In just one day, Xiao Yi's paper appeared again 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 is only the first 8 pages.
This brand-new method, which has begun to be recognized as [Xiao's Polynomial Expansion] by the mathematical community, is gradually understood by more and more scholars in the mathematical community and are surprised by it.
Although the derivation process of Xiao's expansion requires the use of etale algebraic variety automorphism theory and classification sieve theory, not every scholar can understand these two theories, but they do not need to understand the derivation method.
For most people, they only need to know what 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 be able to use it.
Just like the most basic method Taylor expansion, not everyone knows how it is derived, but this does not prevent it from becoming the most commonly used method in the mathematics world.
Probably, the only difference is that the derivation method of Taylor expansion is relatively simple, while the derivation method of Xiao's expansion is much more difficult.
In addition, Xiao Yi mentioned in the paper that using Xiao's expansion to push the critical line of Riemann Hypothesis to 50% is not the limit and can still be improved.
This has also made some scholars flock to it, wanting to try to push Critical Line Theorem to a more extreme level. Maybe they can publish a paper by then.
Even if you can only publish one article from Area 3, for those who are not top scholars, papers from Area 3 are still very good.
After all, not everyone in this world is a great person.
mathoverflow.
This is an online community, but it is exclusive to the field of mathematics. Naturally, the users gathered in this community are basically all professional mathematics scholars.
Normally, it serves as a community for academic exchanges. Mathematics scholars can learn mathematical knowledge from it. If you ask questions on it, there are many experts who can answer it below.
In addition, whenever something big happens in the mathematics world, this online community will also become lively.
For example, these two days.
Regarding the major breakthroughs of Xiao's Polynomial Expansion and Riemann Hypothesis, the discussion on these two topics has exploded on Mathoverflow.
Especially the discussion related to Riemann Hypothesis.
Although professional mathematicians all know that Xiao's expansion is more important, for ordinary scholars, Riemann Hypothesis is obviously more topical.
A title titled [Riemann Hypothesis Critical Line Theorem has made another huge breakthrough. What does this mean for the proof of Riemann Hypothesis? ]'s post attracted a lot of discussion.
[I still have time to ask questions here. I bet a group of people have already started thinking about bringing the Critical Line Theorem implementation closer. How about just publishing a three-zone paper casually? I know that the guy who lives next door to me has already started.]
[It can only be said that a large group of stubborn people will probably get into the dead end of Riemann Hypothesis, thinking that one day they can become the certifier of Riemann Hypothesis]
[Look what you said, who doesn't want to be a mathematician like Perelman? As long as you prove it, you can get Fields Medal, don't you want to?]
[I don't want to because I am over 40 years old.]
[International Mathematical Union will award you a silver Fields Medal stamp]
[Please, not everyone can become a mathematician like Perelman. Before he proved Poincaré Conjecture, he had already been invited by International Congress of Mathematicians to give a report on stage. Can you do it?]
[Although it's a bit rude to say it, I think it's really funny. My tutor has been studying Riemann Hypothesis recently and wants to try to improve last year's 41.7% result to a certain extent. He has already achieved certain results, but now, hahaha! Sorry, I really didn't mean it, but it was so funny!]
[What a coincidence! It turns out that your instructor is also studying critical line approximation methods! The same is true for my supervisor. Today, after he saw the paper Xiao Yi, he became so angry that he almost overturned his desk!]
[This is such a sad story:).]
[Well, I searched the information of the two of you. The first person should be Georgia Randy from the Northeastern University Mathematics Department, and the second person is Pierre George from the Tulane University Mathematics Department. I will send an email to tell your tutor]
[Fake squid! Man!]
[Well done! Support Justice Gossamer!]
Among the bunch of jokes, there was also a more serious reply: [After reading this paper, I took a look at it curiously, and sure enough, there are still a group of idiots discussing Xiao Yi's breakthrough on Riemann Hypothesis.
As long as you have read the paper, you will know that in Xiao Yi's paper, the results of Riemann Hypothesis are not worth mentioning at all. The reason why he mentioned Riemann Hypothesis in the paper is just It is just to show the role of Xiao's expansion. For mathematicians like Xiao Yi, the breakthrough of Riemann Hypothesis Critical Line Theorem is nothing at all.]
[After reading it for a while, it was all filled with worthless comments, and now I finally found a pertinent review!
This is the fact. The most important thing about Xiao Yi's paper is the Xiao's expansion he derived from the content of the previous 8 pages!
As long as you have studied complex analysis and can get an A+ grade in this course, you will definitely be able to see how important Xiao's expansion is for complex analysis. In the simplest way, even if you use it to solve some questions in the complex analysis exam, you can easily find incredible effects, just like Taylor expansion in calculus.
Study hard, friends, maybe as long as you understand Xiao's expansion, you can write a few good papers in the past two years, just like the previous automorphic theory of etale algebraic varieties 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 see this can believe me and I'm not wrong.]
This long reply comes from a mathematics professor named University of Cambridge.
The sincere teachings in the professor's reply immediately made most of the students who saw this reply start to think.
Is this Xiao's expansion really that powerful?
Some undergraduate students began to get excited, especially those who were taking the complex analysis class. They began to think that if they used Xiao's expansion to solve problems during the exam, they would definitely be able to surprise their teachers, right?
Similarly, some graduate students, or postdocs, as well as some mathematics lecturers, associate professors, etc. who are in urgent need of results have also begun to get excited. According to this Cambridge professor, if they can use Xiao's expansion to publish a few more papers, wouldn't their future be bright?
Suddenly, more and more people began to join in the study.
The influence brought by Xiao's expansion is growing, and more and more people are gradually realizing the importance of this new method.
Of course, the research on the Riemann Hypothesis critical line approximation method has not stopped. On the third day after the Xiao Yi paper was released, two more papers appeared on arxiv, one of which approached the critical line to 53%, and the other to 55%.
Obviously, the latter is better, and the author is also a scholar from MIT.
However, both papers stated that what they achieved was not the limit and there was still room for improvement.
The results of these two papers have also excited the mathematics community even more, especially those mathematicians studying Riemann Hypothesis, because this is the first time that they have crossed the critical line across the 50% number, which means that from Critical Line Theorem, they are less than half the way away from proving Riemann Hypothesis.
If they have completed more than half of the journey in the past 80 years, 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 team meeting.
The three professors, old, middle-aged and young, surrounded the young man in front of them, and they all looked at the young man with a look that they didn't know how to describe.
"No, brother, how come you made such a big move in such a blink of an eye?"
Terence Tao pointed at Xiao Yi, not knowing what to say, "Riemann Hypothesis really made such a big noise for you."
Xiao Yi scratched his head and explained, "Isn't this Terence? After you saw my expansion method before, you said that it can be used to study Riemann Hypothesis. Then I simply tried it when I was organizing the paper that night. After all, the paper happened to need a case, and the result was accidentally..."
"As a result, Critical Line Theorem was pushed directly to 50% by accident? Now it has even reached 55%, and it is estimated that 60% is possible."
Terence Tao rolled his eyes fiercely, could you still blame him?
James·Maynard next to me just wanted to express it.
Damn it, I want to go home!
Ahhhhh!
His mentality has begun to become somewhat unbalanced.
How can there be such awesome people in the world of mathematics?
He, who had been known as a mathematical genius since childhood, began to feel a little unbearable.
This guy can even make such important progress with Riemann Hypothesis. Are you kidding me?
When he saw this polynomial expansion for the first time that day, he didn't realize it. The result was good, Xiao Yi was solved the next day.
Isn't this too shocking?
Probably among the three of them, only Kleinrock feels slightly better.
He admitted that he was not good at mathematics and was not as good as Xiao Yi. However, when he saw Terence Tao next to him, who was known as Mathematical Mozart, and Maynard, who was expected to win Fields Medal, he looked like he couldn't stand it.
Hmm~
Feeling comfortable.
How about it?
Do you feel the same madness as he did before?
So he stretched 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."
Terence 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 can they say now?
"Okay, okay, let's talk about the main business of today's group meeting first."
Kleinrock said, "Now, we have completed the paper on the cross-chain protocol. All that is left is to write out the program, but it is not expected to take long."
"It will probably be completed in about four days."
"At that time, we will submit it to World Bank together."
"Well, during this time I also inquired about the trends of other groups. Most of them are still worried about how to solve the problem of classification and screening. The rest have basically avoided this problem."
Speaking of this, Kleinrock also burst out laughing, "They would never have imagined that I would directly bring the person who proposed the classification screen into my group."
"Xiao Yi, this is all thanks to you!"
Kleinrock patted Xiao Yi on the shoulder.
He thought for a while and said, "By the way, do you have any needs? The US$200,000 funding I originally applied for has not been touched much now. If you want to buy anything within US$150,000, I can reimburse you."
"Of course, it has to be related to our topic."
Hearing this, Xiao Yi was stunned.
$150,000?
Let him spend the flowers?
Uh...
"No need!" He waved his hands repeatedly. "This is too much!"
Kleinrock said, "Don't refuse. If this fund is not spent, they will take it back when the time comes, so you don't have to use it in vain."
"You'd better think about how to spend it."