The top student must be diligent.

Chapter 117 How to spend $15? Waiting online

Within just one day, Xiao Yi's paper once again appeared in front of countless people in the mathematics community.

Although it is still difficult to understand his paper, it is obviously easier to understand than the previous twin prime conjecture or the original Elliott–Halberstam conjecture paper.

Especially its real core content, which is only the first 8 pages.

This new method, which has begun to be recognized by the mathematical community as the "Xiao polynomial expansion", has gradually been understood by more and more scholars in the mathematical community, and they are surprised by it.

Although Xiao's derivation process requires the use of Etale algebraic variety automorphism theory and classification sieve theory, not every scholar can understand these two theories, but they don't need to understand the derivation method.

For most people, they just need to know what the Xiao's expansion does and how to use it.

This is a very normal way of thinking. You don’t need to know the source of the tool, you just need to know how to use it.

Just like the most basic method, Taylor expansion, not everyone knows how it is derived, but that does not prevent it from becoming the most commonly used method in mathematics.

Probably, the only difference is that the derivation of Taylor expansion is simpler, while the derivation of Shaw expansion is much more difficult.

In addition, Xiao Yi mentioned in the paper that using Xiao's expansion to push the critical line of the Riemann hypothesis to 50% is not the limit and can still be improved.

This has also attracted some scholars to try to push the critical line theorem to an even more extreme level, and maybe they can even publish a paper at that time.

Even if you can only publish one paper in Zone 3, for those non-top scholars, a paper in Zone 3 is also very good.

After all, not everyone in this world is a great person.

……

mathoverflow.

This is an online community, but it is dedicated to the field of mathematics. The users gathered in this community are naturally basically professional mathematicians.

Normally, it serves as an academic exchange community where mathematicians can learn mathematical knowledge. If you ask questions, there will be many experts answering them.

In addition, whenever something big happens in the mathematics world, this online community becomes lively.

For example, these two days.

The discussion on the Xiao polynomial expansion and the major breakthrough in the Riemann hypothesis has become very popular on Mathoverflow.

Especially the discussion related to the Riemann hypothesis.

Although professional mathematicians know that the Shaw expansion is more important, for ordinary scholars, the Riemann hypothesis is obviously more topical.
A post titled "The critical line theorem of the Riemann hypothesis has once again made a huge breakthrough. What is the significance of this for the proof of the Riemann hypothesis?" attracted a lot of discussion.

[I still have time to ask questions here. I bet that a group of people have already started to think about how to make the critical line theorem closer to reality. They can easily publish a third-tier paper. I know that the guy who lives next door to me has already started. ]

[I can only say that in the future, a large number of stubborn people will probably get into the dead end of the Riemann hypothesis, hoping that one day they can become the prover of the Riemann hypothesis]

[Look at what you said. Who doesn't want to be a mathematician like Perelman? As long as you prove it, you can get the Fields Medal. Don't you want to? ]

[I don’t want to, because I’m over 40. ]

[The International Mathematical Union will award you a silver Fields Medal]

[Please, not everyone can become a mathematician like Perelman. Before he proved the Poincare conjecture, he had already been invited to the International Congress of Mathematicians and gave a report on stage. Can you do it? ]

[Although it may sound a bit rude, I think this is really funny. My advisor has been studying the Riemann hypothesis recently, trying to improve last year's 41.7% result to a certain extent. He has already achieved some results, but now, hahaha! Sorry, I really didn't mean it, but this is really funny! ]

[What a coincidence! It turns out that your advisor is also researching critical line approximation methods! My advisor is the same. After reading Xiao Yi's paper today, he became furious and almost overturned his desk! ]

【This is such a sad story :). 】

[Well, I searched your information. The first person should be Georgia Landy from the Department of Mathematics at Northeastern University, and the second person is Pierre George from the Department of Mathematics at Tulane University. I will email your advisor right away.]

【Fuck! man!】

【Well done! Support Justice Tulle! 】

Among the jokes, there were some serious replies: [After reading this paper, I took a look out of curiosity, and sure enough, there was a group of idiots discussing Xiao Yi’s breakthrough in the Riemann hypothesis.

As long as you have read the paper, you will know that in Xiao Yi's paper, the results of the Riemann hypothesis are not worth mentioning at all. The reason why he mentioned the Riemann hypothesis in the paper is just to show the role of Xiao's expansion. For a mathematician like Xiao Yi, the breakthrough of the critical line theorem of the Riemann hypothesis is nothing at all. 】

[I read for a while and found that all the comments were worthless. Now I finally found a pertinent review!
This is the fact. The most important thing about Xiao Yi's paper is the Xiao development that he derived using the content of the previous 8 pages!

As long as you have studied complex analysis and can get an A+ in this course, you will definitely be able to see how great an impact the Xiao expansion has on complex analysis. In the simplest way, even if you use it to solve some problems in the complex analysis exam, you can easily discover its incredible effect, just like the Taylor expansion in calculus.

Study hard, my friends. Perhaps, as long as you understand Xiao's expansion clearly, you can write a few good papers in the next two years, just like the previous Etale algebraic variety automorphism theory and parity check classification sieve. And I bet that Xiao's expansion will definitely become a hot research topic in the future, and there will definitely be many journals willing to accept such papers.

I hope you who have read this can believe me, I am not wrong. 】

This long reply comes from a mathematics professor at Cambridge University.

The professor's earnest advice in his reply immediately made most of the students who saw the reply start thinking.

Is this Xiao family development really that powerful?

Some undergraduates began to get excited, especially those who were taking the complex analysis class. They began to think, if they could use Xiao's expansion to solve problems during the exam, they would definitely be able to surprise their teachers, right?
Similarly, some graduate students, post-doctoral fellows, and some mathematics lecturers, associate professors, and other scholars who are in urgent need of results have also begun to be interested. According to this Cambridge professor, if they can use Xiao's work to publish a few more papers, wouldn't their future be bright?
All of a sudden, more and more people began to join in the study.

……

The influence of Xiao's expansion is growing, and more and more people are gradually realizing the significance of this new method. Of course, the research on the critical line approximation method of the Riemann hypothesis has not stopped. On the third day after Xiao Yi published this paper, two more papers appeared on arxiv, one of which approached the critical line to 3%, and the other approached it to 53%.

Obviously, the latter is better, and the author is also a scholar from MIT.

However, both papers indicate that what they have achieved is not the limit and there is still room for improvement.

The results of these two papers have also excited the mathematics community, especially those mathematicians who study the Riemann hypothesis, because this is the first time that they have crossed the critical line of 50%, which means that from the critical line theorem, they are less than halfway to proving the Riemann hypothesis.

If they have completed more than half of the journey in the past 80 years, then will they be able to complete the final journey in less than 80 years?
Countless mathematicians began to look forward to it.

……

"you……"

In Terence Tao's office, it was another day of research group meetings.

The three professors, old, middle-aged and young, surrounded the young man in front of them and looked at him with an indescribable look.

"No buddy, how come you made such a big move in such a short time?"

Tao pointed at Xiao Yi, not knowing what to say, "The Riemann hypothesis has really caused such a big fuss for you."

Xiao Yi scratched his head and explained, "After you saw my expansion method, Terrence, you said it could be used to study the Riemann hypothesis. Then I tried it out briefly when I was organizing my paper that night. After all, the paper just happened to need a case study, and I accidentally..."

"So we accidentally pushed the critical line theorem directly to 50%? Now it's even at 55%, and 60% is possible."

Terence Tao rolled his eyes. Could it be that he was to blame?
James Maynard next to him just wanted to express his opinion.

Damn it, I want to go home!
Ahhhhh!

His mentality has begun to become unbalanced.

How can there be such an awesome person in the mathematics world?

Even for him, who had been known as a math genius since childhood, he began to feel a little overwhelmed.

This guy was able to make such important progress on the Riemann hypothesis, is this a joke?
When he saw the expansion of the polynomial for the first time that day, he didn't realize it. But Xiao Yi figured it out the next day.

Isn't this too shocking?

Perhaps among the three of them, only Kleinlock felt slightly better.

He admitted that he was not good at mathematics and could not compare with Xiao Yi. However, when he saw Terence Tao, who was known as the Mozart of mathematics, and Maynard, who was expected to win the Fields Medal, he looked unbearable.

hmm~
comfortable.

how about it?
Do you feel the same madness as he did at the beginning?

So he reached out his hand and patted the two people next to him and said, "Calm down, calm down. After all, we all know that Xiao Yi is a low-probability event."

Tao and Maynard looked at Kleinrock helplessly.

Why are they so familiar with this sentence?
But in the end, the two sighed again. What else could they say now?

"Okay, okay, let's talk about the main business of today's meeting first."

Kleinrock said: "Now, we have completed the paper on the cross-chain protocol. What remains is to write the program, but it is expected to take no long."

“It will probably be completed in about four days.”

"Then we will submit them to the World Bank together."

"Well, I have also inquired about the movements of other groups during this period. Most of them are still struggling with how to solve the problem of classification and screening. The rest have basically avoided this issue."

At this point, Kleinrock also laughed out loud: "They would never have thought that I would directly bring the person who proposed the classification screen into my team."

"Xiao Yi, this is all thanks to you!"

Kleinlock patted Xiao Yi on the shoulder.

He thought for a moment and said, "By the way, do you need anything? I haven't used the $20 I applied for. I can reimburse you for anything you want to buy within $15."

"Of course, it has to be related to our topic."

Hearing this, Xiao Yi was stunned.

$15?
Let him spend it?

Uh……

"No need!" He waved his hands repeatedly: "This is too much!"

Kleinlock said, "Don't refuse. If you don't spend the money, they will take it back later, so don't waste it."

"You should think about how to spend it."

(End of this chapter)