hour report was temporarily arranged last time, in terms of its uniqueness, historical nature, and the subsequent impact of that report, it is obviously more famous than the ordinary one-hour report, no matter who it is.
It's hard to say who is better or worse.
Of course, there is nothing to say about this. The most important thing is that they have received report invitations for two consecutive International Congresses of Mathematicians, and now they are still receiving invitations for one-hour reports. This kind of honor is still meaningful. They looked at it again
Lin Xiao's young face.
Zhao Qi grinded his teeth, wondering why his teeth were sore?
Of course, putting aside the question of whether it is sour or not, Lin Xiao once again received an invitation to give a one-hour report, which is also a benefit to their college and school, although it is not as good as inviting many mathematicians from the world of mathematics to come and participate in an academic event.
The report greatly improves the international reputation, but the domestic reputation is still very good.
Although Peking University is already well-known in China, it will never dislike this opportunity to earn reputation. Just look at how much it helps them compete with Qinghua for students because of Lin Xiao.
.
So Zhao Qi forgot Lin Xiao's Versailles words and said with a smile: "Hey, let me congratulate Professor Lin first. If you plan to give a report at the International Congress of Mathematicians, that's okay. I fully support you.
.”
"Haha, it depends on the situation."
Lin Xiao waved his hand.
"Well, okay, that's it."
Zhao Qi nodded, and then they stopped talking and left Lin Xiao's office.
Lin Xiao tidied up and returned to Yan Beiyuan's house.
After stroking his breasts, he sat down at his desk.
Open his paper that proved Lin's conjecture and browse through it.
But when he looked at it, his eyes flickered slightly.
He had indeed planned to give a report on Lin's conjecture at the International Congress of Mathematicians.
However, when compiling the paper, he was surprised to find that the proof process and results seemed to be applicable to the study of Hodge's conjecture!
Even help prove the Hodge conjecture!
In the past, in order to prove Lin's conjecture, due to the connection between Lin's conjecture and Hodge's conjecture, he had read many papers studying the Hodge's conjecture. Now that Lin's conjecture has been proven, looking back
Let’s take another look at the relationship between Lin’s conjecture and Hodge’s conjecture, and it can even be deepened.
And this will also help prove the Hodge conjecture!
What is Hodge's conjecture?
One of the Seven Millennium Problems!
The seven major problems of each millennium are of great significance to the academic world.
The Riemann Hypothesis can crack the mystery of prime numbers; once the p=np problem is true, we may even be able to use computers to prove other millennium problems; the existence and smoothness of the solution to the Navier-Stokes equation will be able to crack all kinds of problems in the world.
The secret of fluid movement...
The Hodge conjecture can truly connect two seemingly unrelated fields of mathematics, algebraic geometry and topology, and once again make great progress in the unification of mathematics.
Although there is overlap between algebraic geometry and topology and can be used in each other's research, the two are not really connected.
Even Lin's conjecture only connects ordinary functions and layers, which makes the connection between algebra and geometry closer.
Lin Xiao thought in his mind, and finally shook his head and stopped thinking about it.
Although the Lin's theorem he proved was helpful in proving the Hodge conjecture, it is still quite difficult to truly prove the Hodge conjecture.
And he didn't have time to do it yet.
After all, what he wants to study now is an X-ray lithography machine.
Just like what he just told Zhao Qi and others, he proved Lin's conjecture for this purpose.
That is to conduct a more fundamental study of the formation mechanism of chemical bonds.
And now, he already has such an opportunity.
Reopen another document, this document is called "Electronic Topological Bonding Theory".
Over the past few days, he has not paid any attention to the outside discussion about Lin's conjecture, and has been devoting all his attention to the research of this theory.
Electronic topological bonding theory regards chemical bonds as ropes and atomic nuclei as kink. The topology between them is the principle of their bonding and formation of their own molecular structure!
This is the new theory that Lin Xiao will bring to the world again.
In fact, nearly two hundred years ago, a scholar named Kelvin already believed that kink could be used to study atoms. However, that scholar had not escaped the influence of the "ether theory", so in the end this research was still unsuccessful.
Let it go.
But now, Lin Xiao has to use a new way to understand it.
The corners of his mouth curled up slightly.
Proving Lin's conjecture has stirred up the turmoil in the mathematical world, and proposing the electronic topological bonding theory will stir up the turmoil in the three fields of condensed matter physics, structural chemistry, and materials!
Of course, he did not stop at fantasizing about success. After all, he has not succeeded yet.
Taking out his pen, he began to make his own calculations.
[Suppose an atom is a kink p, has m layers of electron orbits, and n electrons...Suppose there are X atoms of this atom in a crystal unit cell...]
[According to the basic bonding theory, the possibility of forming a chemical bond between these atoms is (mn/X)*(√nm/X)*...]
[...φ(x)=∫r∈K|dr|/|xr|=∫2π0|r′(t)|dt/|x?r(t)|]
…
It is quite difficult to use topology to understand such atomic level problems.
This is probably to give a rope of any length, and then twist it into a Rubik's cube, and it has to be 9*9, 18*18 is not impossible, if the unit cell is complex enough.
This first requires a strong spatial imagination.
However, with Lin Xiao's current brain development, he was able to establish a model of light diffraction and interference in his mind, and naturally he was able to establish such a model of kink in his mind.
So, first of all, he solved a major problem in studying this thing.
Then, it’s a game of math.
To study a problem is to drag the problem into the field in which you are good at solving it.
For Lin Xiao, mathematics is a field that he is good at, but this field is relatively versatile and can be used to solve too many other problems.
In this way, a new theory gradually came into being in his hands.
The academic community still has not realized that what kind of storm is hidden behind the charm that has just been faced with the proof of Lin's conjecture, which is about to set off its turbulence.
…
[Sorry to keep you all waiting. I will get home tomorrow, so I squeezed out time to write this chapter at the hotel every night - because I was driving home with my family, which is halfway across the country, which is a bit far. 】