Ultimate Scholar

The flowers outside the window are blooming, and they look a little bright under the sunlight. You can also see a few birds standing on the branches and leaves, their smart heads turning around, playing with each other. \b

Suddenly, these birds turned their heads and noticed a pair of eyes looking at them from behind the window. Finally, these birds flapped their wings together and flew away.

Behind the window, Li Mu sat quietly at his desk. The natural scenery outside the window made him smile knowingly.

Six months have passed and he has not changed much.

Of course, what also remains unchanged is the list of all his achievements.

From being very productive in the past, he has not produced any results for almost a year now, so much so that the academic community now thinks that after he won three awards that are considered heavyweight in the entire academic world in one year, I'm going to start messing with it.

Of course, no one knows what Li Mu is planning, so no one will question him for the time being. No matter what, it has only been less than a year. There are still many people in the world who will not come out for two or three years. It's fruitful.

As for Li Mu's true thoughts, only he knows now. \b

"professor……"

Suddenly, a voice came from the side.

Li Mu turned around and saw Tu Zhizhen, Brahms and Alex standing next to the desk, their faces full of embarrassment.

As Li Mu's students, they can also be regarded as the people closest to Li Mu. Although Li Mu has not produced any results for so long, they know that what Li Mu is studying now is the kind of thing that they cannot understand at all.

Just what Li Mu occasionally wrote on the scratch paper made them look confused, not to mention their desperate thinking efficiency when Li Mu usually guided them. \b

"What's wrong?"

Li Mu asked.

"us……"

The three people looked at each other and finally said: "We now...probably have encountered the last problem."

Li Mu shook his head helplessly, and then said: "Okay, tell me, what problem did you encounter again?"

The three of them each took out a few pieces of scratch paper and spread them out in front of Li Mu.

“When we got to this point in our process, we realized we couldn’t write any more.”

"Here, we need to discuss how many ways there are to write a given number n as the sum of prime numbers and square-free numbers."

"We have come up with several methods, but how to continue later makes us confused about the password."

Li Mu took the draft paper from them and quickly scanned the words on it.

Quickly, he nodded slightly and said, "Well... no matter what, you did write down the last question."

"However, regarding this issue, you need to comprehensively consider all the previous steps, and then realize the link between the previous and the following. Then you will be able to understand what steps should be taken next."

"The point is, the degree of mastery of the entire issue."

Li Mu finally gave a very abstract answer to the questions asked by the three people.

After so many months, the three people's research on Artin's conjecture has entered the final stage.

Of course, Li Mu still gave a lot of help throughout the whole process.

No matter what, this problem is always Artin's conjecture, an unsolved problem with a history of nearly a hundred years in the mathematical world.

If it weren't for Li Mu's help, although these three students also have very high talents, they might not be able to complete even half of the progress by now.

After all, not everyone is him.

After hearing Li Mu's answer, the three people did not continue to ask questions.

In any case, although Li Mu did not give them the most direct guidance, what is certain is that if they follow Li Mu's words, they will definitely be able to find certain clues.

"Thank you Professor, let's go and think about it again now."

After saying that, the three people returned to their positions and began to review all their previous steps.

Seeing the three people thinking, Li Mu shook his head slightly.

It feels like he was still a little bit weak before.

But their speed is really too slow.

He reluctantly pulled out a stack of scratch paper from the cabinet nearby.

It’s not like he hasn’t accomplished anything for so long.

The stack of draft paper in his hand was the result of what he had done during this period of time. \b

That is: reciprocal conjectures.

The reciprocal conjecture is that every Artin L-function from the finite-dimensional representation of the Galois group in a given number field is equal to an L-function from the automorphic cusp representation.

As an important issue in Langlands' program, the reciprocal conjecture is of great significance.

It describes the correspondence between number theory and representation theory. The most general guess is that Motive is equivalent to a considerable number of automorphic forms. In particular, it points out that Galois representation should be equivalent to the representation of algebraic groups, so the motive L function, etc. Valence is an automorphic L function.

The status of the reciprocity conjecture in Langlands' program is equivalent to that of the functority conjecture, and the two together constitute the two major parts of Langlands' program.

The Artin conjecture is contained in the reciprocal conjecture. (The previous article said that Artin’s conjecture is included in the functority conjecture, which is wrong. When I checked the information, I didn’t see clearly that there was a period in the middle==)

Of course, this does not mean that Li Mu has successfully proved the reciprocity conjecture, but he has completed most of the conjecture.

And in his current results, he can already prove Artin's conjecture through derivation.

In other words, Arting's conjecture has basically been proven by him. Now he only needs to write a few pages of derivation process and then publish it. The mathematical world will usher in the fact that another heavyweight conjecture has been solved. .

Of course, for Li Mu, proving Arting's conjecture was not in his plan. Directly proving the reciprocal conjecture was his goal.

I just hope that these three people can prove Artin's conjecture before he proves it.

He shook his head, looked at the time, and suddenly remembered that today was Yun Rongshang's graduation day, and he had to go and take a look.

So he stood up and told several students to continue studying with peace of mind, and then he went to Queen's College.

After arriving here, I saw several students wearing master's uniforms taking graduation photos, and Yun Rongshang was among them.

Yun Rongshang was holding a rolled-up diploma in her hand. Of course, such diplomas were just props and fake.

She smiled as she faced the cameraman, with the iconic building of Queen's College, a chapel, behind her.

Of course, at this time, she also noticed Li Mu's arrival, her eyes lit up, and her smile became more genuine.

"Cheese!"

As these master students shouted out together, the photographer gestured "OK".

"Wai Rui Rui Good, especially Miss Yun, you have a beautiful smile."

The photographers were from their college, so they all knew each other.

"Thank you."

Yun Rongshang nodded slightly and thanked her, but instead of coming together to see how the graduation photos went, she quickly walked up to Li Mu and said, "Here you are."

Li Mu nodded and said with a smile: "From today on, I will become a master."

"I'm not going to work for you from now on."

Yun Rongshang rolled her eyes.

Li Mu laughed and said: "Hey, you can't say that. If you have shares, then you will work for yourself."

"Hmph!" Yun Rongshang snorted softly.

At this time, everyone else also noticed Li Mu, and they also noticed Yun Rongshang.

Li Mu could clearly see that several of the boys had disappointed expressions in their eyes.

"Mr. Linus, can you take a photo for us too?"

Yun Rongshang shouted to the photographer.

"Okay, of course it's no problem." Photographer Linus said OK, then pointed the camera at the two people.

I took a few snaps, then selected the two photos that looked the best, and asked Linus to help develop the photos.

"After I get my degree certificate and graduation certificate, I will return to China, probably on the weekend of next week."

"Well, you might as well go back early. I have already made arrangements with the company. You can start working directly then. In addition, I will also send you information about the company later."

"Okay." Yun Rongshang nodded: "What about you?"

"Wait until I send the three students away." Li Mu said: "About that time, I will go to work at Sheshan Research Institute."

"Are you at work?" Yun Rongshang smiled: "You don't have a leader, I'm at work."

"There is always someone who can control me." Li Mu shrugged: "Who is not a tool?"

"Then...am I also your tool? I just help you manage the company?"

Li Mu hesitated, but just when he was about to answer, Yun Rongshang smiled again: "Well, if you can manage such a company, what's wrong with being a tool? I will be your tool. Willingly."

…

When Li Mu left Queen's College and returned to his office, what he saw was Tu Zhizhen and the other three looking excited.

"Yes, that's it!"

"In the case of R=Ok, we can completely regard Yuillen's group as a high-dimensional simulation of the Ok-like group - for n, and the unit group (Ok)."

"For fixed n, the reduction-induced group homomorphism of Ok primes at p: Kn(OK )-→ Kn(OK /p), for n = 1, can be easily identified by the graph (Ok)."

"After……"

"This is K-theory!"

"Then, we combined it with the elliptic curve method... Oh my God! We actually forgot about such an obvious result!"

"This is what the professor said originally! The elliptic curve in K-module theory!"

The three people held their heads in their hands, showing the surprise and helplessness in their hearts at this time.

"It seems that you have discovered the key point."

Li Mu's voice came from behind them, and the three of them turned to look at Li Mu.

Then they immediately cheered: "Yes, Professor, we have found the key to the problem!"

If Li Mu hadn't asked them to review the entire topic again today, they would probably never have imagined that the answer would be so obvious at the front.

After all, they knew from the beginning that the elliptic curve under the k-module theory originally proposed by Li Mu played a very important role in proving Artin's conjecture.

As a result, they have always been ignored. \b

"Then, I'm looking forward to your final results."

Li Mu said.

"Professor, don't worry! We are very sure now!"

The three young people patted their chests and said in unison.

Li Mu smiled and nodded, and then saw the three of them becoming energetic again.

He returned to his seat, and at this time, Yuan Siping suddenly came over, picked up a printed paper from his hand, and handed it to Li Mu.

"My thesis is finished."

Hearing his words, Li Mu was stunned, "You...finished?"

"Yes."

Yuan Siping nodded: "Of course, this is what I think. I need the professor to help me take a look at the details."

Li Mu raised his eyebrows, took Yuan Siping's paper, and started reading it from the beginning.

His guidance to Yuan Siping was the least among the four students.

And now, has Yuan Siping really completed it?

He looked at it for an hour.

Until the end, he said: "It's done well, although there are still some places that need to be fixed, but..."

"You have basically mastered the mysteries of this universe."

The role of dimensional force in the spontaneous symmetry breaking of the Higgs mechanism, a secret that occurs throughout the universe, is already known to Yuan Siping. \b

Yuan Siping's eyes suddenly widened.

"Really? I'm really done?"

Although he pretended to be calm just now, in fact, his heart was pounding all the time.

Finally, he got an exciting reply from Li Mu.

In order to study this topic, he spent a full year and a half, and now, he finally!

Want to say goodbye to this problem?

Li Mu smiled. He could understand Yuan Siping's excitement and said, "It's not 100% complete. There are still some small problems, but the overall idea is fine."

After receiving the affirmative answer, Yuan Siping suddenly became excited.

Small problems or whatever, it doesn't matter at all, as long as it's over now, that's a good thing!

Immediately, he howled in the office.

Looking at his appearance, Li Mu shook his head in amusement.

But now it seems that his students are almost finished with their results.

It seems that the time for their graduation is just around the corner.

Then, before he leaves here, let him also completely resolve the conflicting conjectures. \b

…

Time flies, and another three months have passed.

"The "Annals of Mathematics" has passed the review and has been officially accepted."

Alex and the three of them were lying on the sofa together, looking at the email sent by the editorial department of "Annals of Mathematics", and all three of them giggled.

On the other single sofa, Yuan Siping giggled alone, "Hehehehe, Physical Review Express...hehehehe..."

Looking at the appearance of these four people, Li Mu shook his head in confusion.

At this moment, there was a sudden loud knock on the office door, and finally, a bunch of people came in all at once.

They were all professors of mathematics at Oxford University, Andrew Wiles, standing at the front.

Donaldson was the first to speak: "Li! That paper you posted on arxiv...is it true?"

"Did you really prove the reciprocal conjecture?"

Faced with the questions from this group of people, Li Mu raised his hands and said, "Isn't the account that published that paper mine?"

A group of people suddenly took a breath of air.

real!

The mutually contradictory conjecture in one of the two parts of the Langlands Program was really figured out by Li Mu!

In the office, the four students looked confused.

What happened?

Conjecture against each other...?

The three people here, Tu Zhizhen, were immediately confused.

Is this the difference between their results and the professor's results?