The top student must be diligent.

Chapter 153: Guess, Proof

In the following days, Xiao Yi returned to his normal life.

Once we have figured out the true theory of circle expansion, proving the Goldbach conjecture will no longer be a difficult problem.

This is often the case for many math problems, and solving the problem may be just a small step away.

However, sometimes the difficulty of taking this small step may be so high that it is unimaginable, and you need to develop a very powerful theoretical weapon to support yourself and take the first step forward.

The new circle expansion theory is such a theoretical weapon.

And just like that, another week passed.

……

"Brother Xiao, you're actually going to class with us today?"

In dormitory 313, Ye Cheng and a few others who were packing their schoolbags were stunned when they saw Xiao Yi who was also packing his schoolbags with them.

Based on past experience, didn't Xiao Yi go out at seven in the morning and come back very late at night?
It was surprising enough that they could see Xiao Yi in the dormitory when they got up this morning.

Xiao Yi smiled and said, "Yes, I haven't been to class for a long time. Today I plan to experience student life again."

Ye Cheng and the others immediately rolled their eyes.

My goodness, they are going to class, and you are going to experience life?

can only say……

As expected, it’s Xiao Yi.

However, Ye Cheng's eyes suddenly lit up at this moment: "Then let's go, it's just right, I have some questions to ask you."
"What's the problem?" Xiao Yi raised his eyebrows and couldn't help but become curious.

This kid isn’t the type who likes to ask questions. Most of the time, Ye Cheng studies alone.
Of course, this does not prevent him from achieving excellent results.

According to the final exam results of last semester, Ye Cheng ranked first in the class with a full GPA of 4.3 - the GPA of their China University of Science and Technology is 4.3, which means that every grade must be above 95 points.

This is really impressive. You know, this class is actually very competitive. After all, there are such excellent people around them, so people in the class can only compete. In order to distinguish their grades, the test questions will be more difficult than the normal test questions of the School of Mathematics.

Being able to get full marks under such circumstances, Ye Cheng must have worked hard.

Of course, Xiao Yi’s results are not included in these results, after all, his test items are different from those of others.

"I'm currently working on a paper and I'm having a bit of a hard time..."

Ye Cheng explained.

However, before he could finish his words, Song Ziyang and Luo Qiao beside him suddenly widened their eyes.

"What? You guys have already started writing your paper? When did you start writing it?"

"Fuck, you play games with us every day, but you're secretly cheating behind our backs, right?"

Ye Cheng argued, "No way! I wrote it openly, okay? It's just that you didn't notice it!"

"When did you write it openly?"

"I wrote it in the library. I never hid it. It's just that you didn't find me when you came to the library."

"Still quibbling! Lao Song, get him!"

"Fuck him!"

Then Xiao Yi witnessed the process of Ye Cheng being hung up and beaten.
He shook his head in amusement.

Then he joined the battle and secretly tickled Ye Cheng twice.

Ye Cheng: "You are bullying in school!"

……

Today's class is number theory.

When they arrived at the classroom, there were already quite a few people sitting inside.

And Xiao Yi's appearance once again attracted the attention of his classmates.

After greeting these classmates, Xiao Yi also found a seat and sat down with his roommates.

"Brother Xiao, I feel like you're a star every time you come to class."

Ye Cheng noticed the various looks coming from around him, and whispered to Xiao Yi.

Xiao Yi rolled his eyes: "You think I want to."

That's why he rarely goes to class.

Ye Cheng chuckled, and then without saying anything more, he took out his laptop from his schoolbag and said to Xiao Yi: "Brother Xiao, help me analyze the problem I am facing now."

They turned on the computer, entered the document, and started reading.

Song Ziyang and Luo Qiao next to them also came over to take a look. Wow, this kid has already written more than ten pages of the thesis.

It’s hidden so deeply.

The two of them looked at it silently for a while, and finally took out the book and started studying.

They have to write papers too!
……

After Ye Cheng took out his computer, he began to talk about his problem. After one look, Xiao Yi quickly figured it out.

His thesis was about problems in the field of algebraic geometry, which surprised Xiao Yi a little. He didn't expect that this kid would actually start studying algebraic geometry.

Perhaps it has something to do with the Schulze edition of "Principles of Algebraic Geometry" that he brought back from Germany.

As for the topic of the paper, it mainly involves layers and layer clusters on algebraic clusters, and explores their applications in algebraic geometry.

"To put it in a nutshell, your question is how to calculate the layer cluster homology group of an algebraic variety in the projective space," Xiao Yi concluded.

Ye Cheng nodded: "Yes, I always feel a little troublesome in this regard."

Xiao Yi smiled and said, "After all, you are a beginner, so it is normal to find it troublesome."

"As for the problem you encountered, I won't give you a detailed explanation. You can solve it yourself later."

"Let me give you an example."

"Suppose we study the sheaf homology group H^i(X, OX(d)) of a bundle of lines OX(d) on an algebraic variety X on the projective plane P^2, where OX(d) denotes a twisted bundle of lines on X and d is the degree of twist."

"To compute the sheaf homology group H^i(X, OX(d)), we can use the sheaf homology theory on projective space."

"Bott's norm theorem, and Searle's theorem."

“Do you know these two theorems?”

Hearing Xiao Yi's question, Ye Cheng nodded: "I know! Searle's theorem is in EGA, and I learned Bott's norm theorem from another book."

"That's good." Xiao Yi raised his eyebrows and said, "Then let's get straight into the specific calculations."

"First, on the projective plane P^2, we consider X=P^2 and calculate the homology group of O(d). According to the Bott norm theorem, for d greater than 2, we have..."

【H^i(P^2, O(d))=0, i>0】

"This result tells us that for sufficiently large d, only H0 can be non-zero."

“After that, we continued to introduce…”

As Xiao Yi spoke, Ye Cheng kept nodding, indicating that he understood.

Finally, he said happily, "So that's it! I understand!"

Xiao Yi smiled and nodded: "That's good, the main thing is to expand your knowledge as much as possible."

"Also, after using the Bott norm theorem, you can use the Riemann-Roch theorem to treat the straight line bundle on P^2."

"Riemann-Roch theorem?" After thinking for a while, Ye Cheng's eyes suddenly lit up again: "I understand!"

"Hmm." Xiao Yi asked again at this time: "How much of that EGA have you read?"

Ye Cheng said a little embarrassedly: "I have finished reading it, and now I have started reading it for the third time, but there are still many things in it that I don't understand at all."

"Just take your time and watch it. There's no rush." ​​Xiao Yi said, "After all, it's EGA."

Looking at Ye Cheng, Xiao Yi couldn't help but recall the scene when he first met him. At that time, Ye Cheng said that his goal was the Fields Medal.

Obviously, he is constantly working towards that direction.

However, Song Ziyang and Luo Qiao next to them couldn't sit still anymore: "What the hell? You're watching this for the third time?"

At the beginning, Xiao Yi also gave them both a copy, but they didn't even finish reading it for the first time. This kid...

Just when they were about to jump up and punish the kid who cheated on the test, they saw the substitute professor for this class walk in.
"I'll deal with you when I get back."

Two people: Husky pointing at people.jpg
……

The substitute professor of their number theory class was named Wang Bolin. After walking into the classroom, he took a quick look and then saw Xiao Yi.

He laughed and said, "Wow! I never thought that my class would attract such a big shot."

Of course everyone knew who Professor Wang was talking about, and they all started laughing.

"If we talk about the most outstanding scholars in number theory in the current mathematics community, the great man who came to our class today can definitely be included in the list."

"I, a little professor, wouldn't dare to give a lecture in front of him."

Professor Wang said, "Well... so I have a suggestion. Why don't we let him give a lecture to everyone? What do you think?"

The students below immediately became happy: "Great!"

Let Xiao Shen give them lectures?
Is there such a good thing?

Everyone looked at Xiao Yi: "God Xiao, go ahead!"

Ye Cheng and others nearby were gloating.

Song Ziyang: "Brother Xiao, you just told Cheng'er so well, tell the brothers about it too!"

Looking at the scene in front of him, Xiao Yi's mouth twitched.

What the hell.

This is the legendary flipped classroom, right?

But other people’s flipped classrooms require all students in the class to take the course, but his class only flips the course to himself, right?
Professor Wang, who was standing on the podium, looked at Xiao Yi with a smile and said, "Go ahead! You see everyone is so enthusiastic, it's hard to refuse such a kind invitation! Today I just happen to be a student, so I will listen to Teacher Xiao's teachings. You can talk about whatever you want."

Xiao Yi sighed helplessly. He originally came here to experience life, so how did he become the one being experienced?
Okay, just tell me!

Stand up, leave your seat and walk to the podium.

Professor Wang sat directly in his seat.

Ye Cheng and the others beside him immediately began to sweat profusely, and they sat up straight, not daring to move. Xiao Yi, who had walked to the podium, was delighted to see this scene, but then it was his turn to get tangled up.

What are you talking about?
He had never attended class before, so he didn't know how far their course had progressed.

However, Professor Wang also said that he could talk about whatever he wanted.

Ok……

His eyes lit up and he had an idea.

Since this is a number theory class, why not just talk about the Goldbach conjecture directly?
It just so happened that he was only a few steps away from solving the Ge guess, and all that was left was to organize the paper. He could use this class to sort out some of the previous parts.

uh-huh.

It's a good opportunity for my classmates to get in touch with these cutting-edge mathematical knowledge.

Of course, in order to avoid students not understanding at the beginning and scaring them, it is better to start with the most basic.

The corners of his mouth curled up.

As his roommates, Ye Cheng and the other two suddenly felt that their lives were in danger.

Xiao Yi said: "Then, I will start with a very basic method in number theory."

The words "Sieve method" were written on the blackboard.

The eyes of the students below suddenly lit up.
They knew how amazing Xiao Yi's achievements in the screening method were. After all, it was an achievement that could change the world's cryptography system.

Even Professor Wang became very interested and began to focus his attention.

Only Ye Cheng and a few others became increasingly uneasy.

……

"I wonder if you still remember that in our joint entrance examination, we took the test on Mr. Chen Jingrun's paper on proving the Goldbach conjecture."

"And in that problem, we need to use the most basic sieve method - the sieve of Ehrlich."

The students present immediately recalled the question they had taken in the exam, and they still remembered it clearly.

"Then, let's start with the sieve method and discuss how Mr. Chen Jingrun obtained the sieve method."

"..."

Xiao Yi began to speak.

Although everyone in the class knew what the Sieve of Ehrlich method was, Xiao Yi's explanation gave them different ideas.

Moreover, as Xiao Yi gradually introduced modern sieve methods, such as the Brown sieve and the Selberg sieve, it also brought them a lot of inspiration.

Ye Cheng and the others were at a loss.

Eh?
What about their ominous premonition?

Is Brother Xiao really teaching seriously?
"... Next, we discuss the sieve method used by Chen Jingrun in his study of the Goldbach conjecture."

"His sieve method was derived from the Great Sieve, and the basic idea was to control the distribution of primes and almost primes by estimating the number of numbers in certain sets - almost prime means that a number has exactly two different prime divisors."

"…he constructed a suitable number set A and defined a sieve set P…then used the large sieve inequality to estimate the number of numbers remaining after removing multiples of P from A…"

As Xiao Yi finished explaining the sieving method used by Chen Jingrun, the students below were gradually fascinated by his speech. He changed the subject and said, "However, we need to note that the sieving method alone is not enough for Mr. Chen Jingrun to complete his conclusion. The circle method is also needed."

He smiled slightly, "Mr. Chen Jingrun combined his sieve method and circle method to finally complete the proof of 1+2."

"But... 1+2 is not 1+1."

"Whether we can turn 1+2 into 1+1 depends on how to further screen the almost prime numbers in the screening set P."

"So……"

"We might as well try to combine the sieve method and the circle method! Let them form a new theory to help us do further screening."

Turning around, Xiao Yi started writing on the blackboard.

[|S(A,P)|≤logP|A|……]

Finally, the students below realized that something was wrong.

What?
Turn 1+2 into 1+1?

Did they hear it correctly?

If it becomes 1+1, doesn't that prove my guess?
Professor Wang was also confused.

What’s going on? Aren’t they in class?

Why did it suddenly feel like the scene of a top-notch mathematics lecture?
Seeing Xiao Yi simply listing a few derivation formulas on the blackboard, the amount of information hidden in them is far beyond what students of this grade can understand.

It’s beyond the scope!

When Ye Cheng and the others next to them saw this, they immediately burst into tears.

As expected, Brother Xiao is still their Brother Xiao.

That's it!

……

"... Now we introduce a type of polynomial expansion method. Well, according to the name in the mathematical community, we generally call this method Xiao expansion."

Xiao Yi said a little shyly.

Although it is quite common in the scientific community to name mathematical methods after one's surname, it still sounds quite pretentious when one says it - of course, he is still slightly different because the Xiao expansion is a name given by the mathematical community, not something he named himself.

"The principle of Xiao's expansion is combined with the parity classification sieve. In the process of using it, we can easily find that there is some harmony between the circle method of Xiao's expansion. In other words, we can use this method to combine the circle method and the sieve method in another form."

[L′/L (s′, ψ)=∑|ρs′|<1(1/s′ρ)+ O(1/α…]

Xiao Yi became more and more engaged as he spoke, which almost helped him to re-familiarize himself with the entire proof process.

However, after seeing the increasingly outrageous deductions, the students in the classroom finally gave up thinking.

Aren’t they here to attend the class?
How did it become like this?
……

"Dingling bell~"

Finally, the long-awaited ringing bell finally rang.

Xiao Yi stopped his hand with a feeling of unfulfilled desire and said, "Since the get out of class is over, let's stop here for this class and continue in the next class."

The students below immediately showed expressions of horror.

what?
Again?

Professor Wang couldn't sit still anymore, so he hurried over and said, "Just stop here. I still have to explain the contents of the book to the students in the next class."

"That's it, okay then."

Xiao Yi had no choice but to nod.

Well, what a pity.

At this time, the students finally breathed a sigh of relief.

Fortunately, fortunately, I don’t have to suffer in the next class.

For the students in Hua Luogeng's class, today's class was a lesson for them. That is, in the future, they should never sit idle and ask Xiao Yi to give them lectures. Otherwise, they will be the only ones to suffer.

……

Although he was unable to continue teaching everyone, Xiao Yi, in the second period, managed to attend the class normally as he wished.

At least I got to experience student life.

After class, Xiao Yi once again plunged into the entrepreneurship base and began to write his thesis.

The class also helped him sort out all the previous processes, which greatly facilitated his final step in completing the Goldbach conjecture.

And so, four days later.

……

"… In summary, we can prove that any even number greater than 2 can be expressed as the sum of two prime numbers."

"Goldbach's conjecture, proved."

"2n, equals p+q!"

He put down the pen and rubbed his wrist.
This problem that spanned hundreds of years of history finally came to an end in his hands.

He also officially solved two of the three problems involved in Hilbert's eighth question, and the only one left was the Riemann hypothesis!

But after waiting for a long time in my mind, I didn’t hear the sound of BUFF upgrading.

Xiao Yi shook his head helplessly.

Obviously, the Goldbach conjecture cannot be evaluated with high value.

It can only be said that this is within expectations. After all, the twin prime conjecture is only of medium value.

“Are we really going to prove the Riemann hypothesis?”

This issue can probably only be discussed later.

"Okay, now the question is, where should I publish the paper?"

Because it hasn't been long since the paper on absolute electronicity calculation was published, and many people are still discussing it, he doesn't plan to put it directly on arxiv, to avoid causing a huge shock to the world once it is published.

It is better to submit directly to the journal.

"We can't take up too many social resources."

This is what he thought in his heart.

Actually... he just wanted to relax a little during the period between submission and review.

Then welcome the attention of the whole world.

He could almost imagine what a huge shock it would cause when the news of the proof of Goldbach's conjecture spread.

"What a happy trouble..."

Xiao Yi rubbed his head which was a little aching.

……

(End of this chapter)