Ultimate Scholar

Li Mu's first report is over.

This report has a certain harvest for every participant.

For those students, they understand Li's space and how to use Li's space simply from Li Mu's report. Significant.

For mathematicians with a certain academic level, Li Mu's narration of Li's space also gave them a deeper understanding. Maybe they can write a paper directly after they go back. \b

As for those big cows, Li Mu's previous narration certainly inspired them to some extent, but what surprised them the most was the new thing Li Mu revealed in a few lines at the end.

A rewrite of the Boltzmann equation?

Regarding this point, those big cows are all interested in it.

There are also many mathematicians who study the Boltzmann equation, just like Carlos Koenig, the chairman of this year's IMU, whose main research direction is the Boltzmann equation, so at the end of Li Mu's report, he also showed that Great surprise.

He could fully see how shocking the change of the Boltzmann equation was in those few lines of formulas at the end of Li Mu.

Of course, among the Fields Medal winners, there are also many who study the Boltzmann equation, such as Pierre-Louis Leon who belongs to the same French Academy as Laurent Laphrogue.

As a very important direction in statistical physics, the Boltzmann equation, like the Navier-Stokes equation, has received the attention of many mathematicians.

All of a sudden, the mathematicians at the International Congress of Mathematicians began to discuss Li Mu's Fields Medal lecture two days later. The bulls are talking about it.

Because basically only they can see the deep meaning in Li Mu's simple formula. \u0001

It's just that the discussion of the big cows naturally caused other people to follow suit.

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're not coming?"

Not long after Li Mu's report was over, Laurent Laphrogue gave Pierre-Louis Lion.

Before coming here, Laurent Laforge specifically asked Leon if he wanted to come, but Leon had personal health reasons and he didn’t believe that Li Mu had proved the Navier-Stowe question in the Millennium Problem. Kess equation, so he did not come to this International Congress of Mathematicians.

Leon on the other end of the phone said, "Huh? What happened? Now that the conference has already started, there is no need for me to come."

Laurent Laforgue laughed: "Trust me, you won't be disappointed. Li Mu's report will definitely make you feel that your trip is worthwhile."

Leon was taken aback for a moment, and asked suspiciously: "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? Isn’t it his external force source that internalizes the space?”

"Hey... No, if I remember correctly, his report should end today, right?" Leon said angrily, "You're making fun of me."

"Huh? Didn't you watch the live broadcast of Li Mu's report?" Laphroaig asked.

"Not really."

"Hey, then I suggest you go and watch the recording again now, especially the ending, go and go."

At this time, Laphroaig seemed to be showing his friend Amway a video that he thought was interesting.

And Leon was a little puzzled, isn't it just a report, what's so special about it?

And it's the end...

What about the ending?

It's just that in view of Laphroaig's enthusiastic appearance, he didn't want to disappoint his old friend's enthusiasm, so he said: "Okay, okay, I'll watch it right away, I'll watch it right away."

After hanging up the phone, Leon logged on to the official website of the 2022 International Congress of Mathematicians, and then entered the interface of Li Mu's report.

Because the report is over, the official has posted the full video of the report on the website, and you can watch it after downloading.

Leon quickly downloaded the video, and then opened it to watch.

As the report began, Li Weng nodded from time to time when he listened to Li Mu's narration of the internalization space of the external force source in the video.

In any case, the internalization space of the external force source is indeed a very excellent new tool, and Leon also very much recognizes this.

"However, Li Mu's reporting method... seems to be a little different from his previous reports, um... it feels like he is in class."

Thinking of this, Leon shook his head with a smile, "Probably because he started to become a teacher."

He knew Li Mu's number theory class, and he even recommended Li Mu's number theory class video to his students. Among the many online number theory classes, Li Mu's class video was very outstanding.

Of course, the most important reason is that Li Mu's lecture method is very special, and a Fields Medal winner like him will be amazed.

Shaking his head, he watched it patiently, and even began to consider whether to let his students watch this video, which should help them better understand Li's Space. \b

In this way, fifty minutes passed.

When Li Mu in the video said that the main content of his report was the above, Leon came back to his senses.

"A very good report, the knowledge is easy to understand and easy to understand. I didn't expect this Li Mu to give such a good report after taking the class for a semester."

Nodding in admiration, Leon gave his evaluation.

But at this moment, he suddenly came back to his senses.

"Hey...Didn't Laphroaig say that there is something I should pay attention to at the end? What should I pay attention to?"

Although the content of the report is indeed very good, it is not enough to make him too surprised by it.

At this time, Li Mu in the video began to write a few lines of his preview on the blackboard.

Leon was immediately attracted to the attention. Following the listing of the first line of formulas, Leon, whose main research direction is the Boltzmann equation, immediately recognized this line of formulas, which is and Boltz Mann equation is related.

As the formulas in the next few lines were listed one by one, as an expert in the Boltzmann equation, Leon couldn't take his eyes off immediately.

"Wait... this is?!"

He stared closely at the blackboard in the video, but when Li Mu wrote a key point, his hand stopped, then turned his head, and announced that the content of his forecast ended here, this report is over, welcome Come to his Fields Medal lecture. \b

"Why did it stop!"

Seeing that it was over suddenly, Leon became anxious immediately.

The few lines of Li Mu's formula are obviously intended to rewrite the Boltzmann equation, but it is not complete, only revealing a corner, but it makes Leon scratch his heart and liver a little anxiously.

He really wants to know how to rewrite it later!

"Okay, okay, you're making this announcement, right?"

Leon sat silently in front of the computer for a while, took out his mobile phone on the spot, and booked a ticket to St. Petersburg this afternoon.

He went to see the report himself, okay?

No way, he really wanted to see a huge change in the Boltzmann equation.

Just like the Navier-Stokes equation, it has undergone several changes to form what it is now.

Perhaps, this improvement of Li Mu will be able to bring great changes to the research of the Boltzmann equation.

...

The International Conference of Mathematicians continued in full swing, and two days passed quickly.

July 10, as scheduled.

The Fields Medal Lecture is scheduled to start at 10:50 in the morning, which is also an hour. The venue is also in the No. 1 conference hall of the St. Petersburg International Conference Center.

Today's conference hall No. 1 is full of voices.

There were even more participants than Li Mu's last plenary report.

There is no other reason. After the publicity in the past few days, his report on the possible rewriting of the Boltzmann equation has become the focus of many relevant researchers. \b

And for all the participants on the scene, this report is more worthy of their attention.

Perhaps, this report, Li Mu will bring some new things to the mathematics world?

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, Cédric Villani saw Pierre-Louis Lion, and immediately greeted him with a smile.

Cédric Villani, winner of the Fields Medal in 2010, is also a student of Pierre-Louis Lion.

As a student of Pierre-Louis Lion, Cédric Villani's main research direction is also partial differential equations, and his greatest achievement is also on the Boltzmann equation.

However, Pierre-Louis Leon seemed a little disliked by this student who should have been his pride.

"Oh? Shouldn't you be sitting in the congressman's office at this time, waving the flag for your vote? Why do you still have the time to attend the mathematics conference?"

Leon sarcastically.

It turned out that Cedric Villani devoted himself to politics seven years after he won the Fields Medal, and basically stopped studying mathematics, so Leon was very disappointed with him.

Cedric Villani probably got used to the sarcasm from his mentor, and probably felt a little ashamed, so he didn't fight back. Instead, he became depressed and said, "I lost the election, the election failed."

Leon snorted: "It deserves it."

Cedric Villani sighed, but then said: "However, don't worry, teacher, I'm already planning 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, and I had no idea that the Boltzmann equation had new angles to study—"

"I want to clarify with you that the reason why I started to devote myself to politics back then was because I had gradually lost interest in mathematics. I felt that there was a limit to the Boltzmann equation, but I think that Li Mu's report today may be It will rekindle my old interest."

Listening to Cedric Villani's sincere words, Leon's brows twitched. No matter what, he always hated this student. If he was really disheartened, he must be scolding I don't bother to scold.

So, Leon finally said: "I hope you can really do what you say."

Of course, their small episode here did not attract the attention of others, and Laurent Laforge, who was also sitting next to him, said to Cedric Villani: "I hope you will not let your teacher down again." gone."

In the first row, today, sitting next to Wiles is Faltings.

Faltins glanced at Wiles and said, "As a student of Li Mu, you don't know anything about it? Can't you reveal anything?"

Hearing what Faltings said, Wiles looked over in surprise, and asked, "Huh? The dignified Mr. Gerd Faltings, is he actually interested in this kind of thing?"

"...Forget it, pretend I didn't ask." Faltins immediately stopped asking.

Indeed, according to his personality, he should disdain to pay attention to such things.

Wiles 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. Let's 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. It's a great feeling that no one else knows, but only you know.

In this way, the mathematics experts in the first few rows waited for the start of the report without saying a word.

In this report, the original text of the report was not shown to them, so no one knew what Li Mu would say.

Time passed quickly, and at 10:50, it was time.

As Koenig, who was the host, stepped onto the stage, after a brief introduction, Li Mu followed suit.

The same podium, the same venue hall.

The dress Li Mu was wearing was also the same as the one two days ago.

But the only two differences are the number of audience and what Li Mu is going to talk about today.

Probably between these two, there is a relationship between the independent variable and the dependent variable.

"I met you again, and thank you all for continuing to attend my report."

Stepping up to the podium, Li Mu said with a smile.

"Then, 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 of the remote control, and the PPT page moved.

【Boltzmann equation and internalization space of external force source】.

"In my last report, I mainly introduced the internalization space of external force sources."

"However, when using external force sources to internalize space, there will be a very obvious problem."

"Then the internalization of the external force source can only combine the external force and the internal essence, but it cannot fuse the two."

"Before, it was like a mixture of water and oil in a bottle. No matter how I shake it, they are always distinct."

"And this, in the end, will still affect our continued research."

"So, how do we solve a problem like this?"

"Let water and oil really blend together without distinction between each other?"

Li Mu turned his head, came to the blackboard, and wrote down the first form of this report.

Then, the big cows present knew immediately that this formula was a continuation of the formulas he listed at the end of the report two days ago.

The first formula immediately made them understand.

"So it is!"

"It turned out to be like this!"

"it is as expected!"

Three different thoughts sounded in their hearts at the same time, but what they expressed together was the wonder in their hearts.

And Li Mu on the stage began to tell: "In an accident, I was surprised to find that the Boltzmann equation can be well combined with the internalization space of the external force source."

"The unique function of Boltzmann can also completely make up for the defects in the internalization space of external force sources."

Li Mu smiled slightly: "Then, next, let me thoroughly deduce this process for everyone."

"How can we integrate the Boltzmann equation with the internalization space of the external force source!"

So, the next he turned around again, picked up a 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 cows in the audience watched it fascinated. \b

This is the art of mathematics!

And there are only people like them who can appreciate such art.

Pierre-Louis Lyon showed an extremely satisfied expression.

The feeling of being scratched by Li Mu's forecast two days ago was completely released at this moment.

He saw that the Boltzmann equation still had a very powerful potential.

Seeing Lion's expression, Laurent Laphrogue next to him smiled and said, "Why don't you regret coming here? Huh?"

Leon waved his hands without turning his head, and said, "Don't disturb me, I'm listening to the report."

Laurent Laphrogue laughed, but obviously, what Leon said had already answered his question sideways.

In the back row, Yun Wei and the others were also sitting together.

Looking at Li Mu's narration above, they all had deep amazement hidden in their eyes.

"Is there anything else that can stop him?"

Zhu Wen murmured, "Number theory, algebraic geometry, differential... He even has such achievements as Li's expansion."

Yun Wei was silent for a moment, and laughed at himself: "Perhaps we have never overestimated our capabilities when compared with him. After all, he is going to become... even surpass Grothendieck."

"Yes."

Of course, for many young math geniuses present, they all had the same feeling at this time.

It was a desperate gap, even to the point of not despairing, but complete acceptance.

...