The top student must be diligent

"But today, I saw an opportunity for a fourth person to emerge from this young Chinese man."

"He has a talent that almost all mathematicians do not have, and that is his independence in thinking and logic. He will not be affected by any existing experience or judgment and can always maintain absolutely independent thinking. Any other knowledge will only serve as a reference for him.”

"With such a talent, no matter what he studies, such as physics, chemistry, or philosophy, I believe he will be able to embark on a great path and lead to a great end."

"Of course," Falting paused, and finally said with a smile: "This young man wisely chose mathematics. This is the path that suits him best and needs him the most. Therefore, I believe he can lead to a greater world. end."

Faltings undoubtedly gave Xiao Yi a very high evaluation.

This is quite rare, because people who are familiar with him know that with his temper, even mathematicians who have been famous for many years do not dare to speak nonsense in front of him. Once he makes a mistake, he will definitely be criticized by him, and he will also Rarely praised.

But obviously, this seventeen-year-old boy made him make an exception.

Of course, Faltings was not the only one. Behind him, the two great mathematicians Deligne and Bombieri were not let go by Euronews.

These two are also among the top mathematicians on the scene, and they are not stingy in their praise at all.

Deligne: "There are many outstanding mathematicians, and there are many outstanding geniuses, but what I can believe is that there should be no geniuses who are younger and better than this seventeen-year-old boy."

Bombieri: "I have said enough about how outstanding this young man is. Faltins and Deligne have said enough. As a mathematician who studies Diophantine analysis, I will simply say abc Conjecture, the most important question in this Diophantine analysis.”

"Once the ABC conjecture is proven, we will easily prove Fermat's last conjecture and Model's conjecture - of course these two have been proven. In fact, there are still many unsolved problems that can also be easily proven. Solve, such as Voita's conjecture, Beer's conjecture, Hall's conjecture, etc. "

"So, the conclusion of the ABC conjecture is very important."

"We were all happy to see it proven before, but when it gets involved in a dispute, we don't want to see it, because it means that other people who want to study this problem may hesitate, such as those who are halfway through the study. Suddenly the dispute was over and it was successfully demonstrated, but the result was never reached.”

"Xiao Yi successfully liberated this issue from the dispute. In the future, anyone can safely and boldly study this issue without worrying too much."

"So the world of mathematics has this boy to thank."

"Of course, no one can say for sure, how many years from now, this boy will be the one to end ABC's conjecture?"

Speaking of this, Bombieri also had some expectations in his eyes.

…

Chapter 72 Faltings’ suggestion

"Professor Faltings, here I come. "

Xiao Yi knocked on the door of an office at the Max Planck Institute of Mathematics.

After walking in, he respectfully said to the math master sitting at the desk.

Faltins smiled and nodded.

According to the previous agreement, Xiao Yilai asked him for help in academic research.

Although it was a pity that Xiao Yi did not ask to become his student, he soon felt relieved. Maybe this young man had his own ideas.

Of course, he would not lose face and force the other party to become his student.

Of course he couldn't do such a thing.

So, today, let’s listen carefully to what this young man wants to know, and then try to give him some good advice.

"Here we go, sit down first."

Faltings left his seat, walked to the coffee machine and asked, "Want to drink coffee or tea?"

Xiao Yi, who had just sat down, didn't even go to jail yet, so he quickly got up and walked over, saying: "I'll come, I'll come, just drink tea."

Faltings nodded with a smile and handed the cup to Xiao Yi.

"You have been all over the news these past two days. Do you have any thoughts?"

Xiao Yi shook his head helplessly: "I don't have any ideas, um... it's too noisy."

"Too noisy?" Faltings was stunned for a moment, then burst out laughing, "That's right, it's indeed too noisy, like a group of monkeys."

"Obviously I don't even understand mathematics, and I'm afraid I can't explain what far Abelian geometry is, but a bunch of media reporters want to talk about this as a major event in the world of mathematics. It's really interesting."

Xiao Yi felt ashamed, probably only a big shot like this could say this, right?

After expressing his disdain for those media, Faltings said again: "Okay, let's not talk about those things. Let's talk about what the question you want to ask me is. "

"Of course I need to say it in advance. If it is something too simple, I will not answer you. Simple things need to be solved by yourself. According to your ability, the question you want to ask should be It’s the kind of question that’s worth at least an IHES article.”

Faltins remained strict.

Xiao Yi thought about the question he wanted to ask. Well, it should be about the same. Not to mention publishing IHES, it should be no problem to publish a mathematics yearbook.

He brought the tea to the table, and then he took out two A4 papers from his bag and handed them to Faltings.

"Professor, I am thinking about the question above now."

"Well... let me see." Faltings nodded, took the A4 paper and started reading.

Soon, his eyebrows were raised.

"Is this... the twin prime conjecture?"

Xiao Yi was amazed in his heart. He really deserves to be a big shot. He could see that his purpose was the twin prime conjecture so quickly.

He nodded and said, "Yes, professor."

"The work of tele-Abelian geometry in etale cohomology reminds me of Bombieri's theorem. I think from a tele-Abelian perspective, perhaps we can continue to improve Bombieri's theorem and use it to further strengthen the results of the three mathematicians G-P-Y."

"With the improvement work of the two mathematicians, Terence Tao and Maynard, perhaps we can really break through the current upper limit of 246 and reduce this number. It is even possible to successfully prove the twin prime conjecture."

Listening to Xiao Yi's words, Faltings couldn't help but look at the young man again.

Prove the twin prime conjecture?

He didn't dare to say such words when he was 17 years old.

This young man not only has talent, but also courage.

No wonder he can write an IHES paper right away.

He lowered his head again and continued to look at the two A4 papers of Xiao Yi.

"Bombieri's theorem... You can ask that old guy Bombieri to come over and talk about this problem. Maybe he can tell you a lot."

Enrico Bombieri, who proposed this theorem, is probably next door now.

"However, about your idea..."

Faltings continued to look at it for a while, and then asked: "Have you considered the problem of the Siegel-Walfisz hypothesis? If this premise is not included, etale will not be applicable in the first place."

Xiao Yi replied: "I have considered it."

"How to solve it?"

Xiao Yi looked around.

Faltings understood what he meant and dragged a blackboard behind him.

"Use this."

Xiao Yi's eyes lit up, and then he picked up the blackboard pen next to the blackboard and started writing on it.

[Siegel-Walfisz hypothesis: ∑n≡a(r)(n,q)=1β(n)1φ(r)∑(n,qr)=1β(n)……]

"Since the modulus d is at most slightly larger than x^1/2 on the logarithmic scale, after simplifying the problem to estimating the sum of some incomplete Kloosterman, we only need to save a small power of x from the trivial estimate."

"In this case, Siegel-Walfisz is not a problem."

Looking at what Xiao Yi wrote, Faltings thought for a while, then nodded.

"Not bad, you solved this point."

No more talking, he continued to look down, and soon asked again.

"Then, what about the boundary problem of S1? Have you ever thought about this? Don't forget the requirements of the Chinese Remainder Theorem."

"This problem directly involves the application of far Abelian geometry in number theory."

This problem is a key problem that Faltings believes is more important than the above problem. Moreover, from the difficulty of solving it, Faltings estimates that it is also much more difficult.

If this problem is solved, it is estimated that it can be easily published in a letter in the first area.

However, Xiao Yi's expression still did not show any entanglement, and he said directly: "I have also considered this problem."

Then, he continued to pick up the pen and wrote on the small blackboard next to him.

After a while, Faltings looked at the new derivation processes on the blackboard with a little surprise.

"Not bad, very good."

"It seems that you are indeed well prepared for this idea."

In this way, he continued to look down, and then asked questions about some of the questions from time to time, and Xiao Yi was always able to give ready answers to these questions.

Even if Xiao Yi was not prepared, he only needed to think for a short time and then give an answer.

Probably, these questions that he had not prepared for were all questions that he had thought about before, but they were not difficult for him at all.

In this way, in more than half an hour, Faltings asked more than a dozen questions, and each question was successfully answered by Xiao Yi.

Finally, Faltings put down the papers.

"Your preparation is more than I thought."

"So, if you come to seek my help, I may not be able to give you any practical and useful help."