Ultimate Scholar

Everyone present looked at Li Mu's very dull expression and didn't know what to say for a moment.

Oh my gosh, that's a reciprocal conjecture!

Although the reciprocity conjecture is not well-known among ordinary people, and has not been selected as one of the seven major mathematical problems of the millennium, its reputation in the entire mathematical community is not small at all.

After all, the Langlands Program is already well-known in the mathematics community. As a grand unified law in mathematics, its influence is no less than that of the seven major problems of the millennium.

As an important part of realizing one-half of Langlands' program, the significance of reciprocal conjecture cannot be overstated.

Everyone present looked at me and I looked at you. Finally, they all looked at Li Mu again, and then sighed: "You are still the same Li Mu!"

Who said that Li Mu had not made any achievements in nearly a year and was starting to fail?

It’s so funny, even though I haven’t achieved any results in nearly a year, now that I have achieved results, I will be a king.

Does reciprocal conjecture create any concepts?

This is half of the Langlands Program, and the other half is to prove the functority conjecture. Then the entire Langlands Program is completed, and their grand unified theory of mathematics is officially completed.

This kind of achievement can't help but make these mathematics professors marvel in their hearts.

And suddenly at this time, they also noticed the other four students in the office. At this time, they suddenly remembered that not long ago, three of Li Mu's four students completed Artin's conjecture, and the other He solved a hot issue in the theory of dimensional forces and demonstrated the relationship between the Higgs mechanism and the theory of dimensional forces, which caused a sensation in the physics community.

Farke.

Their students are all so awesome.

It’s really hard to compare people to death, and you have to throw away goods when comparing goods!

Regardless of how much help Li Mu gave to his students, it is already very commendable that his students dare to choose these topics as their directions.

And now that the paper has been completed, and the names of the authors are also the names of these students, what else is there to say?

Of course, word quickly spread throughout the academic community.

In other words, Li Mu's paper had just passed the review of arxiv. After it was published, the news was already known to many people.

No matter what, Li Mu's publication of a paper will always attract attention.

Last year, once Li Mu published a paper, people would wonder, what kind of paper did this genius publish that could shock the academic world?

But now, people would think, this super genius who is said to have been messing around for a year suddenly published a paper, what kind of paper will it be?

Then, there was a shock in the entire mathematical world.

On the mathoverflow forum, the atmosphere that was originally a little cold because there were no major events in the mathematics world suddenly became rekindled because of Li Mu's paper.

[Li Mu stated in his latest paper that he successfully proved the reciprocity conjecture. What do you think?]

The poster posted a post and started this topic.

Then, it naturally attracted a lot of people who wanted to eat melons. Of course, there were also some big guys hidden among the crowd.

For ordinary people who eat melons, this news has triggered all kinds of reveries.

【What do you think? How else can I watch it? I must sit down and watch it]

[I really defeated God. Didn’t it mean that Li Mu’s talent was exhausted after he won the Nobel Prize? What about the mutually contradictory conjecture that is suddenly proved now?】

[Exhausted talent? Do you really think talent can be exhausted? 】

【Why not? 】

[I can still believe it if other people will run out of talent, but for Li Mu... In short, we can bet that Li Mu is still secretly working on a big project! 】

[Tsk, isn’t reciprocal conjecture a big project? 】

[Maybe? 】

[Friends, I am taking a huge risk to tell you something. In fact, I traveled back from a hundred years later. In fact, Li Mu is an alien. His ultimate purpose is to lure aliens. After arriving on Earth, more than a hundred years later, aliens arrived. I used their time machine to travel back while they were not paying attention. You must! @##@#】

[Where are the brothers? Abducted by aliens? 】

[Tell me another dollar story, hurry up, I like to hear it. 】

[But let me tell you something, is Li Mu really not an alien? 】

[Some people also said that Einstein was an alien back then! 】

…

For ordinary melon-eating people, discussing whether Li Mu is an alien is probably the most interesting thing to them.

As for the big guys, they all discussed the mutually contradictory conjectures proved by Li Mu.

[Li Mu’s proof process is still as good as before. With such a perfect proof process, I really can’t find any possible problems. 】

【Who is not? I never expected that he could think of such a proof method. 】

[Perfect cohomology theory, perfect automorphic form, I simply can’t believe that he can combine the two so beautifully, but thinking about it, this is also the fundamental reason why he can prove the reciprocal conjecture. 】

[In his proof, the use of this part of the motive theory is also a masterpiece. I even doubt that he can prove Grothendieck's standard conjecture. 】

[Motive theory... When did he study the motivation theory so deeply? Is there anything else he doesn't know? 】

【……】

A Ph.D. student in mathematics at a well-known university looked at the names of these commentators. They were all big names in mathematics, which made him look shocked.

Good guy, Peter Schultz, Terence Tao, Wu Baozhu... Even the big boss Faltings is here.

But it happened that he understood what these big guys said word by word, but when they were connected, why did he feel like he was in a fog?

Is this how people from another class talk?

[Ah...what are the big guys talking about? I know that the motive theory is an important idea of ​​Grothendieck, but is there any application of this theory in Professor Li Mu's proof? Can you explain it to us weaklings? 】

[Weak chicken +1]

[Weak chicken +2]

…

There are still a lot of weaklings, although the worst among them are New York University mathematics undergraduates.

So in the end, Tao Zhexuan, who loves surfing the Internet the most, gave a simple summary.

[According to the generalization of the Langlands program on the theoretical framework of automorphic representation, when we find an appropriate generalization of the Dirichlet L-function, it will be possible to generalize Artin's reciprocity law. In the past, cohomology was a well-used method in this process, and in his proof of the reciprocity conjecture, Li Mu innovated a brand new cohomology calculation method - for the time being we can It's called Li's cohomology.

This Li's cohomology can be connected with the motive theory in thought. Of course, it can also be connected in application. However, it needs to be said that motive may be a theory that can combine "arithmetic" and "geometry" at a deep level. The existence of unification, so no one knows how far we are from it, but what we can know now is that Li Mu has probably got a glimpse of it.

These are the comments I can give roughly. The difficulty of Li Mu's paper is not low at all. I still need to read it carefully for a while before I can make a complete review. Therefore, everyone can just take a look at it. If If you can do some research on motivation theory, I believe your understanding will be deeper. 】

Following Tao Zhexuan's comments, it attracted comments from some people who know something about motivation theory.

For those who do not understand motivation theory, they also understand Tao Zhexuan's words from another perspective.

All in all, that is one word - difficult!

After all, even Tao Zhexuan thinks this paper is not low in difficulty. This is what the big guys who can usually deduce conclusions from other papers just read the abstract say, and this is even more true for ordinary students or scholars.

In this way, the discussion became more and more heated, and mathematics scholars all over the world were waiting for the final conclusion of the mathematics community.

Of course, as usual, Li Mu did not pay attention to the outside discussion and continued to do his things normally.

"Professor Li, thank you very much for trusting us in the Annals of Mathematics again and submitting your paper to us."

On the other side of the phone came the voice of Peter Sarnak, editor-in-chief of the Annals of Mathematics.

As for the reason why he specifically called Li Mu, it was naturally because Li Mu submitted this paper proving the reciprocity conjecture to their "Annals of Mathematics".

Li Mu smiled and said: "Okay, Professor Sanak, we are all old friends, so there is no need to say so many polite words."

"Haha, of course, I am also an editor-in-chief after all, so I should be more formal." Sanak said: "We will set up the most authoritative review team, which will include Deligne, Faltings, Schur Ci, Homosan and others, the review date will probably last about one to two months."

"Okay, of course that's no problem."

Li Mu said.

He was not surprised at all by such a review team. Of course, after submitting other papers before, he would usually form a high-level review team like this. Sometimes there would even be all Fields Medal winners. .

Without him, any paper submitted by him can be called "historical". As the journal to which the paper is submitted, the "Annals of Mathematics" must of course give a corresponding attitude.

He took a look at the review team. Needless to say, the first few names were all Fields Medal winners as usual. As for the one named Homosan, he should be a master figure in motive theory in the contemporary mathematics community. , although he did not win the Fields Medal, but in terms of motivation theory alone, this person is indeed considered authoritative.

In short, such a review team is indeed worthy of proof of mutual conjecture.

"But having said that, what I'm actually curious about now is that by suddenly submitting this paper to us, do you want us to post the paper by your students in advance?"

"Huh? What are you talking about? Why can't I understand?"

"Hey, stop pretending, it must be like this." Sanak said with a tone that saw through Li Mu: "You have proven the reciprocity conjecture, which is equivalent to proving Atin's conjecture by the way. "

"Then the paper by your three students that proved Artin's conjecture happened to be accepted by us, and the copyright agreement has been signed. In this way, their paper must be published before your paper. What? You are so calculating."

To put it bluntly, Sarnak has been the editor of the "Annals of Mathematics" for so many years and has never seen such an operation.

In order to get their students' papers published in journals as soon as possible, they ended up writing a more awesome paper, which forced them to publish their students' papers in journals in advance.

Seeing that he had been discovered, Li Mu chuckled and stopped pretending: "Actually, it was just a coincidence. They just proved Artin's conjecture, and I happened to prove the reciprocal conjecture. It's a coincidence."

"Yes, yes, it's a coincidence."

Sanak said angrily. Of course, he didn't say anything else. After all, what could he say? This was all about his strength.

"I would like to tell you by the way that we have also decided to put your student's paper in next month's issue. After all, Artin's conjecture is still very important, so you don't have to come up with such an amazing thing. matter."

Li Mu smiled and said, "I told you, it's all coincidence, it's all coincidence."

"Anyway, thank you. I would like to express my gratitude to you on behalf of my students."

"It doesn't matter, I won't say much more, I have to continue working."

"ok."

Then, they hung up the phone without saying anything more.

Li Mu smiled and shook his head. Calculating this way, he could apply for graduation for Alex and three others at the beginning of next month, and of course, Yuan Siping.

However, the publication frequency of "Physical Review Letters" submitted by Yuan Siping is much faster than that of "Annals of Mathematics". The former is a weekly, while the latter is bimonthly, and the former can publish more than ten or twenty papers in one issue. The latter can have five articles in one issue, which is considered unparalleled.

This is the difference between physics and mathematics.

Therefore, Yuan Siping’s paper will most likely have to be queued, but as long as it is confirmed to be accepted, the queue should be relatively faster.

Calculating the time, it is estimated that it will be published by the end of this month.

There is no need for him to write another article "On the Relationship between Dimensional Force Theory and Gauge Fields".

In this way, time passed again, and just as Li Mu expected, Yuan Siping's papers and the papers of three other people were published one after another.

Four students, two top journals, and in terms of results, it is not the kind that is barely enough to be in the top journals, but the kind of results that top journals will probably compete to invite submissions.

Suddenly, the four students of Li Mu all became famous in the academic world.

"Congratulations."

After walking into the office and looking at the four people who were celebrating each other, Li Mu smiled slightly and sent congratulations.

"professor!"

"Thank you Professor!"

All four people gathered around him, full of gratitude.

"This is what you deserve after your hard work." Li Mu waved his hand and said, "I also hope that you can continue to work hard in the future."

"I have applied for graduation for you, and your results have met my graduation requirements."

"In addition, as for where you want to go next, it only depends on your own wishes. I will not interfere. Of course, I also have gifts for you."

Then, he took out four letters from under the desk and handed them to four people.

"This is a letter of recommendation that I wrote for you. This letter of recommendation... I am not talking big words. It should be able to guarantee that you will go to any university in the world to continue your studies, unless it is a women's college."

The four people were stunned immediately.

This is...Li Mu's letter of recommendation!

Li Mu's words were not exaggerated at all.

Yes, this letter is a ticket for them to go to any university!