Professor Liu Couldn't Understand It

Seeing the title, Liu Bin was a little confused.

What was this supposed to be?

Non-singular Analytic... Absolute Remote Abelian Conjecture?

The title seemed somewhat familiar, but he had forgotten where he had seen it before.

But wasn't this topic more than just number theory?

Although it included number theory, its main focus was Far Abelian Geometry. This was a rather niche field, studied mostly by big names, or Graduate Students who wanted to develop in a niche direction.

But why was Xiao Yi's paper titled this?

Could he have sent the wrong file?

He immediately switched to WeChat and asked, "Xiao Yi, did you send the wrong thing? Did you send me one of the papers you were reading?"

Xiao Yi replied quickly, "No, Professor. This is my paper, and it's also the research topic you suggested to me back then."

A topic I suggested to Xiao Yi?

Liu Bin racked his brains for a while. Then, all of a sudden, his cerebellum seemed to shrivel.

When he had recommended topics to Xiao Yi, he had picked directly from the topic bank. It seemed that he really had accidentally sent Xiao Yi a topic he had once selected for himself.

But he had figured that Xiao Yi wanted to write a paper on number theory, so he probably would not choose a topic that combined number theory and Algebraic Geometry from the dozen or so topics he had sent.

Even he himself was not very confident about this topic.

And yet...

Xiao Yi had actually produced a paper on it?

He immediately scrolled up through their chat history to the topics he had sent Xiao Yi back then. Sure enough, buried among them was "Non-singular Analytic and the Absolute Remote Abelian Conjecture."

Liu Bin rubbed his forehead.

How had this kid picked this one from so many topics?

No wonder he had said from the beginning that he hadn't done very well.

Even this professor wouldn't have done very well with it!

"Professor, is there something wrong with the file I sent?"

At that moment, Xiao Yi sent another message asking.

Liu Bin rubbed his temples and took a moment to recover before typing, "How did you end up choosing this topic?"

Xiao Yi replied, "I looked through all the topics and found that this one actually required some Algebraic Geometry. That made me interested in it. And it looked harder than all the other topics, so I chose it."

Liu Bin: "..."

Well, what else could he say?

He should have expected this. After knowing Xiao Yi for so long, he had noticed that the kid had always been fascinated by difficult problems.

Still, the kid had a good sense of his own limits. Though fascinated by difficult problems, he did not pursue them blindly. The problems were generally within his abilities, allowing him to improve.

Only this time, perhaps because Liu Bin had recommended it, Xiao Yi had misjudged the difficulty.

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

"...That's what happened. So this topic really is one of the more difficult ones for you. If you feel you didn't do very well, that's completely understandable."

Xiao Yi froze. So after all this effort, he had actually been researching a topic at Professor Liu Bin's level?

A professor's topic?

"Professor, then I..."

Liu Bin continued to comfort him. "You don't need to panic too much. At the very least, it gave you experience writing a paper. Even if you didn't arrive at the conclusion, or there were errors in the process, it can still give you some lessons and experience for your next paper."

However, Xiao Yi, who had just been somewhat lost, paused when he saw Liu Bin's message. Then he replied, "Professor, I think I proved the conclusion. The Absolute Remote Abelian Conjecture—I don't think there's a problem with the derivation. I checked it."

This time, Liu Bin was the one who froze.

What?

You proved it?

Liu Bin: "Are you sure?"

Xiao Yi: "There shouldn't be a problem. I checked it."

Liu Bin: "Wait a moment."

After sending that final message, Liu Bin immediately switched back to the document. His mind was filled with one sentence.

This kid proved it?

This kid really proved it?

If he had really proved it, then he...

He did not even know what to say.

The purpose of this topic was to solve a conjecture. There were many conjectures in mathematics—not only famous ones like the Goldbach Conjecture and the Riemann Hypothesis, but also many obscure conjectures intended to address particular problems. The Absolute Remote Abelian Conjecture in Xiao Yi's topic was one of them.

As long as a topic like this successfully proved the conjecture, it already had sufficient value.

It was unlike other papers whose goal was to construct new theories. In those cases, the value of the paper depended on what problems those new theories could solve.

So, if Xiao Yi had really proved this conjecture, then...

He really was a Math Demon King.

"Read it first. Read it first."

Liu Bin tried to calm himself down.

Turning the page, he shifted his gaze to the paper.

First was the abstract... Forget it, why read the abstract? He would go straight to the main text.

Abstracts were for others to read after a paper had been published. He would skip it and save time.

He entered the main text.

The first section was an introduction to the topic. It mainly introduced Grothendieck's Remote Abelian Conjecture, explained that Shinichi Mochizuki had already resolved the issue addressed by that conjecture, and used that to introduce the Absolute Remote Abelian Conjecture.

There was no problem with the first section. He moved on to the second, where the proof began.

"Non-singular Analytic. Let K be a complete non-Archimedean field of mixed characteristic (0, p), let O_K be its ring of integers, and take its residue field... If, for every point x of the second type of X^an, there exists a finite covering f: Y → X... then X is said to satisfy non-singular analytic..."

"..."

Like that, Liu Bin began reading almost every sentence with painstaking care.

And the more he read, the more shocked he became.

This kid was simply born to study mathematics!

The proof was incomparably rigorous, without any of mathematicians' bad habits, such as "obviously" or "it is easy to obtain." At least from a reader's perspective, the paper was exceptionally comfortable to read.

Liu Bin could only hope that Xiao Yi would maintain this good habit.

But beyond his amazement at the rigorous proof, what Liu Bin found even more unbelievable was that there were no errors. He could not find a single mistake.

Could Xiao Yi really have solved this conjecture?

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

That was—he could no longer understand it.

A full professor could not understand a paper written by a high school student.

If this got out, people would generally assume that the high school student's paper was so poorly written that the professor could not understand it.

But Liu Bin knew that it was because the contents of this paper had exceeded his area of expertise.

His primary field of research did lean toward number theory and Algebraic Geometry, but this topic involved the Remote Abelian Conjecture after all. That went beyond the scope of his research.

For a moment, he was left in an awkward bind.