From all-round academic master to chief scientist

After sighing for an unknown amount of time, Professor Peter Sarnak finally looked back at the end of the paper.

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

Seeing the content of Lin Xiao's last two pages, Sanak raised his eyebrows and couldn't help but sigh.

Zhou's guess is also a famous problem in the study of Mersenne prime numbers.

However, because the value range of Zhou's guess is very large, it does not provide much help in studying the distribution of Mersenne prime numbers, because Zhou's guess predicts the total number of prime numbers before a certain term in the Mersenne number. Therefore, in the plan of the Internet Mersenne Prime Search, Zhou's guess was not used, but the Lucas-Lemmer test method was used. Before this method, the fast Fourier transform was used.

However, these two methods only take advantage of the characteristics of the computer, that is, the ability of the computer to perform repetitive work, so as to continuously calculate to larger numbers. However, because this method is more random, it will often appear that Some fish slipped through the net.

But now it seems that the Internet Mersenne Prime Search project has come to an end.

Sarnak sighed and felt a sense of relief in his heart. I believe that every mathematician who has studied Mersenne prime numbers will feel this way, because a huge mountain in the world of mathematics has finally been climbed by them.

With this kind of achievement, it is no wonder that Lin Xiao has not submitted the report until now. Professor Sarnak even began to think about when Lin Xiao began to study this topic. It started when I gave the report last time, and it was really amazing.

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

"Professor Deligne should have finished reading it too."

Professor Sarnak smiled slightly.

Although Professor Deligne does not mainly study the field of number theory like him, as a mathematician who has won the Fields Medal, the Abel Medal, the Wolf Medal, the Crafford Medal and other majors in mathematics, take a look at this That's totally fine too.

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

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

So he answered the phone and said with a smile: "Professor Deligne, how are you?"

"Who wrote this paper?"

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

"I read it, but did you know that Professor Pompieri has such a student? Professor Pompieri and I are both retired, so he shouldn't have any students, let alone a Chinese student."

Professor Sarnak was stunned: "Professor Pompieri? Isn't he traveling in Europe now? Why do you mention him again?"

"In the acknowledgments at the end of the paper, Lin Xiao expressed his gratitude to Professor Pompieri. Professor Pompieri provided him with Professor Atler Selberg's manuscript. I asked him why there was such a thing in his paper. Parts of it felt familiar to me, having heard Selberg mention it before in discussions with him.”

Sarnak couldn't help but be stunned. How could Lin Xiao know Professor Pompieri again?

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

"I do not know."

That was all he could answer.

In the end, the two professors put it together 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 pleasantly surprised.

"When I was traveling in Europe, I was invited by the IMO to go to Romania. After arriving there, I unexpectedly learned that one of the players on the Chinese team was Lin Xiao. It happened that his Fibonacci article I have also read the paper on deed sequence and I was very interested in it, 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, right?"

After hearing what Professor Pompieri said, both Sarnak and Deligne felt that it was such a coincidence.

"Yes, if I read it 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 , the combination of modular forms, and the prime number problem. Oh, I seem to feel that the topic I studied before on the L function can also be used... In short, with this result, even if I go to the International Congress of Mathematicians in August to do a The hourly report was fine, but it’s too late now.”

Professor Deligne sighed.

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

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

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

Sanak: "No, you don't want to. You have to let him finish his master's and doctoral studies with me first. Your IAS will not recruit a student who has not even graduated from postgraduate school. Besides, you are retired."

"You can re-appoint your position even after you retire. I am an IAS lifelong researcher, so I can retire."

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

You are a big boss and cannot be offended.

The tenured researcher seat at the Institute for Advanced Study in Princeton is one of the most famous honors in academia. There are very few professors who can get this seat, and Professor Deligne is one of them. Even Sanak would be envious.

"Okay, let's go here first."

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

Deligne also said: "I am also looking forward to that day."

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

Since everyone including Professor Deligne has approved it, and he has not found any errors, it is basically certain that there is no problem. Of course, during this period, he will probably have to read this paper several times to confirm again and again. No matter how rigorous this important achievement is, he will also look for professors from other mathematicians conferences in the field of number theory to take a look at it. Likewise, this is also to help Lin Xiao publicize it.

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

Professor Sanak couldn't tell.

So, after the three giants in mathematics said goodbye to each other, they closed the meeting video.

…………

[Thanks to the leader of Guwendao for the reward, thank you very much! 】

About the update:

1. Yesterday, it was updated at 0:00 due to the launch. Later, before the update time is restored, it will be around 11:00 a.m.

2. Try to ensure that 10,000 words are updated every day after it is put on the shelves. However, because the author needs to complete his graduation thesis, sometimes it may not be possible to update 10,000 words. Please understand.

3. There are no plans to add updates yet. It is already very difficult to keep the 10,000 words updated (╥_╥)

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