Li Mu's first report is over.
This report has certain gains for every participant.
For those students, they understood Li space from Li Mu’s report and how to simply use Li space. This is very useful for students who study geometry or are interested in studying fluid mechanics. Significant.
For mathematics scholars with a certain academic level, Li Mu's description of Li's space also gave them a deeper understanding. Maybe they can write a paper directly after returning home.
As for the experts, Li Mu's previous narration certainly inspired them to some extent, but what surprised them the most was the new things Li Mu revealed in just a few lines at the end.
Rewrite the Boltzmann equation?
Regarding this point, the big guys are all interested in it.
There are many mathematicians who study the Boltzmann equation. For example, Carlos Koenig, the current president of IMU, whose main research direction is the Boltzmann equation, so at the end of Li Mu’s report, he also showed A great surprise.
He could completely see how shocking the changes to the Boltzmann equation in the last few lines of expressions by Li Mu were.
Of course, there are also many Fields Medal winners who study the Boltzmann equation, such as Pierre-Louis Lion, who is a member of the Collège de France and Laurent Laforgue.
As a very important direction in statistical physics, the Boltzmann equation, like the Navier-Stokes equation, is valued by many mathematicians.
All of a sudden, the mathematics scholars at the International Congress of Mathematicians began to discuss Li Mu’s Fields Medal lecture two days later. Those experts were even more looking forward to it. Of course, it was mainly these experts who They are discussing it hotly.
Because basically they were the only ones who could see the deep meaning in Li Mu's simple lines.
However, the discussions among the experts naturally led to discussions among others.
So just like that, Li Mu's report two days later became the focus of everyone's attention.
…
"Hey, Leon, are you still sure you don't want to come?"
Not long after Li Mu's report ended, Laurent Laforgue gave Pierre-Louis Leon.
Before coming here, Laurent Laforgue specifically asked Leon if he wanted to come. As a result, Leon had personal health reasons and did not believe that Li Mu had proved the truth about Neville Stowe in the Millennium Puzzle. He did not attend this International Congress of Mathematicians.
Leon on the other end of the phone said, "Huh? What happened? Now that the conference has started, there is no need for me to come."
Laurent Laforgue laughed: "Believe me, you will not be disappointed. Li Mu's report will definitely make you feel that your trip is worthwhile."
Leon was stunned and asked doubtfully: "Li Mu? I knew he won this year's Fields Medal and became the youngest Fields Medal winner in history. What did his report say? Could it be that he won this year's Fields Medal and became the youngest Fields Medal winner in history. Isn’t it the internalized space of his external force source?”
"Eh... no, if I remember correctly, his report should have ended today, right?" Leon said angrily: "You are making fun of me."
"Huh? Didn't you watch Li Mu's report live?" Laphroague asked.
"That's not true."
"Hey, then I suggest you go and watch the recording again now, especially the ending. Go, go, go."
Laphroaig seemed to be giving his friend Amway a video that he found interesting.
And Leon was a little confused. Isn't it just a report? What's so special about it?
And it’s the end…
So what about the ending?
But since Laphroaig was so enthusiastic, he didn't want to let his old friend's enthusiasm be disappointed, so he said: "Okay, okay, I'll watch it right away, I'll watch it right away."
After hanging up the phone, Leon logged into the official website of the 2022 International Congress of Mathematicians, and then entered Li Mu's report interface.
Because the report has ended, the official has released the complete video of the report on the website, which can be watched after downloading.
Leon quickly downloaded the video, then opened it and started watching it.
As the report began, Li Weng nodded from time to time as he listened to Li Mu's description of the internalization space of external force sources in the video.
No matter what, the internalization space of external force source is indeed a very excellent new tool, and Leon also fully recognizes it.
"However, Li Mu's reporting method... seems to be a little different from his previous reports. Well... it feels like he is in class."
Thinking of this, Leon shook his head with a smile, "Maybe it's because he started to become a teacher."
He was aware of Li Mu's number theory classes, and he even recommended Li Mu's number theory class videos to his students. Among the many online number theory classes, Li Mu's class recordings were outstanding.
Of course, the most critical reason is that Li Mu’s teaching method is very special, and Fields Medal winners like him would be amazed.
Shaking his head, he then continued to watch it very patiently, and even began to consider whether to let his students watch this video, which should help them better understand Li's Space.
Just like that, fifty minutes passed.
When Li Mu in the video said that the main contents of his report were the above, Li Weng came back to his senses.
"A very good report. The knowledge is easy to understand and explained in a simple way. I didn't expect that Li Mu would give such a good report after taking the class for a semester."
Nodding in admiration, Leon gave his evaluation.
But this time he suddenly came back to his senses.
"Hey... Laphroaig said, is there anything at the end that I should pay special attention to? What should I pay attention to?"
Although the content of the report was indeed very good, it was not enough to surprise him.
At this time, Li Mu in the video began to write a few lines of his trailer on the blackboard.
Leon's attention was immediately attracted. As the first line of equations was listed, Leon, whose main research direction was the Boltzmann equation, immediately recognized that this line of equations was the same as Boltzmann's equation. Mann equation is related.
As the following lines of formulas were listed one after another, as an expert on the Boltzmann equation, Leon couldn't take his eyes away.
"Wait...this is?!"
He stared closely at the blackboard in the video, but just when Li Mu was writing the key points, his hand stopped, turned his head, and announced that the content of his preview was over. The report was over. Welcome. Come to his Fields Medal lecture.
"Why did you stop!"
Seeing that it ended suddenly, Leon immediately became anxious.
A few lines of equations written by Li Mu were obviously intended to rewrite the Boltzmann equation, but they were incomplete and only revealed a small part of the equation. However, it made Leon anxiously scratch his head.
He really wanted to know how to rewrite it later!
"Okay, okay, you're doing this to give a warning, right?"
After Leon sat in front of the computer in silence for a long time, he took out his mobile phone on the spot and booked a ticket to St. Petersburg this afternoon.
He should read the report himself!
No way, he really wanted to see a huge change in the Boltzmann equation.
Just like the Navier-Stokes equation, it has gone through several changes before it became what it is now.
Perhaps, Li Mu's improvement will bring huge changes to the study of the Boltzmann equation.
…
The International Congress of Mathematicians continued in full swing, and the two days passed quickly.
July 10th arrived as scheduled.
The Fields Medal Lecture is scheduled to start at 10:50 in the morning, which is also an hour long. It is also held in Conference Hall 1 of the St. Petersburg International Conference Center.
Today's Conference Hall No. 1 is bustling with people.
There were even more people participating than in Li Mu’s last general report.
There is no other reason. After these few days of publicity, his report that may rewrite the Boltzmann equation has become the focus of many relevant researchers.
For all participants at the scene, this report deserves more attention.
Perhaps, in this report, Li Mu will bring something new to the mathematics community?
No one wants to miss such an important moment.
…
"Hey, teacher, why are you here? I remember you didn't come a few days ago?"
In the second row of seats, Cedric Villani saw Pierre-Louis Lion and immediately said hello with a smile.
Cedric Villani, winner of the 2010 Fields Medal, is also a student of Pierre-Louis Lion.
As a student of Pierre-Louis Lion, Cedric Villani's main research direction was partial differential equations, and his greatest achievement was also in the Boltzmann equation.
However, Pierre-Louis Leon seemed to dislike this student who should have been his pride.
"Oh? Aren't you supposed to be sitting in the congressman's office right now, waving flags and shouting for your votes? Why do you still have time to attend the mathematics conference?"
Leon sarcastically said.
It turned out that Cedric Villani devoted himself to politics seven years after winning the Fields Medal and basically stopped studying mathematics, so Leon was very disappointed with him.
Cedric Villani was probably used to his mentor's sarcasm, and he was probably a little ashamed, so he did not fight back. On the contrary, his face became frustrated and he said: "I lost the election. The election failed."
Leon snorted: "You deserve it."
Cedric Villani sighed, but then said: "But don't worry, teacher, I have already planned to start studying mathematics again. Li Mu's prediction about the Boltzmann equation in his last report made me feel It was a huge shock. I didn’t expect that there were new angles to study the Boltzmann equation—”
"I want to clarify with you that the reason why I started to join politics was because I had gradually lost interest in mathematics. I felt that there were limits to the Boltzmann equation. But I think that Li Mu's report today may Rekindled my old interest.”
Listening to Cedric Villani's sincere words, Leon's brows moved. No matter what, he had always hated this student. If he was really frustrated, he would definitely scold him. Too lazy to scold.
Therefore, Leon finally said: "I hope you can really do what you say."
Of course, their little episode here did not attract the attention of others. Laurent Laforgue, who was also sitting next to him, said to Cedric Villani: "I hope you will not let your teacher down again." ”
In the first row, today, sitting next to Wiles is Faltings.
Faltings glanced at Wiles and said, "As Li Mu's student, you don't know anything? Can't you reveal anything?"
Hearing what Faltings said, Wiles looked over in surprise and asked, "Huh? The dignified Mr. Gerd Faltings is actually interested in this kind of thing?"
"...Forget it, just pretend I didn't ask." Faltings stopped asking immediately.
Indeed, according to his character, he should not bother paying attention to such things.
Wilers suddenly laughed.
"I'm interested, I'm interested, tell me quickly." Terence Tao, who was sitting on the other side of Faltings, came up and asked.
Wiles spread his hands: "I don't know. We'll find out after Li Mu's report is over in an hour."
Terence Tao rolled his eyes.
Wiles sat down with an innocent face, but he was secretly happy in his heart. This feeling that no one else knew but only him felt was really good.
In this way, the math experts in the first few rows remained silent, waiting for the report to begin.
The original text of this report was not shown to them, so no one knew what Li Mu would say.
Time passed quickly, and at 10:50, the time was up.
As the host Koenig walked onto the stage, after a brief introduction, Li Mu followed.
The same podium, the same venue hall.
The dress Li Mu was wearing was the same as the one two days ago.
But the only two things that were different were the number of spectators at the scene and what Li Mu was going to talk about today.
Probably there is a relationship between the independent variable and the dependent variable between these two.
"I've met you all again, and I'd like to thank you all for continuing to attend my report."
Walking up to the podium, Li Mu said with a smile.
"Well, without further ado, today's report will officially begin."
"And the topic of today's report is——"
Li Mu turned around and looked at the PPT on the big screen behind him. At the same time, he pressed the button on the remote control and the PPT page moved.
[Boltzmann equation and external force source internalization space].
“In my last report, I mainly introduced you to the internalization space of external force sources.”
"But when using external force sources to internalize space, there is a very obvious problem."
"Then the internalized space of the external force source can only combine the external force with the inner essence, but it cannot fuse the two."
"Before, it was like a mixture of water and oil in a bottle. No matter how I shook it, they were always distinct."
"And this will ultimately affect our continued research."
"So, how do we solve a problem like this?"
"Let water and oil truly merge and become completely indistinguishable from each other?"
Li Mu turned his head, came to the blackboard, and wrote the first form of this report.
Then, the big guys present immediately knew that this formula was a continuation of the formulas he listed at the end of the report two days ago.
The first move immediately enlightened them.
"So that's it!"
"It's actually like this!"
"it is as expected!"
Three different thoughts echoed in their hearts at the same time, but what they expressed together was the wonder in their hearts.
Li Mu, who was on the stage, began to talk: "In an accident, I was surprised to find that the Boltzmann equation can be well combined with the internalized space of external force sources."
"And Boltzmann's unique function can also completely make up for the defects in the internalized space of external force sources."
Li Mu smiled slightly: "Then, let me thoroughly deduce this process for everyone."
"How can we integrate the Boltzmann equation and the internalized space of the external force source!"
So, next, he turned around again, picked up the pen, and started writing on the blackboard.
[(f/t)c=gI(g,Ω)[f(p'A,t)...]
As the formulas were listed one by one, the big guys in the audience all watched with fascination.
This is the art of mathematics!
And the only people who can appreciate such art are people like them.
Pierre-Louis Lion showed an expression of great satisfaction.
The heart-wrenching emotions that Li Mu had predicted two days ago were completely released at this moment.
He saw that the Boltzmann equation still has very powerful potential.
Laurent Laforgue, who was next to him, saw Leon's expression and said with a smile: "How come you don't regret coming here? Huh?"
Leon waved his hand without turning his head and said, "Don't disturb me, I'm listening to the report."
Laurent La Forgue laughed, but obviously, Leon's words had already answered his question sideways.
In the back row, Yun Wei and others were also sitting together.
Looking at Li Mu's narration above, there was deep amazement in their eyes.
"Is there anything else that can stump him?"
Zhu Wen murmured, "Number theory, algebraic geometry, differential calculus... He even has achievements such as Li's expansion."
Yun Wei was silent for a moment and laughed at himself: "Perhaps when we compare with him, we never overestimate our capabilities. After all, he wants to become... or even surpass a figure like Grothendieck."
"Yes."
Of course, for many young mathematical geniuses present, they all had the same feelings at this time.
It was a despairing gap, even to the point of not despairing, but of complete acceptance.
…
(End of chapter)
