The top student must be diligent

Because he also saw it.

Perhaps this method will become the most immortal method in the entire field of complex numbers, just like the analytic extension in complex analysis!

…

After Faltings and Schultz finished reading this short 21-page paper, more and more people in the mathematics community have discovered this quietly appearing paper.

Just like the two of them, these scholars in the mathematics community were initially very curious about the title and abstract of Xiao Yi's paper.

How awesome is the expansion of this polynomial to make the major breakthrough of the Riemann hypothesis just a kind of extra content.

And similarly, after they finished reading the first 8 pages, what was left in their hearts was a strong sense of disbelief.

Mathematics, can it be studied like this?

Chapter 117 How to spend 10,000 US dollars? Waiting online

Chapter 117 How to spend 150,000 US dollars? Waiting online

Chapter 117 How to spend 150,000 US dollars? Waiting online

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

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

Although the derivation process of Xiao's expansion requires the use of Etale algebraic cluster automorphism theory and classification sieve theory, and not every scholar can understand these two theories, they don't 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 know how to use it.

Just like the most basic method of Taylor expansion, not everyone knows how it is derived, but it 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 relatively simple, while the derivation of Xiao expansion is much more difficult.

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

This also makes some scholars flock to it, wanting to try to approach the critical line theorem to a more extreme degree, maybe they can publish a paper at that time.

Even if they can only publish a third-area paper, for those non-top scholars, a third-area paper is also very good.

After all, not everyone in this world is a big shot.

…

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.

Usually, it is a community for academic exchanges. Mathematicians can learn mathematical knowledge from it. If they ask questions on it, there are many big shots answering below.

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

For example, these two days.

The discussion of Xiao's polynomial expansion and the major breakthrough of Riemann hypothesis has exploded on Mathoverflow.

Especially the discussion of Riemann hypothesis.

Although professional mathematicians know that Xiao's expansion is more important, for ordinary scholars, Riemann hypothesis is obviously more topical.

A post titled [The critical line theorem of Riemann hypothesis has made another great breakthrough. What is the significance of proving Riemann hypothesis? ] attracted a lot of discussion.

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

[I can only say that next, it is estimated that a large number of stubborn people will get into the dead end of Riemann hypothesis, thinking that they can become the prover of Riemann hypothesis one day]

[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 give 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 by the 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 this is really funny. My mentor has been studying the 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's really funny! ]

[What a coincidence! It turns out that your advisor is also studying the critical line approximation method! My advisor is the same. Today, after he saw Xiao Yi's paper, he became furious and almost overturned his desk! ]

[This is a really sad story:). ]

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

[Fuck! man! ]

[Well done! Support Justice Tulpa! ]

Among the jokes, there were also more serious replies: [After reading this paper, I took a look out of curiosity. Sure enough, there are still 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 it for a long time, and it was all worthless comments. Now I finally found a pertinent evaluation!

The fact is that the most important thing about Xiao Yi's paper is the Xiao expansion he derived from the first 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 great the role of Xiao's expansion is for complex analysis. The simplest way is to use it to solve some problems in the complex analysis exam, and you can easily find incredible effects, just like the 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 next two years, just like the previous Etale algebraic cluster 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 see this can believe me, I will not be wrong. 】

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

And the earnest teachings in the professor's reply immediately made most of the students who saw this reply start thinking.

Is this Xiao's expansion really that powerful?

Some undergraduates began to be tempted, especially those who are taking the complex analysis class. They began to think that if they use Xiao's expansion to solve problems during the exam, they will definitely be able to surprise their teachers, right?

Similarly, some graduate students, or postdoctoral fellows, and some mathematics lecturers, associate professors, and other scholars who are in urgent need of results have also begun to be tempted. According to this Cambridge professor, if they can use Xiao's expansion to publish more papers, their future will not be bright, right?

At one time, more and more people began to join in the study.

…

The influence of Xiao's expansion is getting bigger and bigger, 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 did not stop. On the third day after Xiao Yi published this paper, two more papers appeared on arxiv, one of which approached the critical line to 53%, and the other approached it to 55%.

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

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

The results of these two papers have also made the mathematical community more excited, 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 perspective of the critical line theorem, they are less than halfway to prove the Riemann hypothesis.

If they have completed more than half of this journey in the past 80 years, then can they walk the last journey in less than 80 years?

Countless mathematicians began to look forward to it.

…

"You..."

In Tao's office, it was another day of the research group meeting.

The three professors, old, middle-aged and young, surrounded the boy in front of them, and looked at him with a look that they didn't know how to describe.

"No, buddy, how come you made such a big move in a blink of an eye?"

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

Xiao Yi scratched his head and explained: "Isn't it that Terrence, after you saw my expansion method before, you said it could be used to study the Riemann hypothesis, and then I tried it simply when I was organizing the paper that night. After all, the paper just needed a case, and I accidentally..."

"As a result, I accidentally pushed the critical line theorem directly to 50%? Now it has even reached 55%, and it is estimated that 60% is possible."

Tao rolled his eyes fiercely. Could it be that he was still blamed?

James Maynard next to him just wanted to express in his heart.

Fuck, I want to go home!

Ahhhh!

His mentality has begun to become unbalanced.

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

This made him, who was also known as a mathematical genius since childhood, start to feel a little bit overwhelmed.

This guy could make such an important progress even on the Riemann hypothesis, what a joke?

When he first saw the polynomial expansion that day, he didn't realize it, but Xiao Yi figured it out the next day.

Isn't this too depressing?

Among the three of them, only Kleinrock felt a little better.

He admitted that his math was not good and could not compare to Xiao Yi, but seeing the so-called Mathematical Mozart of Tao and Maynard who was expected to win the Fields Medal, they all looked like they couldn't stand it.

Well~

It feels good.