The top student must be diligent.

Chapter 37 Professor Liu Can't Understand
Seeing this title, Liu Bin was a little confused.

What is this?

Non-singularity analysis…absolutely far Abel conjecture?
The title seemed familiar, but he forgot where he had seen it before.

But, this question is not purely about number theory, right?

Although number theory is included, the main content is in the direction of far Abelian geometry. This area is relatively niche, and the researchers are basically big guys, or they are graduate students who want to develop in a niche direction.

But why is this the title of the paper written by Xiao Yi?
Did I send it to the wrong person?
He immediately switched to the WeChat interface and asked: [Xiao Yi, did you send the wrong message? Did you send the documents you read? ]

Xiao Yi quickly replied: [No, Professor, this is my thesis, and it was also the topic you suggested to me.]

My topic suggestions for Xiao Yi?
Liu Bin pondered for a while, and suddenly, his cerebellum shrank.

When he recommended a topic to Xiao Yi, he chose it directly from the topic database, and it seemed that he accidentally sent Xiao Yi a topic that he had chosen for himself before.

However, he thought that Xiao Yi wanted to write a paper on number theory, and he would not choose a paper topic that combined number theory and algebraic geometry from the dozen or so topics he had published.

Even he himself was not very sure about this topic.

The result is this...

Xiao Yi really wrote an article?
He immediately flipped through the chat history and found the topics he had given to Xiao Yi. Sure enough, he found the "Non-Singularity Analysis and Absolute Far-Abel Conjecture" mixed in.

Liu Bin held his forehead with his hand.

How on earth did this guy pick this one out of so many options?
No wonder you said at the beginning that you weren’t doing very well.

It wouldn't work if this professor replaced him!
[Teacher, is there any problem with the file I sent? ]

At this time, Xiao Yi sent another message asking for information.
Liu Bin rubbed his temples, relaxed a little, and then typed: [How did you choose this topic? ]

Xiao Yi replied: [I looked at all these topics and found that this topic actually requires the use of algebraic geometry, so I became interested. In addition, it seemed to be more difficult than the other topics, so I chose this one.]

Liu Bin: “…”

Well, what else can I say.

He should have expected this. Since he had known Xiao Yi for so long, he found that this kid had always been fascinated by difficult problems.

However, this kid is quite capable. Although he is fascinated by difficult problems, he is not blindly obsessed with them. Basically, he only solves problems that are within his ability, which can help improve his abilities.

But this time, probably because he was the one who recommended it, Xiao Yi made a misjudgment.

Shaking his head helplessly, he then told Xiao Yi the truth.

[…That’s how it is. This topic is indeed quite difficult for you. If you feel that the result is not good enough, it is completely understandable.]

Xiao Yi was stunned. It turned out that after all this time, he was actually researching a topic of the same level as Professor Liu Bin?
Professor's topic?
[Professor, then I...]

Liu Bin continued to comfort her: "Don't worry too much. At least it gives you some experience in writing papers. Even if the conclusion is not reached or there are mistakes in the process, it can at least provide you with some experience and lessons for your next writing."

However, Xiao Yi, who was a little confused just now, was stunned after seeing Liu Bin's message, and then replied: [Professor, I should have proved this conclusion. It is the absolute far Abel conjecture. There is no problem with the derivation process. I have verified it.]

This time it was Liu Bin's turn to be stunned.
What the hell?

Have you proved it?
Liu Bin: [Are you sure?]

Xiao Yi: [It should be fine, I have verified it. ]

Liu Bin: [Wait a minute.]

After sending the last message, Liu Bin directly switched back to the document interface, with one sentence in his mind: Has this guy proved it?
Did this guy really prove it?
If this is really proven, he...

I don’t even know what to say.

The purpose of this topic is to solve conjectures. There are many conjectures in mathematics, not only well-known ones like the Goldbach conjecture and the Riemann conjecture, but also many unknown conjectures. The purpose is to solve some relative problems, such as the absolute far-Abel conjecture in Xiao Yi's topic.

For this type of topic, as long as the conjecture is proved, it is valuable enough.

Unlike some other papers whose purpose is to construct new theories, at this time we need to see what problems these new theories can be used to solve, thus determining the value of this paper.

Therefore, if Xiao Yi really proves this conjecture, then...

He is really a math devil.

"Look first, look first."

Liu Bin tried to calm himself down.

Turning the page, his eyes shifted to the paper.

First is the abstract... Never mind, why read the abstract, just read the main text.

The abstract is for other people to see after the paper is published, so he should not read it as it is a waste of time.

Enter the main text.

The first part is an introduction to the topic, which mainly introduces the Grothendieck-Far Abel conjecture and explains that Shinichi Mochizuki has solved this conjecture and derived the Absolute Far Abel conjecture from it.

The first part is fine, let’s move on to the second part and start the argument.
"Non-singular analytic, let K be a completely non-Archimedean field of mixed characteristic (0, p), let Ok be its integer ring, and take its remainder field... if for every point X of the second kind X^an there exists a finite cover f:Y→X... then X is said to satisfy a non-singular analytic..."

"..."

In this way, Liu Bin read every sentence carefully.

The more he looked, the more surprised he was.
This kid is a natural at math!

The arguments are extremely rigorous and do not contain any of the bad habits of mathematicians, such as "obvious" or "easy to obtain". At least from the reader's perspective, such a paper looks quite comfortable.

In this regard, Liu Bin can only hope that Xiao Yi can maintain this good habit.

In addition to being amazed at the rigorous argumentation process, what made Liu Bin even more incredible was that there were no mistakes, and he could not find any mistakes at all.

Could it be that Xiao Yi really figured out this conjecture?

However, before he could confirm this fact, he discovered a problem.

That is - he couldn't understand it.

A full professor couldn't understand a paper written by a high school student.

If this is said to others, it will generally be regarded as that the paper written by this high school student is so bad that the professor cannot understand it.

But Liu Bin knew that this was because the content of the paper had exceeded his level of expertise.

His main research direction is indeed inclined towards number theory and algebraic geometry, but this topic involves far Abelian after all, which is beyond the scope of his research.

For a moment, I was embarrassed.

(End of this chapter)