The top student must be diligent.

Chapter 264: Pass the math level?

By late night, the news had spread completely.

At this time, Xiao Yi had already fallen into a deep sleep, but the mathematics community could not sleep at all.

For a while, there were discussions about this matter everywhere.

People were either amazed that Chief Engineer Xiao had solved such a well-known mathematical conjecture just a few months after he solved nuclear fusion, or they were amazed that Xiao Yi's idea of ​​solving the hail conjecture was really a bit unexpected.

But more people were amazed at how Xiao Yi's energy gave people a feeling of inexhaustibility. He was able to accomplish so many important results in succession. Doesn't he feel tired?

But in the end, when they thought about Xiao Yi's age, the question of whether he was tired or not was self-defeating.

……

It was late night in China, and daytime on the other side of the earth.

Terence Tao, who was far away in the United States, learned about this matter on this day.

"Wait, you mean, the Hailstone Conjecture has also been solved?"

At this time, Terence Tao, who was talking on the phone in the office, suddenly stood up and listened to the news told to him by the other party with a look of surprise.

Although he was not the first to know the news, naturally someone would tell him.

After receiving a positive response from the other party, he asked, "Is it Xiao Yi? Did he do it?"

"Terence, you were able to guess it was him so quickly?"

The other party was slightly surprised.

Tao said: "Who else in this world, besides him, can solve this problem right now?"

"Especially after I heard that he had completed the research on controlled nuclear fusion, I guessed that he would spend time on theoretical research next."

"That's what you said."

"Well, thank you for bringing me this news. I have to go and take a look at his paper."

After a brief expression of thanks, Tao hung up the phone, quickly turned on his computer, found Xiao Yi's website in his favorite websites, and clicked on it.

Sure enough, after two years, a new paper finally appeared on this website.

Tao Terence downloaded the paper immediately.

"Hailstone conjecture, hailstone conjecture..."

"How will Xiao Yi solve this conjecture?"

At this time, Tao Zhexuan's thirst for knowledge became quite strong.

As an expert in the field of number theory, he is very interested in every conjecture in the field of number theory. Otherwise, he would not have studied these problems.

He studied the Goldbach conjecture and achieved some results. He also studied the twin prime conjecture and achieved some results.

The same is true for the hail conjecture. His original result was already quite close to the final proof.

However, for most of the problems he studied, no matter how hard he thought about them, he could only reach that level.

As for why not spend more time on it?
That's simply because he knows very well that he can do his best.

But now, Xiao Yi is always able to overcome his limits and achieve his ultimate goal.

For him, this feeling was quite powerless.

It’s as if the other person is the complete version of oneself, and oneself is just an incomplete version.

He once fell into such a state of confusion.

But later he felt relieved.

Why should I have such thoughts?

At least, Xiao Yi solved these problems, didn't it also satisfy his desire for answers?

Although I didn't solve it myself...

I opened the paper and looked at the abstract first.

However, despite the simple summary, the message revealed is not simple at all.

"Representation theory? Is he crazy?"

When Terence Tao saw the first sentence of the abstract, he couldn't help but rub his eyes.

Using representation theory to solve the hailstone conjecture?
Isn’t this idea a bit...

Too outrageous?
He is now reading Xiao Yi's paper mainly because he wants to verify some of his previous thoughts.

See if Xiao Yi's method of proof is the same as the method he had thought of before. This way, it would bring him some comfort.

[I almost thought of it at the beginning! ]

[What a pity! I had considered this step before, but I was stumped when it came to the next step. What a pity!]

And so on.

However, now it seems that the methods used by Xiao Yi are completely beyond his imagination.

Representation Theory...

Before this, he had never thought that representation theory could be used to prove the hailstone conjecture.

How did Xiao Yi come up with this idea?

He couldn't help but have such doubts in his mind.

But then he gave another bitter smile.

I seem to ask myself this question every time I read Xiao Yi's paper.

Okay, now let’s see…

Perhaps it was because Xiao Yi thought of using representation theory that he was able to prove success?
However, as he continued to look down, he realized that his idea was only half right...

Maybe even less than half.

"It's actually like this!"

Just the first few steps had already made him see the extraordinary nature of Xiao Yi's method.

He was originally very confused about how Xiao Yi combined the methods of representation theory with the hailstone conjecture, but after seeing the first few steps, he understood it in his mind, and then he was amazed at this cross-disciplinary thinking.

Translating a problem from number theory and dynamical systems into the language of representation theory requires a deep understanding of different fields and a unique mathematical perspective.

Even thinking about this step is difficult enough, let alone successfully integrating these steps into it.

Therefore, it was not because Xiao Yi found the method of representation theory to study that he successfully proved the hailstone conjecture, but it was precisely because Xiao Yi chose the method of representation theory that representation theory could be used to prove the hailstone conjecture.

Otherwise, this method will most likely not be discovered for a very long time, even until someone else successfully proves the hail conjecture using other methods.

Unless... a long time after the Langlands Program is successfully implemented.

However, when he suddenly thought of the Langlands Program, Tao suddenly realized something, and then continued to read on. In the end, he discovered one of the most valuable conclusions in this paper, in addition to proving the hail conjecture.

That is to establish a closer connection between Diophantine theory and representation theory.

This achievement can naturally be regarded as a major breakthrough in the Langlands Program. Diophantine theory itself is an important field in number theory. It can achieve a deeper connection with representation theory, which can naturally be regarded as an achievement of the Langlands Program.

"It's really unbelievable..." Tao Zhexuan sighed. Xiao Yi could actually think of such an idea.

This result was achieved inadvertently.

Of course, it is normal to think about it. In order to solve the hail conjecture, there must be some equally important results involved.

The value of the hail conjecture has never lay in its conclusion but in its process.

The same is true of most problems in number theory.

If you continue reading, you will find more exciting ideas or methods, and each step is so brilliant.

Of course, the writing style of Xiao Yi's papers back then has not diminished at all.

One of the most important styles is that it is detailed and easy to understand. Xiao Yi's papers do not have many simplified steps, so they have always been considered unique in the mathematics field in terms of readability, and therefore have been highly praised by the academic community.

Until now, Xiao Yi still maintains this advantage. Many students who have just entered the field of mathematics often receive recommendations from their teachers to read more of Xiao Yi's papers and learn his writing style.

Therefore, now quite a number of students learn Xiao Yi's style when writing mathematics papers.

And not only these students, but now quite a number of mathematicians have begun to learn Xiao Yi's writing style.

This is not to say that they want to learn well, but mainly because they found that learning Xiao Yi's writing style can help improve the citation rate of their papers. Many journals have also discovered this. Therefore, in order to improve the impact factor of the journal, editors will be more inclined to accept such papers when accepting articles.

To some extent, Xiao Yi has also brought changes to the mathematics community.

Tao Terence has always praised this.

Continuing to read below, Xiao Yi connected the invariant vectors with the periodic orbits, and successfully discovered the one-to-one correspondence between the invariant vectors in the representation space and the periodic orbits of the hail sequence. This ability to connect abstract algebraic concepts with specific number theory problems once again made Tao feel that he had gained something.

Until the end, the paper proved the limitations of classification trees, and the methods demonstrated in the process also demonstrated the depth of this paper.

“Another such a perfect paper.”

It was not until the page on the computer turned to the side with the literature citations that Tao finished reading all the contents of the text and uttered a final sigh.

Xiao Yi's papers always surprised him and never disappointed him.

"Perfect!"

After snapping his fingers, Tao began his daily routine after reading a heavyweight paper - writing a review on his blog.

Especially for such a brilliant paper, it is necessary for him to express his own views.

As for whether Xiao Yi's proof is correct...

Need more to say?
Anyway, after reading the whole article, he couldn't find any mistakes because it was written in sufficient detail.

Since he couldn't find any mistakes after reading it once, he didn't plan to read it again.

Anyway, just take it as a tacit acknowledgement that Xiao Yi has successfully proved it.

Is this a bit imprecise?
Ok……

Considering that the person was Xiao Yi, Tao Zhexuan felt that he had read it in its entirety, which was already rigorous enough.

After entering the blog, he started typing.

[There is no doubt that we have received another good news today, that is, the hail conjecture has been successfully proved!
It has been almost 100 years since this problem was born. It is amazing that such a problem has stumped our mathematics community for so many years.

Fortunately, Xiao successfully solved this problem when it was about to reach its 100-year history. Perhaps this can be said to have saved the face of our mathematics community?
Ahem, now let's get back to the topic. In short, I have read the paper once. Although it is not rigorous enough to conclude that Xiao has succeeded, I think the hail conjecture can be called the hail theorem, just like what I wrote in my first paragraph.

Xiao still demonstrated quite amazing proof skills and ideas in his paper. The idea of ​​trying to solve the problem from the perspective of representation theory alone can be regarded as a completely new idea.

In particular, the construction of hail groups is very clever. It perfectly captures the generation rules of hail sequences and lays the foundation for subsequent theoretical analysis. I believe that if we can study the construction ideas of hail groups more, it may bring considerable inspiration to many other problems.

Of course, the most outstanding thing is that Xiao incorporated the idea of ​​Diophantine approximation into it. I would like to call this the most brilliant step in the entire paper and also the most important achievement in this paper. He combined Diophantine theory and representation theory, which made the proof of Langlands conjecture further realized.

As for the dynamical system theory used later and the construction of the periodic orbit classification tree, no logical errors were found at all.

All in all, I am very happy to see Xiao's return. I haven't seen Xiao's papers in all these years, and now I am finally satisfied.

Now, we can continue to look forward to Xiao’s next paper!

XD】

After clicking send, his comments were uploaded to his personal blog.

He turned around and looked at the paper again, then he started reading it again without saying anything else.

The first time I watched it was to learn the method, and now the second time, it is just for appreciation.

Then he began his appreciation.

……

After Terence Tao published this blog, it immediately attracted a lot of attention.

The proof of the hailstone conjecture had already spread when he was still reading it for the first time, so the mathematical community has been waiting for his response. After all, everyone knows that Terence Tao had made important achievements on the hailstone conjecture, so everyone is curious about his thoughts on this issue.

People in the mathematics community all know that Professor Tao has the habit of posting blogs, so when this blog post was published, it was immediately discovered and immediately caused a lot of discussion.

For a time, this issue once again aroused discussions among various mathematicians in some international mathematics discussion forums.

[Sure enough, even Terence Tao thought that Xiao Yi's proof using representation theory was a very impressive thing. Before, no one could have thought that the hail conjecture had such a thinking angle.]

[Hailstone conjecture, Hailstone conjecture, didn't Erdős say that the current mathematical community is not ready to face this problem? How come it was suddenly solved? ]

[Hey, I think you should change this sentence now. It should be called: Hail Conjecture is not ready to welcome Xiao Yi.]

[That's right. Bing Hail probably didn't expect that he would be taken care of in just two or three months.]

[So, what you mean is that Xiao Yi really solved the hail conjecture not long after he completed controlled nuclear fusion? ]

[I'm just guessing, but I think it's very likely. Otherwise, who would have the spare time to study a notoriously difficult conjecture in mathematics while studying nuclear fusion?]

[So, only Xiao Yi can do it. ]

[Oh my god, I can't believe that such a genius could appear in such a backward country! ]

[Hey bro, we are the backward country now, they have developed the 1.0 civilization of controlled nuclear fusion. ]

[So, is there anyone who can stop Xiao Yi from completely mastering mathematics? ]

[No one can stop him anymore! Now only he can stop himself! ]

【…】

(End of this chapter)