The top student must be diligent

Hey, he never said that he was studying the twin prime conjecture?

"How do you know that I'm studying the twin prime conjecture?"

"Brother Xiao, don't you know?" Ye Cheng asked back: "Last month, the video of you using three methods to solve problems in Professor Liu's mathematical analysis class was taken by Qin Le from our class. He then posted it on Bilibili, and it became popular. Then..."

Listening to Ye Cheng's story, Xiao Yi was surprised. He simply wrote his ideas about the sieve method on the blackboard, and others guessed directly that he wanted to study the twin prime conjecture?

Even now the entire mathematics community knows about it, and they are all paying close attention to it?

Is it really that exaggerated?

Well, it's actually quite reasonable, and it can indeed be connected. After all, the Elliott-Halberstam conjecture he studied before is closely related to the twin prime conjecture.

At this time, Ye Cheng said again: "Oh, by the way, there is one more thing. I saw in the news two days ago that your previous theory of self-restraint of etale algebraic clusters and the paper proving the Elliott-Halberstam conjecture have passed the review of the Annals of Mathematics. You don't know this, do you?"

Xiao Yi slapped his head immediately. In the past two months of studying the twin prime conjecture, he almost forgot that his previous two papers were still under review.

But fortunately, it was just a few days ago, and it was not too late.

He immediately returned to his seat, turned on the computer and entered the mailbox.

As a result, as soon as he entered the mailbox, he saw that he had more than 100 unread emails.

"I remember that I had dealt with all the emails that communicated with me about the self-restraint theory of etale algebraic clusters before?"

He was so confused that he clicked in and scratched his hair frantically.

"This is fucking..."

In addition to the more than 100 new emails, there are now many more emails from mathematicians who want to discuss the classification of parity problems with him because they watched his video.

Most of them were sent last month. This month is relatively less, but there are still some, such as one yesterday.

If I reply to these emails one by one, I don't know how long it will take.

What's more...

He has already solved the classification of parity problems, and the twin prime conjecture has been proved.

These emails that want to discuss with him are no longer necessary.

He pinched his eyebrows.

It seems that his original plan to have a good rest today will also be in vain. He has to sort out the paper as soon as possible as a response to these emails.

Otherwise, someone might send him an email in a while.

Just as he thought of this, he saw a notification pop up on his mailbox, prompting that he had received another new email.

As expected, it was an email from a mathematics professor at Trinity College, Cambridge University.

He shook his head helplessly and ignored it.

He first looked for any emails from the Annals of Mathematics. Since the two papers had passed the review, he had to sign a Copyright Transfer Agreement with them so that the papers could be published.

He flipped through his mailbox and saw a notification email from the Annals of Mathematics four days ago, informing him of the final review results of the two papers.

First, there was a big [Accepted], and then the comments on his two papers.

As the chief reviewer of the review committee, Enrico Bombieri gave the following evaluation: [Rigorous, innovative, high-value, and major breakthroughs, there is no doubt that these two papers are a gift from a mathematical genius to the entire mathematical community. ]

The other three main reviewers also gave similar evaluations.

Tao also added a joke: [I think many people in the mathematical community will be unable to sleep. 】

Looking at these comments, Xiao Yi couldn't help but smile, then he clicked on the copyright transfer agreement link below, signed the electronic agreement, and finally replied to the email with a thank-you letter.

The three roommates who had been watching him busying around couldn't help but feel envious in their hearts.

This is probably a case of talking and laughing with great scholars, and no unlearned people coming and going, right?

After doing all this, Xiao Yi began to prepare to organize the twin prime conjecture and his optimized sieve method paper.

This is a big project. He estimated that he would have to organize sixty or seventy pages. The draft paper used in the past two months is estimated to be hundreds of sheets.

Without saying more, he skillfully entered LaTex and began to edit the document.

Ye Cheng and others watched Xiao Yi constantly edit some words and mathematical formulas in the document that seemed like heavenly books to them, and probably guessed that this was the proof of the twin prime conjecture.

Of course, the title of the paper has also made this clear.

"Parity Check Sorting Sieve and Twin Prime Conjecture"

The plain title is completely extraordinary in the world of mathematics.

The three people watched helplessly as such a paper that might... should be "definitely" able to go down in the history of mathematics was born.

No one knows what they are thinking, but after a while, Ye Cheng returned to his seat, took out his books and started studying.

A few days passed leisurely.

…

In the office of a professor in the Department of Mathematics at the University of California, Santa Barbara.

The owner of this office is Zhang Yitang.

The world of mathematics is a very pure world, or in other words, a world where the strong are respected.

As long as you have strength and have made real achievements, you can get everything, no matter how down and out you have been.

And Zhang Yitang is obviously a good example.

Before officially publishing the paper "Bounded Gaps Between Prime Numbers" in 2013, he was just an ordinary lecturer at the University of New Hampshire, which is a non-first-class university in the United States. It is not an exaggeration to describe it as a fake university.

Ordinary, indistinguishable from the crowd.

After that, he went directly to the University of Santa Barbara, became a professor of mathematics, had his own office, won 4 mathematics awards in less than two years, and became a respected master of analytic number theory.

Perhaps the only regret for him is that he was already close to 60 years old when he became famous, so he once said that his favorite poem was: Yu Xin's life was the most desolate, and his poems in his old age moved the Jiangguan Pass.

Of course, after achieving such outstanding results, he did not devote his energy to enjoyment, but still devoted himself to solving more mathematical problems in his old age, such as the Landau-Siegel zero conjecture he is currently studying.

The Landau-Siegel zero conjecture may not be so famous outside the mathematical community, but for people in the mathematical community, half of the answer to this question can help them find the truth of the Riemann hypothesis.

Its purpose is to prove whether the Landau-Siegel zero exists. Once it exists, it is equivalent to finding a counterexample to the Riemann hypothesis, which is equivalent to directly proving that the Riemann hypothesis is wrong.

Of course, for the mathematical community, it is generally believed that the Landau-Siegel zero does not exist. After all, the mathematical community also generally believes that the Riemann hypothesis must be established.

Standing in front of the blackboard, Zhang Yitang pinched his chin, his eyes under the black-framed glasses were full of thoughtful light.

"The existence range of the real number sequence depends on Cantor's real number continuum hypothesis, but the hypothesis is not a proof. Unfortunately, Gödel had already stated that the continuum hypothesis was unprovable..."

"It's difficult."

Shaking his head.

As he got older, he could no longer find the feeling when he broke through the twin prime conjecture.

"If you want to achieve a breakthrough, you may still have to rely on the sieve method. How to push the sieve method to a more extreme level?"

Thinking of this, a name flashed in his mind.

Xiao Yi.

He had also watched Xiao Yi's video, but unfortunately, like most people in the mathematics community, even if he saw how Xiao Yi took the first step, he couldn't think of how to take the second step.

"I don't know if he has replied to the email I sent him."

He returned to his desk at this point, opened his mailbox on the computer and took a look. There was no email from Xiao Yi.

"I heard that other people haven't received his reply either. I guess they are still studying the twin prime conjecture."

"Forget it, go to arxiv to see if there are any papers on this topic."

Thinking of this, he opened arxiv and browsed it.

But just after searching, he saw a title.

"Parity Check Sorting Sieve and Twin Prime Conjecture", author, YiXiao.

His eyes widened immediately.

What is this?

He took off his glasses and rubbed his tired eyes, then put on his glasses again and looked at it, and he was immediately refreshed.

"Did Xiao Yi...complete the proof of the twin prime conjecture?"

He immediately clicked on this paper in a hurry and downloaded the PDF file.

Then he looked at the abstract.

[It is proved that lim(n→∞)inf(pn+1pn)=2, where pn is the nth prime number.

The method used in this paper is an improvement on the work of Zhang Yitang, Tao Zhexuan, and J. Maynard on sieve theory. A major component of the proof is a stronger version of the Friedlander-Ivaniec theorem. At the same time, a relatively accurate classification is completed for different categories in the parity check problem, so as to achieve an accurate estimate of the number of prime factors of infinite natural numbers. Although the final result is less than 3, it is enough to meet the purpose of proving the twin prime conjecture. 】

……

Chapter 100 The shock of the mathematical community

After reading this abstract, Zhang Yitang couldn't help but get excited.

If this paper is completely correct, then he already has a hunch that this parity check classification sieve will definitely provide great help to his current research on the Landau-Siegel zero conjecture!

"The previous Etale algebraic variety automorphism theory did not make me a beneficiary. Could it be that this time, I will become a beneficiary?"