The top student must be diligent

"In the past, the mathematical community expected that any irreducible polynomial with integer coefficients would assume an infinite number of prime values, provided that it satisfied some obvious local conditions."

"It is also expected that the frequencies of these primes obey a simple asymptotic law."

"However, these asymptotic laws have been shown to only apply to a few special polynomials and not all, so this is also quite a pity."

"To give a simple example, prime numbers in the form x^2+y^4."

"However, I just stated that these are all situations in the past, and now, these problems have been solved to a certain extent."

"That is, the sifting method. In this lesson, I will start with you about the sifting method."

…

The classroom was very quiet, with almost no other sounds except the old professor's voice. The students listened to the old professor's lectures very seriously.

As for the students' seats, they were almost full, and even the aisles were almost full.

No one else, because this old professor is called Henryk Ivanets.

Master of sieve theory and expert in analytic number theory.

Together with another mathematician named Friedlander, he once proved that there are infinitely many prime numbers in the form a^2+b^4. Previously, the mathematical community generally believed that this result was out of reach.

They were able to prove this problem because they further optimized the screening method, thus overcoming various previous difficulties and achieving this heavyweight result.

Later, Zhang Yitang's breakthrough in the twin prime conjecture was also inseparable from the sieving method optimized by Ivanets and others.

The number theory class taught by such a talented mathematician even taught about the sieve method, which naturally attracted many students.

Maybe among so many students, there are some students who came from Princeton University to attend the lectures.

Time passed slowly, and Ivanets spoke very slowly but in detail. At least, every student in the audience could understand it.

Just like that, at the end of the class, Ivanets said with a smile: "Okay, that's it for this class. Now, students who have questions can ask me questions."

Soon, many students in the audience raised their hands, and Ivanets also began to call names and answer these students' questions.

In this way, it was until the fifth student asked a question.

"Professor Ivanets, I recently saw a video on the Internet, and there is some content in it about the sieve method. Some people say that the content above may be useful in solving the sieve theory, which you just mentioned. The parity issue can provide some help. Can I write it down for you to see?"

"Oh?" Ivanets smiled: "I'm glad that students can understand things related to sieve theory before class. Of course, you can come forward and write these things down."

"Okay!" The student nodded excitedly, then quickly walked to the blackboard, took out a piece of copied paper, and started writing on the blackboard.

【A(x)A(√x)(log x)^2】

[∑_(d≤y)μ^2(d)g(d)=c1·log y+c0+O((log y)^-8)】

…

Chapter 98 Twin prime numbers, theorem! 【10,000 updates completed】

【∑_(p≤x)aplog p=HA(x){1+O(log(x)/log(x)}】

…

Seeing what the student in front of him was gradually writing on the blackboard, Ivanets, who was still smiling, began to restrain his smile and analyze these formulas seriously.

To be honest, he didn't think that some videos the student saw on the Internet could provide any so-called help in solving the parity problem.

They studied for so long before they managed to come up with something and achieved a small victory on the issue of parity. How could these young students be able to achieve such cutting-edge results by just finding something in a corner? play a role in the problem?

joke.

Besides, if someone in the mathematics community really came up with such a result, he would definitely be among the first to know about it, because after the mathematics community has such a result, people will definitely think of him and publish it. Give it to him and ask him to evaluate it.

He was among the reviewers of Zhang Yitang's paper.

Therefore, if he were young, he would have immediately criticized this student for reading useless things. As a student of their mathematics department, he would actually believe in some street literature or folk science stuff.

But now that he is older, he wants to be gentle, point out the mistakes first, and then tell these young people not to believe things on the Internet.

Well, with this plot development, everything makes sense.

But now, things are starting to develop in an unreasonable direction.

"Is this a plan to study from the perspective of classification? Such a first step...hiss, a very smart step!"

Ivanets was filled with surprise.

He had discussed the idea of ​​classification with many sieve theory researchers, but they had never come up with a conclusion on how to take the first step of classification.

So in the end they could only shelve such ideas temporarily. In one sentence, their mentality at the time was: believe in the wisdom of future generations.

Although they will most likely never see that day again.

But who would have thought that he would see him today?

Or in your own class?

At this moment, he saw the student stopped and did not continue writing.

He couldn't wait to ask: "What's next? What should we do next?"

"Well, that's all the content of the video I saw."

The student scratched his head sheepishly and said.

"That's all?" Ivanets' heart suddenly felt like it was scratching.

Now he just wants to know how to prove that such sieve classification is feasible!

"Who wrote these things in the video you watched?"

"It's Xiao Yi!" the student replied: "It's the Chinese genius who proved the Elliott-Halberstam conjecture some time ago! I saw in the video that he studied the sieve method to prove the twin prime conjecture, so I I want to ask you if this is possible!”

"It turns out to be that genius..."

Ivanets breathed a sigh of relief. This way, it was logical and reasonable.

After all, Xiao Yi has already used the Elliott-Halberstam conjecture to prove his amazing talent.

However, could that young man from China really be able to bring them some surprises?

He didn't know what to say.

"Professor?" The student asked when he saw the old professor's dazed look.

Ivanets came back to his senses and glanced around the classroom. At this time, all the students were obviously attracted by the news.

That's the twin prime conjecture. Who doesn't want to know about it?

Finally, Ivanets said: "Any success in mathematics is not achieved overnight, but what I want to say is that Xiao Yi has shown that he is ahead of the mathematics community."

"So, I hope and expect that he can succeed!"

The bell rang at exactly this moment, and Ivanets immediately announced: "get out of class is over!"

Then, he quickly left the classroom. He wanted to tell his friends about this.

As Ivanets left, the students in the entire classroom immediately started discussing, and their words were full of disbelief.

Will the twin prime number conjecture be solved by a student younger than them?

crazy!

…

When Ivanets knew about it, it basically meant that the entire mathematical community knew about it.

[Xiao Yi is trying to improve the sieve theory and optimize its existing parity problems. 】

[Xiao Yi is conquering the twin prime conjecture. 】

For a time, there was quite a stir in the mathematical world.

Because he proved the Elliott-Halberstam conjecture and developed the automorphic theory of etale algebraic varieties, and these two papers are still in the review process, there are actually not many people in the mathematics community paying attention to Xiao Yi.

But no one expected that just a short time ago, Xiao Yi would actually start trying to solve the century-old problem of the twin prime number conjecture.

Even, according to those experts, Xiao Yi's first step has been a step that the mathematics community has never thought of before, which means that he is already ahead on this issue.

Even Zhang Yitang stood up and said that Xiao Yi's idea was "advanced" and "innovative".

Of course, there are still some difficulties. Whether he can truly solve this problem will not only take time, but also luck.

After all, inspiration doesn't just come.

…

Max Planck Institute for Mathematics, Bonn, Germany.

"I really didn't expect that he actually started to study the twin prime conjecture."

In the lounge, Schultz looked at the messages on his phone and said to Faltings next to him in surprise.

However, upon hearing this question, Faltings just said with emotion: "It seems that he did not give up on this issue in the end."

Schultz was stunned: "You mean... you already knew that Xiao Yi was studying the twin prime conjecture?"

"Yes." Faltings nodded, "Last time in my office, he told me as soon as he came in that he wanted to study the twin prime conjecture."

"Your office?" Schultz recalled that day and wondered, "I was there at the time. Why didn't I know?"

Faltings shrugged: "You came later, of course you don't know."