From Almighty Scholar to Chief Scientist

This seems to be number theory, but it's not like number theory. There are some homomorphic group structures in it, and there seems to be a bit of modular form theory in it. Could it be someone who studies the Langlands program?

The Princeton University mathematics doctoral student gave up thinking and chose to make coffee for the professor honestly.

In this way, time passed slowly.

The paper of more than 70 pages is of course very long. Although the first dozen pages are relatively easy to understand and can be read quickly, the middle 40 pages are not so easy, because a new mathematical method has been involved. So Professor Sanak has to be serious about it.

The east coast wind blew from daytime to evening, until the sun disappeared west of Princeton, a city full of rural scenery, in the office, Professor Sarnak finally raised his head.

"Probably, Gauss was also so amazing at the beginning..."

He sighed slightly. From this paper, he saw the thoughts of great mathematicians burst out in it, as if the truth was conceived in it.

For all famous scientists in history, the most important achievements in their lives were made between the ages of 20 and 40, such as Einstein's theory of relativity, Newton's calculus, the law of universal gravitation and so on.

And this Lin Xiao, who is only 18 years old now, has already created such an excellent mathematical theory and put an end to the problem of the distribution of Mersenne prime numbers.

Since Euclid, the father of geometry, began to study this problem 300 years ago, until now I don’t know how many great mathematicians have continued to try to achieve breakthroughs in the extremely simple form of 2^p-1. , until now, the final result has finally been completed in the hands of this young man.

If it is said that this is Lin Xiao's peak period, Professor Sanak naturally does not believe it.

If he used the normal distribution image as an example, he believed that Lin Xiao's state at this time was somewhere on the left side of the image, and there was still a long distance from the highest position.

However, this is just what he thinks. As for whether Lin Xiao is really a normal distribution image, or y=x^2 (x>0), it is unknown.

Chapter 95 Two Filipino Award Winners and One War Award Winner's Amazement

After feeling emotional for an unknown amount of time, Professor Peter Sarnak finally looked at the end of the thesis again.

"Huh? By the way, did you prove Zhou's conjecture?"

Seeing the contents of the last two pages of Lin Xiao, Sanak raised his eyebrows and couldn't help feeling a little bit.

Zhou's conjecture is also a well-known problem in the study of Mersenne prime numbers.

However, due to the large value range of Zhou's conjecture, the research on the distribution of Mersenne prime numbers cannot provide much help, because Zhou's conjecture predicts the total number of all prime numbers of Mersenne numbers before a certain item, Therefore, in the Internet Mersenne prime search plan, Zhou's conjecture was not used, but the Lucas-Lehmer test method was used, and the fast Fourier transform was used before this method.

However, these two methods only use the characteristics of computers, that is, the ability of computers to perform repetitive work, so as to continuously calculate to larger numbers. However, due to the greater randomness of this method, so often Some slip through the cracks.

But now it seems that the Internet Mersenne prime number search project is coming to an end.

Sarnak sighed with emotion, feeling a sense of relief in his heart, and I believe that every mathematician who has studied Mersenne prime numbers will have this feeling, because a mountain in the mathematics world has finally been overcome by them.

With this kind of achievement, it’s no wonder that Lin Xiao didn’t submit the report until now. Professor Sanak even started to think at this time, when did Lin Xiao start researching this topic? It started at the time of the last report, which is really amazing.

While he was thinking in his mind, his phone rang suddenly, and he looked at the caller, it was Professor Pierre Deligne's phone.

"Professor Deligne should have read it too."

Professor Sanak smiled.

Although Professor Deligne does not mainly study the field of number theory like him, as a mathematician who has won the Fields Medal, Abel Prize, Wolf Prize, Craford Prize and other mathematicians, take a look at this It's also perfectly fine.

So looking at the time, Professor Deligne should have finished watching it at this time.

I just don't know what Deligne thinks, at least after reading it himself, he didn't find any problems. The whole argumentation process was very rigorous, and he couldn't find any faults at all.

So he connected the phone, and he smiled and said, "Professor Deligne, how is it?"

"Who wrote this paper?"

"Lin Xiao, didn't you read the name?"

"I read it, but, do you know that Professor Pompieri has such a student? Professor Pompieri and I are both retired. He should have no students, right? Let alone a student from Huaguo."

Professor Sanak was taken aback: "Professor Pompieri? Isn't he traveling in Europe now? Why did you mention him again?"

"In the acknowledgments at the end of the paper, this Lin Xiao expressed his gratitude to Professor Pompieri. Professor Pompieri provided him with the manuscript of Professor Atle Selberg. I said why his paper contains Part of it felt familiar to me, and I’d heard him bring it up in previous discussions with Selberg.”

Sarnak couldn't help being stunned. How did Lin Xiao meet Professor Pompieri again?

One is in Europe and the other is in East Asia. Could it be that Professor Pompieri has also contacted Lin Xiao?

"I do not know."

That's all he could answer.

In the end, the two professors made up their minds and decided to ask Professor Pompieri directly, so they made a conference call to Pompieri.

After Pompieri knew their purpose of coming, he was not only surprised, but also quite surprised.

"When I was traveling in Europe, I was invited by the IMO to go to Romania. After arriving there, I accidentally learned that Lin Xiao was among the players of the Huaguo team. It happened that his Fibonacci I have also read the paper on the deed sequence, and I am very interested, so I went to get to know it."

"...he talked about his recent research problem, so I provided a little help. By the way, you said...he successfully determined the distribution law of Mersenne prime numbers?"

Hearing Professor Pompieri's statement, both Sarnac and Deligne felt that it was such a coincidence.

"Yes, if I read correctly, his new group transformation method can already predict the distribution of Mersenne prime numbers, and I can guarantee that those who study the Langlands program will also be surprised. Group theory , modular form, and the prime number problem, oh, I seem to feel that the topic I studied about the L function before can also be used... All in all, with this achievement, even if I go to the International Conference of Mathematicians in August to do a Hourly reports are fine, but it's too late now."

Professor Deligne said with emotion.

Professor Sanak said: "He did not receive an invitation for a one-hour report, but he received an invitation for a 45-minute report in the field of number theory, and this paper is exactly what he plans to report later."

"This..." Professor Deligne was surprised again.

In the end, he could only sigh with emotion: "If he was studying at IAS, I would want him to be my student."

Sanak: "No, you don't want to, you have to let him finish his master's and doctoral degree with me first, and then your IAS will not recruit a student who has not graduated from graduate school, and you are all retired."

"I can re-employ after I retire. I am a lifelong researcher of IAS, even after I retire."

Hearing Professor Deligne's ostentatious words, Sanak was helpless.

You are a boss, you can't afford to be provoked.

The tenured fellowship of the Princeton Institute for Advanced Study is one of the most famous honors in the academic world. There are very few professors who can get this seat, and Professor Deligne is one of them. Even Sanak will feel envious.

"Okay, let's go here first."

Seeing that there was nothing to say, Professor Pompieri said, "It seems that I also have to prepare and set off for Rio de Janeiro."

Deligne also said: "I also look forward to that day."

At this time, Professor Sanak thought of Professor Wiana again, and he still wanted to inform Professor Wiana of the results.

Since Professor Deligne has approved it, and he has not found any mistakes, it is basically certain that there is no problem. Of course, during this period of time, he probably needs to read this paper a few more times to confirm repeatedly. This is an important achievement, no matter how rigorous it is, he will also find other professors in the field of number theory at the Mathematicians Conference to have a look at it. Similarly, this is also to help Lin Xiao publicize it.

Maybe, this simple 45-minute report will trigger a shock no less than a one-hour report?

Professor Sanak is also not sure.

So, after the three experts in mathematics bid farewell to each other, they closed the conference video.

Chapter 96 Look at Your Trophies

A passenger plane that took off from Romania and headed for Huaguo Shangjing flew across the boundless sky, finally entered the airspace of Huaguo, and was getting closer and closer to its destination.

On the plane, all the passengers were chatting about their own affairs, waiting to arrive.

"Lin Shen, can I see your trophy?"

Lin Xiao said angrily: "Get out, how many times is it?"

This group of guys have been saying this to him from time to time since he won the special award trophy. At first, he thought it was nothing, but after thinking about it later, he realized what these people were talking about.

"Can't you keep me simple and handsome?"

Several other people rolled their eyes, "Ah, yes, yes."

Lin Xiao shook his head, this group of people still refuse to listen to repeated teachings.

Sure enough, he can only appreciate things like being handsome alone.

At this time, Chen Qiusheng who was next to him suddenly took out a few banknotes from his pocket and handed them to Lin Xiao.

Lin Xiao took a look. He didn't recognize any of these banknotes, and he didn't know which country they belonged to. Oh, he knew a dollar bill. After watching so many American movies, of course he had to recognize it.

He asked without doubt: "This is?"

Chen Qiusheng smiled: "Didn't I say that? During the exam the next day, I will make a bet with the deputy team leaders from other countries. I will bet on whether you can come out an hour earlier. Several team leaders bet with me. The bet was two one-dollar bills from their own country, and I won, so we split half and half."

Lin Xiao couldn't help crying and laughing, you really gambled with others.

However, the bet was not too high, it was probably purely for the entertainment of these deputy leaders when they were bored.

After that, he didn't refuse, took the banknotes and glanced at them. There were five banknotes in total, which meant that five deputy team leaders bet with Chen Qiusheng.

"Here, here's the dollar, this is the pound, this is the ruble, and Singaporean and Romanian money."

Lin Xiao nodded, he is now considered to be a foreign exchange holder.

Putting the five banknotes into his pocket, he then looked back at the computer in front of him, and it was his paper that was displayed on the screen.

Reading your thesis, in addition to checking if there are any problems or mistakes, it is also for reviewing the past and learning the new.

At this time, what he was thinking about was the new method in his thesis.

Group theory, modular form theory, number theory...

The combination of these things easily reminded him of one thing, which was the Langlands Program.

The simplest understanding of the Langlands program is that it is a set of conjectures that point to three relatively independently developed branches of mathematics: number theory, algebraic geometry, and group representation theory, which are actually closely related.

If it is more complicated, all good Euler products of n times are all automorphic L functions of GLn.

Research on this grand unified theory of mathematics is not uncommon in the entire mathematics community. Once the proof of the entire Langlands Program is completed, it means that we can link it to several once completely independent Theory is used as a thing.

This is obviously of great significance to the entire mathematics community, just like the grand unified theory in physics, which unifies quantum mechanics and general relativity.

Both of these two grand unified theories mean further access to the truth of the universe.

Although the Grand Unified Theory in mathematics is mere scribbles, it is difficult for ordinary people to know the use of those Arabic numerals, strange symbols, and the arrangement and combination of gaudy Greek letters, but even if these mathematics are useless, they are It will be used in the field of application at a certain time. Who knows whether the Langlands program will have an effect on the grand unified theory of physics once it is unified?

Of course, Lin Xiao did not pay so much attention to algebraic geometry. He only limited himself to a textbook he read at the beginning, and did not conduct in-depth research, but his "Lin's group transformation theory" - he decided to use this The theory is named 'Lin's group transformation theory' because the range of the group is larger than the modular form.

And his theory, unknowingly, solved a problem in a certain subdivision of the Langlands program.

"Express this group matrix, and then deal with it in this simple way..."

Lin Xiao remembered the lecture he had attended at the Institute of Mathematics of the Chinese Academy of Sciences.

"The law of quadratic reciprocity?"

He briefly ran it through his head, and finally shook his head, not getting anything of value.

However, at this moment, a stewardess came over and said to him: "Sir, the plane is about to land, please put away your computer and small table to avoid accidents."

Hearing what the stewardess said, Lin Xiao nodded, turned off his computer, put it in his bag, and packed it up. He stopped thinking about these problems, let his mind go, and prepared to land.

About half an hour later, the plane landed smoothly, Lin Xiao and the others got off the plane quickly, took the suitcases, and went straight out of the lobby.

But when they arrived at the gate of the pick-up hall, they saw a surprised scene.

I saw a group of people standing in the hall, holding red flags in their hands, and a few banners by the way, which read "Congratulations to the IMO Huaguo team for winning the first place in the team!", "Welcome the IMO champion team home!", "The boy is wearing the red flag and returning home for the glory of the country!"

Obviously, these people are here to greet them.

"Damn it, why are there so many people?"

Sun Yu exclaimed.

"There are still a lot of reporters there, what the hell!"

Li Huaimin, who was walking beside him, said with a smile, "We are all here to welcome you. You are our heroes."

Hearing Li Huaimin's words, the exhaustion of the teenagers after sitting on the plane for so long was instantly swept away, and a sense of honor rose in their hearts.

Can they be called the young heroes of the motherland now?

Probably ok.

Lin Xiao also showed a smile on his face. No matter what, in the face of this kind of recognition, I believe there are not many people who can not be happy about it.

Then, they walked into the reception hall together, and the group of people quickly recognized them, and all rushed towards them immediately.

And the person who rushed to the front was Gong Zhou, the secretary-general of Huaguo Mathematical Society.

He came to Lin Xiao and the others with a smile, opened his hands, and said loudly, "Welcome everyone home!"

Afterwards, Lin Xiao and the others were submerged in the crowd. The people who came to greet them took the initiative to take the luggage of each of them, and then greeted each other in various ways.

Especially here at Lin Xiao, as the winner of the special award, of course he received the most attention, and several beautiful young ladies smiled at him.

"Student Lin, you've worked hard!"