From Almighty Scholar to Chief Scientist

Soon, George Eagle looked at Lin Xiao's answer, from the first question to the third question.

As the chairman of IMO, he is naturally familiar with these questions, and can easily understand the problem-solving process of these contestants.

As for the first two questions, Lin Xiao's answers were brilliant, and the methods he used caught his eye. But when he saw the process of Lin Xiao introducing Euler's formula in the third question, he couldn't help applauding. stand up.

"It's amazing!"

This question was the one he posed, and he never thought that such a combination question of his own could be solved by using Euler's formula, and even after it was inserted, the whole question could be simplified to such an extent.

It's really... wonderful!

And the beauty of mathematics is also reflected here, just like the beauty of Euler's formula, e^(iπ)+1=0, concise and amazing, linking symbols of three different dimensions together, so that its Known as the 'God's Formula'.

George Eagle felt an inexplicable joy in his heart at this time, probably because the problem he posed could be solved with this solution, which made him happy, and another reason was that he was happy for the wonder of mathematics. .

"Chairman, what's the matter?"

At this time, the people next to him couldn't see the answer sheet, so they couldn't help being curious when they saw the chairman like this.

But George Iger just smiled, then closed the answer sheet, handed it to the staff next to him, asked him to take it back, and put it away with other students' answer sheets later, then turned back and said to these people: "Don't read it, you should read it the day after tomorrow when the test papers are corrected."

The others were speechless, are you too old?

George Iger smiled without explanation.

He didn't intend to share such joy, but enjoyed it alone for two days.

In addition, he is also planning to surprise Lin Xiao later.

……

Time passes quickly.

The first day of the exam was over, the contestants returned to the hotel, and then they started to answer the questions. When they found out that they were wrong, they were naturally annoyed, but when everyone was right, everyone was happy.

Of course, the Huaguo team is also the same. In addition to expressing their sincere admiration for Lin Xiao's miracle of handing in the test in more than 40 minutes, Sun Yu and the others also compared with Lin Xiao.

After comparison, the first two questions were in good condition, but they all had more or less problems with the third question, so Ouyang Sheng and Sun Yu felt good.

And Chen Qiusheng also approached Lin Xiao, and asked him directly why he handed in the result so early in advance. Lin Xiao just said, Lin Xiao naturally told the truth, he finished writing everything, why did he stay there?

"Then you continue to behave like this tomorrow, and then I will make a bet with the other deputy team leaders on whether you can continue to write all the questions within an hour tomorrow, and we will win half and half of the winning money."

In the examination room the next day, Lin Xiao recalled what Chen Qiusheng said yesterday. At this time, he had already completed the last geometry problem in minutes. He smiled and shook his head, not knowing that the deputy team leader Did you win any money.

Then, he held up the sign again, and waited for the staff to come over, telling him that he had to hand in the test paper.

Next, he once again left the examination room under everyone's attention.

And this also means that this IMO is completely over for Yu Lin Xiao.

Chapter 85 IMU and Pompieri's Mail

Lin Xiao left the examination room and bumped into Professor Li Huaimin who hadn't seen him for a few days.

"Your boy really came out so early again."

Seeing Lin Xiao coming out, Li Huaimin pointed at him and cursed with a smile.

"Coach, have you been released?"

Lin Xiao greeted Li Huaimin when he saw him, and made a joke along the way.

"What does it mean to be 'released'?"

Li Huaimin said angrily.

As the team leader, he came here on July 7rd and participated in the team leader meeting a few days before IMO.

These team leaders are responsible for selecting the test questions and translating the questions, which means that he knew the questions in advance, so he has been under the request of the organizing committee these days and has not contacted the rest of the team. So when Lin Xiao and the others talked about Li Huaimin recently, they would tease him that he was locked up by the IMO organizing committee.

And now that the last exam is over, he can naturally meet them.

"During your exams yesterday, the leaders of our national teams were arranged to travel by Romanian officials. Would you like to show you the photos?"

"so good?"

"That's not it?" Li Huaimin said, "Forget it, let's not talk about this, how do you feel? Can you get full marks?"

Lin Xiao made an "OK" gesture, "You can scold me if you don't get full marks."

"Hehe, how dare I scold you now." Li Huaimin waved his hand: "Professor Pompieri wants to talk to you, maybe you can bring back a Fields Medal to Huaguo in the future, and I'm fine too. Dip in the light."

Although he couldn't meet Lin Xiao and the others directly, he was also at the opening ceremony, but he didn't sit with Lin Xiao and the others.

So he also knew about Lin Xiao's "great achievements" in the past few days, such as having a cordial conversation with the Fields Medal boss at the opening ceremony, and then leaving the exam room less than an hour after the exam started yesterday.

Regarding this situation, he can only say, as an old guy, don't compare yourself with this young man.

Before he knew that Lin Xiao had received the invitation from the International Conference of Mathematicians, he was actually a little envious in his heart. Now that he thought about it, it was enough to maintain a normal attitude towards this kind of person who could not be understood by common sense.

"It depends on whether you have such luck in the future."

As for the Fields Medal, Lin Xiao certainly didn't utter big words directly. To solve the Fields Medal, one must prove some famous conjectures or invent some important mathematical tools to be eligible for selection. He has not done so yet. Qualifications, even if the distribution of Mersenne primes is solved, it is also impossible.

"It's good to have confidence in yourself." Li Huaimin smiled, and then said: "Okay, are you going back to the hotel now? Or continue to wait for them?"

"I'll go back to the hotel first."

"Okay, let's go."

Li Huaimin didn't stay either. He knew what Lin Xiao was researching recently, which seemed to be a world-class problem. He was not interested in the research of this kind of problem, and he didn't want to get involved, so he could get a share of it.

Moreover, for a student like Lin Xiao, if any professor wanted to steal his achievements by virtue of his status, then Li Huaimin would only say 'idiot'.

There are two kinds of students that cannot be offended, one is those with family background, and the other is those who are really capable.

Lin Xiao obviously belongs to the latter, and with his ability, he doesn't look down on those with family background at all.

Who knows what Lin Xiao will develop into in the future?

If Lin Xiao really became a Fields Medal winner in the future and returned to China, even if he was not awarded an academician like Professor Tu Youyou, the attention he received at the national level must not be underestimated.

……

Soon, Lin Xiao returned to the hotel, and then turned on the computer non-stop, and continued to work on his thesis.

Now there is less than a week before the deadline. If he still can't figure it out, then he can only submit it as a phased result, which will also give him a sense of frustration.

And at this moment, he suddenly saw an email in his mailbox.

"Did it come from Professor Pompieri?"

Seeing the email, Lin Xiao couldn't help but look forward to it.

However, upon opening the email, he was disappointed.

It was sent by the International Mathematical Union.

And the content was what urged him to submit the manuscript as soon as possible.

Although it was said that it was before July 7th, the other party obviously did not think about Lin Xiao's plan to solve the problem of the distribution of Mersenne prime numbers, but just wanted Lin Xiao to sort out the method in the previous paper. It's not difficult.

So the other party didn't think that Lin Xiao hadn't finished it after a month.

Looking at the other party's reminder, Lin Xiao couldn't help scratching his hair, what should he do next?

Suddenly, at this moment, he received another email.

The email address of the sender is: [email protected].

Seeing this mailbox, Lin Xiao thought for a while, and suddenly realized that EB is Enrique Pompielli, and ias is the Institute for Advanced Study in Princeton.

Professor Pompieri has written to him!

He was overjoyed, and immediately quit the email from the International Mathematical Union, and then opened this email that was like a life-saving straw for him.

Although there is no guarantee that those manuscripts from Professor Atle Selberg will help me to reach the final result, but at least it can bring me some inspiration.

After all, it is the research of a Fields Medal winner. Even if he did not succeed, it is quite valuable to be able to understand some of the ideas embodied in his manuscript.

And as long as there is inspiration, then the problem can be solved.

Soon, the email entered, besides the attachment, there was also a line of text from Professor Pompieri.

[Mr. Lin, hello.

Attached is a scanned version of Professor Atle Selberg's manuscript, which includes his research on the distribution of prime numbers in the Fibonacci sequence and Mersenne numbers, hoping to give you some inspiration.

In addition, I also sent my own manuscript to you. I also did research on Mersenne prime numbers at the beginning-of course, in fact, many respected mathematics professors I know have studied this problem, but they all encountered There are some difficulties, so I also hope that you can complete this relay step for us, so that our mathematics world can add more young and more energetic blood.

Enrique Pompieri

Attachments (click to download)]

After reading the email, Lin Xiao couldn't help but sigh with emotion, such a pure scholar is really admirable.

Then, he impatiently downloaded the attachment and looked it up.

In this way, after about two hours passed, Lin Xiao finally came back to his senses, with relief in his eyes.

Then, he solemnly returned to the mailbox page, replied a letter of thanks to Professor Pompieri, and then replied a letter to the International Mathematical Union.

[I will submit the report on time before July 7th, please give me time, and then bring a small surprise to this year's International Congress of Mathematicians. 】

Chapter 86 At Your Fingertips

Mathematician Eichler once said that there are only five basic operations in mathematics, addition, subtraction, multiplication, division, and modular forms.

Perhaps this is a very personal argument, but it does show that modular forms are ubiquitous in today's deeper mathematics.

The modular form is an analytical function, and this function will become a certain type of functional equation under a group operation of the model group, and the value calculated by the function will also show a certain growth trend.

All in all, this is a mathematical tool with a wide range of applications, including the Taniyama Yutoshi-Shimura Goro conjecture in the process of proving Fermat's Last Theorem, and also uses modular form theory.

Research on the connection between modular form theory and group theory also exists widely in the mathematical community.

At this moment, Lin Xiao saw such an application in the proof process of Professor Selberg in front of him.

"Yeah, why didn't I think of that?"

While absorbing the knowledge in these manuscripts as if he had been enlightened, he felt the enlightenment brought to him by the knowledge in it.

As expected of Professor Atle Selberg, who once proved the prime number theorem, this kind of application of knowledge is truly worthy of the master's masterpiece.

"After studying group theory and Li groups for so long, I couldn't think of such a change. In this way, I can match my previous steps..."

Lin Xiao's eyes became brighter and brighter.

Then he quickly picked up the pen and scratch paper, and started the next interpretation.

These manuscripts did not tell him the answer. After all, Professor Atle Selberg did not succeed at the beginning, so he needs to follow the ideas conveyed in the manuscripts to complete the next work.

And the next job is a big project. He needs to combine group theory and his previous research, and then integrate modular form theory into it to complete a new mathematical method with more applicability.

And through this new method, he had a hunch that he would be able to accomplish his ultimate goal.

However, he had to try to know, after all, sometimes inspiration can also become an illusion.

Even the original Professor Selberg only used this method in it, but in the end it was not and did not succeed.

Of course, having a direction is the most important thing for mathematical research.

So, Lin Xiao continued his work.

【……F2k（τ）=（2ζ（2k））^（－1）G2k（τ），τ∈H。

……

log|P（ζ1，ζ2，ζ3）|＞－μT^4（logT）^24……】

Lin Xiaoyue writes, the more he feels that his thoughts are springing up, although this does not allow him to find the state where the brain development rate reached more than 4% in the sage state, but this state of continuous inspiration is also commendable.

Even if he encounters certain problems in the middle, he can still solve them quickly.

In this way, with the listing of formulas line by line, and the continuous combination of piles of English letters, Arabic numerals, and Greek letters, pieces of draft paper were used by him, and some were thrown aside by him. , and some were kept by him.

Time passed.

He could already feel that he was getting closer to the final result than ever before.

After an unknown period of time, Sun Yu, Ouyang Sheng and others who also finished the exam have also returned with the two team leaders. When they saw Lin Xiao's closed room, they all shook their heads and did not bother.

"I don't know if Lin Shen can solve that problem."