From Almighty Scholar to Chief Scientist

"Just call me by my first name."

"Hehe, we don't need to talk about these things. I didn't come to you to get entangled in such things." Professor Pompieri waved his hand.

"I have read the "Annual of Mathematics" in May this year. In "The Proof of the Fibonacci Sequence Existing Infinitely Many Prime Numbers", you solved the problem that I spent several months studying. So I'm here to thank you specifically for solving this regret for me!"

Lin Xiao couldn't help being stunned, so it was for that paper?

Isn't it just an "Annual Journal of Mathematics", dozens of papers are published every year...

Cough cough, this is a bit too much.

He smiled and said modestly: "It's just luck. Compared with you, this achievement is still insignificant."

"No, no, no, that's not insignificant. No matter how many people want to achieve your achievements." Professor Pompieri shook his head with a smile, and said, "Of course, if you just solve this problem, I will at most I will only express my gratitude to you in my heart, but the key is the method you used. I have considered it and studied it for a period of time, and I am very confident that this method can be successful. Professor Berger bet a dollar that I would make it, but after months of trying, it still didn't work."

"Well, you should know Professor Selberg, right?"

Lin Xiao nodded.

He wrote that paper, and of course he also had to know Professor Selberg.

Atle Selberg, a master in analytic number theory, was also the winner of the second Fields Medal in 1950. He completed the elementary proof of the prime number theorem, and Lin Xiao used the prime number theorem in his thesis .

Professor Pompieri said with a smile: "Now that you have succeeded, it can be regarded as making up for my regrets, and it also proves that the direction I chose was correct."

Lin Xiao knew that there was such a deep-seated reason, and he said with a smile: "It seems that you can win back that dollar now."

Pompieri waved his hand: "That probably won't work. In one month's time, he will be the 11th anniversary of his death. The bet happened more than 30 years ago. In addition, when the time comes, I will send you Printed out that paper, and then burned it to him that day—this seems to be a traditional custom in your country of China, but now the United States has also learned it."

Lin Xiao was taken aback for a moment, listening to Pompieri's words, he almost thought that Professor Selberg was still alive.

"Feel sorry."

Pompieri shook his head: "I'm not sorry, if I burn your paper to him, if he can receive it in heaven, I believe he will be happy too, because he also conducted research on this issue at the beginning, of course he Didn't make it either, lost $1 to me too, we owe neither of us."

"So that's the case."

Lin Xiao nodded, feeling rather interested in their bet.

When Professor Pompieri talked about this former friend, he seemed to be interested in it for a while, and then asked: "Do you know what method he wanted to use at the beginning?"

"What?" Lin Xiao asked curiously, of course he didn't know.

"Modular form theory! He expressed every prime number in the Fibonacci sequence, and then used lattices to represent these partially ordered sets, and then found the function of these lattices, and then he..."

Professor Pompieri said it like this, as if it was a familiar treasure.

However, what he didn't notice was that Lin Xiao fell into deep thought while listening to his words.

Modular formalism?

as a function of the lattice?

If he expresses the Mersenne primes in Mersenne numbers with lattices, wouldn't it be...

He had learned about this aspect of knowledge, and at this moment, he felt as if an inspiration burst out in his mind, but when he wanted to grasp this inspiration, the inspiration was fleeting.

This is also because his knowledge of modular formalism is not deep enough.

Modular form theory is a category of analytic number theory. He has learned about it in his own book, but there is not much ink on it in the book, so he still needs to know more.

At this moment, he had a faint guess in his heart that there was a key key, right here!

"Huh? Lin, what are you thinking?"

At this moment, seeing Lin Xiao's appearance, Professor Pompieri stopped his narration and asked.

Lin Xiao came back to his senses and said, "The modular form theory you mentioned has inspired my recent research."

"Oh? You are here to participate in the IMO competition, do you still have time to study other new things?" Professor Pompieri became interested, "What are you studying?"

"Now I have summarized the method in my paper, and then I want to use it to solve the problem of Mersenne prime number distribution, but I have encountered some difficulties, and now I need to continue to develop this method. The modular form you mentioned On, let me find a little direction."

"It turned out to be a Mersenne prime number?" Professor Pompieri was surprised, and then said with a smile: "Then I hope you can bring a little surprise to the mathematics world again."

"Oh, by the way, if you need to see Selberg's manuscript, I can send you a scanned version. His other manuscripts are stored in the Flint Library of Princeton University, but this part of the manuscript Because he didn’t get any results, he gave them to me before he died.”

Chapter 79 Look at the eyes of the gods

Hearing Pompieri's words, Lin Xiao couldn't help being surprised, there is such a good thing?

If you can see the manuscript of this master, I believe it will be of great help to his research.

However, he quickly thought that there was only one week left before his deadline, could Pompieri send the stuff in time?

He was not hopeful about this, but he still said truthfully: "Thank you for your kindness, but because the problem I am studying now is going to be used as a report at the International Congress of Mathematicians next month, and the International Congress of Mathematicians The deadline given to me is July 7th, which means that I have to submit the paper before next Sunday, so if I can’t get it done before July 15th, I can only omit this part The content is reported directly.”

Hearing Lin Xiao's words, Pompieri was very surprised: "You said you also received a report invitation from the International Congress of Mathematicians?"

"Yes." Lin Xiao nodded, "Because in the 45-minute report, a speaker who was also in the field of number theory could not be present, and then the International Mathematical Union contacted me, hoping that I could make up for it. Due to time constraints, they allowed I have until July 7 to file the report."

"So this is ah."

Professor Pompieri couldn't help giving Lin Xiao a thumbs up.

To be able to give a report at the International Congress of Mathematicians at such a young age, even he, a Fields Medal winner, has to be called a 'genius'.

Then he said, "Well then, give me your email address, and I'll ask my colleagues from the institute to help, and I'll send you the picture of Professor Selberg's manuscript."

Lin Xiao was overjoyed: "Thank you so much!"

"Hehe, being able to help a young mathematician solve a problem is a waste of time that an old guy like me can use." Professor Pompieri waved his hand and said with emotion: "Ah, Mersenne prime numbers, the time I spent studying them, It is longer than the prime numbers in the Fibonacci sequence, but unfortunately there is still no achievement, and in the end it can only play a role in the Bernstein problem."

"Bernstein problem?" Lin Xiao was stunned for a moment, "You are the professor Enrique who solved this problem?"

Seeing Lin Xiao's appearance, Enrique Pompieri couldn't help but smiled and said, "Didn't you recognize me before?"

Lin Xiao touched his nose in embarrassment. When he first learned differential geometry, he saw about the Bernstein problem and knew that the person who finally solved this problem was called Enrique Pompieri, but he only remembered I remembered the first three words 'Enrique', but I didn't remember the latter.

At this time, he heard Pompieri mention it, and he remembered it.

"Uh... sorry, I really didn't recognize it before."

"Haha, it's nothing. I didn't think I just won a Fields Medal, so it is necessary for everyone to know me. In fact, when I knew you were in the Huaguo team at IMO, I took a special look at you I didn’t recognize you when I stood in front of you just now, so even if you have seen my photo before, it’s probably hard to recognize me.” Pompieri waved his hand and smiled, not paying attention It's a little thing.

When people of different races look at each other, they will basically have face blindness.

"That's true." Lin Xiao also laughed.

"Okay, I won't say much else, the opening ceremony will start soon, please leave me your mailbox." Pompieri said.

"Ok."

Then Lin Xiao told Pompieri his email address, and Pompieri wrote it down on his mobile phone, and then said: "Well, I am very happy to chat with you. I seem to see the image of a young mathematics master in your body." Shadow, I hope you can always maintain this interest in mathematics in the future, and if possible, I also hope to see you at the Institute for Advanced Study in Princeton."

"That's where I work. Although I've been retired for ten years, I've always been there. It's a good place to retire. I was traveling in Europe recently, and I happened to be invited by IMO, so I came here. "

"Princeton?" After Lin Xiao heard this, it can be said to be a world-renowned research holy place for mathematics and theoretical physics.

The Institute for Advanced Study in Princeton, where Einstein worked after he immigrated to the United States, died in Princeton when he died.

Another example is Yang Zhenning, Chen Shiingshen, and Li Zhengdao, who were born in China, and they are all professors at the Institute for Advanced Study in Princeton.

Even now, the Institute for Advanced Study in Princeton is one of the institutions with the largest number of Fields Medal winners.

As for the Princeton University next door, although it is not the same institution as the Princeton Institute for Advanced Study, they are too close after all. It is obviously bullshit to say that they have nothing to do with each other. One of the famous universities.

Lin Xiao then said: "If there is a chance, I will definitely go there and have a look."

"Just to take a look?" Professor Pompieri smiled, then turned and left without further words.

Lin Xiao was baffled by Pompieri's last words.

Why don't you go and see?

Could it be that you still let me stay there?

Lin Xiao shook his head. He still hadn't made up his mind on whether to study abroad in the future.

Seeing Professor Pompieri walking away, he stopped thinking about it and turned around to return to his seat.

It's just that at this moment, he suddenly felt that something was wrong with the eyes around him.

He turned his head and saw a group of people around him looking at him, whether it was a few members of their Hua Guo team, or people from other national teams.

The look in their eyes reminded Lin Xiao of the way the trainee researchers he met on the road looked at him when he was at the Chinese Academy of Sciences.

Probably... looking at the eyes of the gods?

"Uh, did you speak a little louder to Professor Pompieri just now?"

He couldn't help but think so.

In fact, although the voice of their conversation is not particularly loud, people around can definitely hear it. The most important thing is that a Fields Medal winner is standing in front of them, and they have no choice but to pay attention.

In particular, this Fields Medalist actually took the initiative to talk to a young player from the Hua Guo team. Among the surrounding national teams, there are inevitably some from English-speaking regions, including the American team.

So they naturally heard what Pompieri and Lin Xiao had said.

And they all knew that the Huaguo player who came to participate in the IMO competition with them, probably just like that, had already published a paper in the "Annual Journal of Mathematics".

This had to shock the members of these other national teams.

Such a math genius appeared in Huaguo?

They just couldn't believe it.

Let’s not talk about those students, even those team leaders, no one has published the "Annual of Mathematics", otherwise, if they can publish "Annual of Mathematics" or any of the four top journals, they will come to be the team leader ?

I have already gone to work as a professor with peace of mind to do research in the field of mathematics.

Chapter 80 Exam Preparation

As for those foreign contestants, they couldn't help casting envious and admiring glances at Lin Xiao. They were able to talk to the Fields Medal winner, and even got praise from the Fields Medal winner.

Including, at the end, Professor Pompieri actually invited Lin Xiao to the Institute for Advanced Study in Princeton. In the eyes of these foreign students, it was simply a great honor, especially for these mathematics lovers.

In the American team not far away, the team leader glanced back at his six players. Among the six American players, four of them were of Chinese descent, and they looked at Lin Xiao with envy.

The team leader reminded: "You don't have to be envious. If you pass the test in the next two days and get the gold medal, you can also go directly to Princeton University to study, and you will be able to see all kinds of Fields Medal winners at that time. , After you get a master’s or a doctor’s degree, with the IMO gold medal, you have a good chance even if you apply to be a student of the Fields Medal winner.”

Hearing the leader's words, the six students all nodded, but no matter what, they were still envious.

If you have won the IMO gold medal, you still have to apply. At that time, you have to see if the Fields Medalist agrees. But look at the student from Huaguo, Professor Pompieri came to him on his own initiative.

Also, the International Congress of Mathematicians invites others to give reports. What is the International Congress of Mathematicians?

That is a place where big shots gather, and it must be such a glorious thing to be able to give a report in that kind of place.

One contestant couldn't help asking: "Professor Daisy, did you give a report at the International Congress of Mathematicians?"

Their team leader, Professor Dais, froze and said, "Don't ask so many questions, just watch the opening ceremony carefully."

The player rolled his eyes. It seemed that their team leader didn't have the ability either.

Of course, not only the players of the US team were envious of Lin Xiao, but also some other national teams, and their team leaders also encouraged them by saying that as long as they won the IMO gold medal, they could choose any university in the world.

But no matter what, the team leaders kept their players calm, but they were actually envious of Lin Xiaoneng's presentation at the International Congress of Mathematicians.

It's a pity, envy can't come.

……

Under the eyes of the surroundings, Lin Xiao sat back in his seat.

"Lin Shen, you drink water, you must be thirsty after talking so much just now?"

Sun Yu directly handed over a bottle of water and said courteously.

"My Zhuo, Lin Shen, why is your English so 6?! What did you say to that boss just now?"

"Lin Shen, how did you learn English?"

Several people were shocked. Lin Xiao was able to have a conversation with a foreigner in English just now, and it seemed that the conversation was about mathematics, which surprised them again.

As for what they were talking about, they didn't know, otherwise they would definitely not have asked. Wasn't that someone who was idle and had nothing to do, looking for a blow on purpose?

After hearing the questions of these guys, Lin Xiao thought about it for a while, and it seemed to be so.

When he talked with Pompieri just now, it was very natural to chat in English, and he could fully understand what Pompieri said.

Even if he can understand those mathematical proper nouns, this is also related to his recent special study. After all, sometimes he reads foreign papers, because they are downloaded as PDF files, and it is troublesome to translate them into Chinese. He basically reads them directly. English original.

And reading English papers has also improved his English level, coupled with the development of his brain, there is no problem in English conversation.