The top student must be diligent

"Perfect!"

"It's so perfect!"

As a mathematician who regards number theory as his lifelong pursuit, James Maynard is very happy to see any great achievements in number theory.

Even though it was not something he had researched, it still made him happy.

Suddenly, the anger he felt towards Xiao Yi for playing Fermat's tricks two days ago was calmed down at this moment.

For the sake of these two papers that impressed me so much——

Of course I forgive him!

With excitement in his heart, he immediately took out his mobile phone and called one of his seniors in research and his good friend, Terence Tao.

Terence Tao.

Soon, the call came through.

As a result, just when he was about to speak, Tao Zhexuan across from him spoke first.

"Hey! James, have you read Xiao Yi's two papers?"

“I really can’t believe that a problem we have been studying for so long was suddenly solved like this!”

"There is also the theory in the first paper that combines far Abelian geometry and automorphic forms. Well... In the paper, Xiao Yi named this theory [the automorphic theory of etale algebraic varieties]. This theory I After looking at it for a while, you can be surprised to find that the polymath project we once worked on will be able to achieve a breakthrough directly! ”

"The only regret is that Xiao Yi has already proved the Elliott-Halberstam conjecture, and he directly solved the prime number gap problem into 6..."

"Ha, this can't be said to be a pity, it should be said to be a good thing!"

"besides……"

Just when Terence Tao wanted to continue speaking, he suddenly realized something and asked, "James, why don't you speak?"

James Maynard suddenly said helplessly: "You have always been the one talking, how can I speak?"

"Ah ha ha ha~" Terence Tao laughed awkwardly, and then said: "Okay, okay, you say it first, you say it first."

Maynard said helplessly again: "But you have already finished what I want to say."

"Ah..." Tao Zhexuan paused for a moment, and finally asked: "Then how about...you continue to listen to me?"

"Okay, keep talking." Maynard sighed.

Tao Zhexuan was not polite and started talking immediately: "Also, using the etale algebraic variety automorphic theory, maybe we can make more achievements on prime number problems, such as the x^2+1 prime number problem superior."

Maynard: "Why not consider twin primes? Now we are within 4 of the final answer."

"Hmm... Because I thought about it briefly, and the final conclusion I can draw is that the limit that Etale's algebraic variety automorphic theory can achieve is 6. If you want to go further to [less than 3], maybe Still need to think of other angles.”

"So, we might as well study the application of this theory in other aspects!"

"That's the real shame."

Although it is a pity that the twin prime conjecture cannot be further directly proved.

But the undeniable fact is -

This jewel in the crown of number theory has been officially pushed to the number 6 thanks to Xiao Yi's achievement!

…

The influence of the two papers continues to grow. More and more mathematicians have read them, and more and more mathematicians have expressed great recognition of them.

Some mathematicians are even beginning to believe that these two papers can be regarded as one of the biggest breakthroughs in mathematics this year, and "Science" should include this matter in the selection at the end of the year.

There are still quite a few mathematicians who agree with this point of view, and there is no objection at all. Even IHES editor-in-chief Bergeron also stood up and said that when "Science" begins to select the top ten most important breakthroughs in the scientific community this year, he will definitely I will vote for [Etale algebraic variety automorphic theory].

Of course, there are quite a few mathematicians who are making a fortune in silence.

These mathematicians are looking forward to Xiao Yi's two papers because Xiao Yi's theory will help them achieve major breakthroughs in their own projects, or even complete them directly!

Chapter 88 salute!

Princeton University, in a laboratory belonging to graduate students in the Department of Mathematics.

"Ahahaha, I'm done! I'm done!"

At a certain workstation, someone suddenly threw away the pen in his hand, picked up the draft paper on the table, waved it, and shouted excitedly.

For a moment, the other graduate students in the laboratory looked sideways at this person.

Could it be that he is another person who went crazy studying mathematics?

Then I took a closer look and realized, well, this person is the PhD senior brother of their laboratory, a Chinese named Wen Chenghua.

Their senior brother has been studying for a doctorate for four years, but has not yet graduated because his doctoral thesis was not completed.

Of course, for a PhD student in mathematics, it is not too late to study for four years, but who doesn’t want to graduate this morning?

"Wen, what are you so excited about? Calm down!"

Their mentor, Andrei Okunkov, was also in the laboratory at this time, sitting at the front, studying his things.

Compared to other professors who may prefer to sit in the office, Okunkov prefers to sit in the same laboratory with his students, so that his students can ask him anytime if they have any questions.

Of course, it is also convenient for him to supervise his students to see if they are studying seriously.

Hearing the tutor's reprimand, Wen Chenghua immediately shrank his head and apologized quickly, "Sorry, professor, I was wrong."

Their tutor from Russia has a very bad temper. Once their students make any mistakes, no matter whether they are big or small, or academic or in their daily performance, they will be severely criticized, so they are all afraid of this tutor.

However, the other party's ability and the help they provide to them academically also make them have to respect this tutor.

After all, Okunkov is the winner of the Fields Medal in 2006. It is their luck to be a student of a Fields Medal winner.

Although he kept quiet, Wen Chenghua still brought his draft paper to his tutor and said, "Professor, I have finished that problem!"

Okunkov frowned, "That problem? It is about the p-entry Galois representation problem of non-Archimedean local domain under residual feature p?"

Wen Chenghua was surprised that his professor could still remember the problem he had just told him a few months ago, and then he nodded, "Yes, professor! I have solved it!"

"Are you kidding?"

Seeing his eldest disciple's happy look, Okunkov raised his eyebrows and was a little surprised. He was very clear about the difficulty of this problem, otherwise it would not have stuck his student for so long.

He remembered that Wen Chenghua's thesis topic was the observability of Galois representation, which involved the second part of the Tate conjecture. It can be said to be a very difficult problem, even no less than what most mathematics professors are studying.

If this problem is solved, it will be able to achieve more refined results of previous research, which will play a particularly important role for any scholar who is studying this aspect.

Well, in short, there is a chance to publish in the four major journals, although it may take a long time to wait in line, but it is definitely more than enough to publish in the second-tier journals.

But obviously, it is very difficult.

The problem that Wen Chenghua was stuck on before was the problem of Galvaro representation in p-adic Hodge theory.

This problem has not been solved by Okunkov himself yet, otherwise Wen Chenghua would not have been stuck for so long.

Surprised, Okunkov said: "Show me how to solve it."

"Okay!"

Hearing the tutor's question, Wen Chenghua immediately straightened his chest, then walked to the blackboard and started writing.

Soon, Okunkov was surprised: "Wait! What method are you using here? Could it be that Yi Xiao came up with the theory of self-restraint of etale algebraic clusters?"

"Professor, you also know it?" Wen Chenghua said in surprise.

"Are you kidding? You know it, how can I not know it?" Okunkov glared at him, "I am studying this thing recently."

Wen Chenghua immediately realized that he had said the wrong thing.

However, Okunkov did not say much, and then said: "Don't stop, keep writing, I also want to know how much this theory can play a role."

"Okay, professor!"

Wen Chenghua nodded quickly, and then continued to write on the blackboard.

Soon, with the help of Xiao Yi's etale algebraic cluster automorphism theory, this problem that had stumped him and Okunkov, the Fields Medal winner, for a long time was easily solved.

This means that Wen Chenghua's graduation thesis finally has a destination, and it is a top journal-level paper. He has become the first batch of the biggest beneficiaries after the birth of Xiao Yi's etale algebraic cluster automorphism theory.

Even at the end, Okunkov took the initiative to ask Wen Chenghua about some things about this theory. Even though he is Wen Chenghua's mentor and a Fields Medal winner, due to subtle differences in research directions, he may sometimes need to ask his students some questions that he may not understand yet.

This is also the characteristic of the discipline of mathematics.

For a moment, Wen Chenghua seemed to be able to feel the admiring gazes from his juniors.

He was so good!

That night, after returning to the dormitory, Wen Chenghua, whose graduation thesis was no longer a problem, lay down on the bed with ease, opened his mobile phone, and browsed the foreign version of Quora.

He clicked in and saw a problem in the field of mathematics recommended to him.

[In his two recent papers, the Chinese mathematical genius Xiao Yi created a theory called etale algebraic variety self-restraint. What role does this theory play in mathematics? ]

There are already more than 20 people who have answered this question. When Wen Chenghua clicked on it, he was surprised to find that the great god Terence Tao also appeared among the respondents.

[This theory has many uses! On the positive side, it is of great help to us in any number theory problem. In fact, I am now planning to discuss the x^2+1 prime number problem with J. Maynard.

Looking back, we will be able to use the method of automorphic form and trace formula to study any problem related to the Etale fundamental group, and thus extend it to all aspects of algebraic geometry, such as p-adic Hodge theory, Tate conjecture, and of course, far Abelian geometry. Maybe Shinichi Mochizuki will also generate more inspiration on the ABC conjecture after reading Xiao Yi's paper? 】

Seeing this comment from Terence Tao, Wen Chenghua was immediately amazed in his heart. He is really a great god. He can see at a glance that this theory can play a role in the Tate conjecture.

Looking at other comments, there are many doctors and professors from various prestigious universities, all of whom have expressed great recognition of the Etale algebraic variety automorphism theory.