Time passed quickly.
When there were only five minutes left before the Mathematical Analysis class started, as a substitute teacher, Liu Bin also appeared in the classroom.
I simply glanced at the students in the classroom, mainly to see if the number of students matched the impression I had. Hua Loo-Keng Class had allocated so many resources, so naturally it did not want the students not to study seriously enough, or even to be absent from class.
However, it seems that there is no shortage of people.
Suddenly, his eyes stopped at the third row, showing a little surprise.
Xiao Yi actually came to his class?
Then he smiled and nodded towards Xiao Yi.
Xiao Yi was the one he discovered USTC. At first, he only thought that this was a very talented student, but he never expected that not long after this child had just emerged, he would start to make waves in the entire mathematics world.
Now he has become a rising star in the world of mathematics, which makes him deeply moved.
Xiao Yi noticed Liu Bin's gaze, and then nodded to the professor who had provided him with a lot of help.
Of course, he is very grateful to Liu Bin. To a certain extent, it was Liu Bin who officially brought him into the mathematics major. The many books Liu Bin gave him at the beginning were also the key to his ability to achieve this level in multiple directions of mathematics.
This is a respectable elder.
Five minutes passed quickly.
As the class bell rang, Liu Bin stood on the podium.
"Today's class begins."
"Let's continue the limit of the sequence that we talked about in the previous lesson. What we are going to discuss in this lesson is the existence criteria of the limit of the sequence."
"First, we have to consider whether there is a limit to a certain sequence..."
When the class started, every student in the class quieted down and began to listen to the class carefully.
As students of Hua Loo-Keng Class, they often preview in advance before class. This is also the most basic requirement for being an "elite" among mathematics students.
There are also some students who have read the entire book.
However, even if they have finished studying, they will still listen to this lesson carefully. After all, maybe they can get some other insights from the teacher's narration?
However, for Xiao Yi, the things taught in this class are still too simple for him.
Maybe he can write an SCI with any idea in his mind about the existence criteria of the limit of a sequence, and expand it a little.
However, he still listened carefully, and at the same time, he was thinking about his next goal in his mind - doing two things at once was not difficult for him now.
The solution to the Elliott-Halberstam conjecture did not satisfy him, because the completion of this problem, and even the [etale algebraic variety automorphic theory], were to some extent a by-product of his efforts to achieve his ultimate goal.
And his ultimate goal has never changed.
That is, [Twin Prime Conjecture].
Probably 99.9...% of the scholars in the mathematics community have never thought about it, nor will they think about it, that Twin Prime Conjecture is the ultimate goal of Xiao Yi.
Perhaps, only Faltings can probably guess this.
After all, when he was in the offices of Max Planck Institute for Mathematics and Faltings, he found Faltings just for Twin Prime Conjecture.
The Elliott-Halberstam conjecture also comes from the suggestion of Faltings.
Now, the Elliott-Halberstam conjecture has become a theorem. With this result, the progress of Twin Prime Conjecture has reached the number "6".
But what to do next?
Xiao Yi felt like he had touched the final chasm of Twin Prime Conjecture.
And this gap is too far, so he can't even find a bridge that can bridge the gap, let alone other things.
"Sure enough, my understanding of mathematics is not deep enough."
He couldn't help but sigh in his heart.
Of course, he was not discouraged by it.
After all, no mathematician has ever developed a method to directly prove Twin Prime Conjecture under the assumption that the Elliott-Halberstam conjecture is true, but it can only be advanced to within 6.
This fully shows that there are still some difficulties in between.
Shaking his head slightly, he took his mind away from Twin Prime Conjecture and focused on this class again.
"... Then next, I will give an example and talk about it."
At this time, Liu Bin on the stage said.
He has finished talking about the knowledge to be taught in this class, and is ready to consolidate the knowledge just taught based on the questions.
Soon, he wrote a question on the blackboard.
A relatively classic question.
[If lim(n→+∞)xn=a, prove that lim(n→+∞)(x1+x2+...+xn)/n=a.]
"Let's think about this question and see how to do it." Liu Bin said.
After about a minute, he asked, "Does anyone know how to do this?"
Most of the students nodded.
"Very good, then I will pick two people to come up and give it a try." Liu Bin nodded, and then called the names: "Ye Cheng, Zhang Zhilan."
Ye Cheng immediately stood up and went on stage with Zhang Zhilan.
Soon, the two people started writing on the blackboard, and two completely different proof methods also appeared on the blackboard.
"Well, very good. Zhang Zhilan uses the simplest method, which is to use Stolz theorem to solve it. It simplifies the whole problem and then it can be easily solved."
"As for Ye Cheng... although I don't agree with his method of hard proof, it is indeed a strength to be able to prove it hard."
"That's right, I'll give you a regular score."
"Oh yeah!"
Ye Cheng returned to his seat and shook his fist.
Liu Bin continued at this time, "Well, I believe you all have seen that classmate Xiao Yi has come to this class. Recently, classmate Xiao Yi solved a conjecture related to prime numbers in mathematics. Then I will also come up with another extreme problem related to prime numbers. It is also a challenge problem. Let's try it."
Then he began to write the challenge question on the blackboard.
The students in the class immediately paid attention.
Challenge questions related to prime numbers?
[Record w(n) as the number of different prime factors of the positive integer n, record the prime number sequence as pn, and record the sequence an=n∏k=1(pn).
Proof: lim(n→+∞)[w(an) lnw(an)]/ln(an)=1.]
"Well, let's see who of you can solve this question." Liu Bin said.
Most of the students present immediately masked their pain.
Is this challenge a bit too challenging?
Of course, there are also students like Ye Cheng who immediately started thinking.
Although it is difficult, you still have to think about it!
And Xiao Yi...
When Liu Bin finished writing this question, he already had an idea.
However, his idea is slightly different...
"If you use the sieving method..."
His eyes narrowed slightly.
A flash of inspiration suddenly flashed in his mind.
On a certain gap, the shadow of a bridge seemed to flash.