In the following days, Xiao Yi returned to his normal life.
Once the real Circle Method Expansion theory is figured out, proving Goldbach Conjecture will no longer be a problem.
This is often the case for quite a few mathematical problems. There may only be a small step away from solving the problem.
However, sometimes it may be unimaginably difficult to take this small step, and you need to develop a very powerful theoretical weapon to be able to support yourself and take it completely.
The new Circle Method Expansion theory is such a theoretical weapon. What to charge
Just like that, another week passed.
"Brother Xiao, you actually want to go to class with us today?"
In the 313 dormitory, Ye Cheng and several others were packing their schoolbags. They were stunned when they saw Xiao Yi who was also packing their schoolbags with them.
According to past experience, wouldn't Xiao Yi have already gone out at seven o'clock in the morning and come back very late at night?
It was surprising enough just to see Xiao Yi in the dormitory when they got up this morning.
Xiao Yi smiled, "Yes, I haven't gone to class for a long time. Today I plan to experience the life of a student again."
Ye Cheng They all rolled their eyes immediately.
Good guys, they are going to class, and you are going to experience life?
All I can say is...
As expected of Xiao Yi.
However, at this moment, Ye Cheng's eyes suddenly lit up. "Let's go, let's go. 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 is not the kind of person who likes to ask questions. Most of the time Ye Cheng is doing research alone.
Of course, this does not prevent him from doing very well.
According to the final exam results of last semester, Ye Cheng ranked first in the class, and their full grade point was 4.3 - their grade point of University of Science and Technology of China is 4.3 points, which means that each score must be above 95 points.
This is very impressive. You must know that their class is actually very difficult. After all, they are surrounded by such outstanding people, and the people in the class can only take the exam. In order to distinguish their grades, the test questions will be more difficult than the normal test questions in the Mathematics School.
Being able to still get full grade points under such circumstances is a tribute to Ye Cheng's hard work.
Of course, Xiao Yi's scores are not included in these scores. After all, his exam items are different from others.
"I'm currently working on a paper, and now I'm having a little difficulty..."
Ye Cheng explained.
However, before he finished speaking, Song Ziyang and Luo Qiao next to him suddenly stared.
"What? You guys have started writing papers? When did you write them?"
"What the hell, you play games with us every day and secretly play games with us, right?"
Ye Cheng quibbled. "No way! I obviously wrote it openly, okay? It's just that you didn't notice it!"
"When did you start writing openly and honestly?"
"I wrote it in the library. I never hid it! It's just that you didn't notice me when you came to the library."
"Still quibbling! Old Song, get him!"
"Get him!"
Then Xiao Yi witnessed the process of Ye Cheng being hung up and beaten.
He shook his head in amusement.
Then he also joined the battle and secretly scratched Ye Cheng twice.
Ye Cheng: "You are school bullying!"
Today's class is number theory.
When they came to the classroom, there were already many people sitting inside.
The appearance of Xiao Yi once again attracted the attention of the students.
After greeting each other with these classmates, Xiao Yi also found a place to sit down with his roommates.
"Brother Xiao, I feel like you are like a star every time you come to class."
Ye Cheng noticed the looks from around him and whispered to Xiao Yi.
Xiao Yi rolled his eyes. "You think I do."
That's why he doesn't go to class much.
Ye Cheng chuckled, and then without saying much, he took out his laptop from his schoolbag and said to Xiao Yi, "Brother Xiao, come and help me analyze the problems I am encountering 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. Oh my god, this guy's paper has already written more than ten pages.
It's so hidden.
The two of them watched in silence for a while, then finally took out the book and started studying.
They also have to write papers!
After Ye Cheng took out the computer, he began to talk about his problem. After going through it, Xiao Yi quickly figured it out.
His thesis was on a problem in the field of Algebraic Geometry, which actually surprised Xiao Yi. Unexpectedly, this kid actually started studying Algebraic Geometry.
Perhaps, it has something to do with the Schultz version of "Principles of Algebraic Geometry" he brought back from Germany.
As for the topic selection of the paper, it mainly involves layers and layer varieties on algebraic varieties, and discusses their application in Algebraic Geometry.
"To put it more generally, your problem is how to calculate the homology group of the layer cluster above an algebraic variety in the projective space." Xiao Yi concluded.
Ye Cheng nodded. "Yes, I always feel that I have a little trouble in this aspect."
Xiao Yi smiled and said, "After all, you are a beginner, so it is normal to find trouble."
"As for the problem you encountered, I won't give you a detailed explanation. You can solve it yourself later."
"I'll give you an example."
"Suppose we study the layer cluster homology group H^i(X, OX(d)) of a straight beam OX(d) on an algebraic variety X on the projective plane P^2, where OX(d) represents a twisted wire bundle on
"In order to calculate the layer cluster homology group H^i(X, OX(d)), we can use the layer cluster homology theory on the projective space."
"Bott's norm theorem, and Searle's theorem."
"Do you know these two theorems?"
Hearing Xiao Yi's question, Ye Cheng nodded. "Yes! There is Searle's theorem in EGA, and I learned Bott's norm theorem from another book."
"That's good." Xiao Yi raised his eyebrows and said, "Then we will go directly to 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 Bott's 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 may be non-zero."
"After that, we continue to introduce..."
As Xiao Yi spoke, Ye Cheng kept nodding to show that he understood.
Until the end, he said happily, "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."
"In addition, after using Bott's norm theorem, you can also use the Riemann-Roch theorem to deal with the straight line bundle above P^2."
"Riemann-Roch theorem?" After Ye Cheng thought for a moment, his eyes suddenly lit up again. "I understand!"
"Uh-huh." Xiao Yi asked again at this time, "How many copies of EGA have you read?"
Ye Cheng said with a little embarrassment, "I have finished reading it. I have now started to read 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, don't be in a hurry." Xiao Yi said, "After all, it is EGA."
Looking at Ye Cheng, Xiao Yi couldn't help but recall the scene when he saw him for the first time. At that time, Ye Cheng said that his target was Fields Medal.
Obviously, he is constantly working hard in that direction.
However, Song Ziyang and Luo Qiao next to them couldn't sit still at this time. "What the hell? You guys have already started watching it for the third time?"
Xiao Yi also gave each of them a copy, but they didn't even finish reading it for the first time. This kid...
Just when they were about to get ready to punish this child who secretly took exams, they saw the substitute professor of this class walk in.
"I'll take care of you when I get back."
Two people: Husky pointing at people. jpg
The substitute professor of their number theory class was called Wang Bolin. After walking into the classroom, he glanced and saw Xiao Yi.
He then laughed, "Yo! I didn't expect that my class actually attracted a big shot."
Of course everyone knew who Professor Wang was talking about, and they all laughed.
"If we talk about the scholars with the most outstanding achievements in number theory in today's mathematics world, the big guy who came to our class today can definitely be included among them."
"I wouldn't dare to let a little professor like me lecture in front of him."
Professor Wang said, "Well... So I have a suggestion right now. Let's let him give lectures to everyone. What do you think?"
Many students below suddenly became happy. "Okay!"
Let Scholar Xiao teach them?
Is there such a good thing?
Everyone looked at Xiao Yi: "Scholar Xiao, come on!"
The Ye Cheng people next to them were even more gloating.
Song Ziyang: "Brother Xiao, you just told Cheng'er so well, tell your brothers too!"
Looking at the scene in front of him, Xiao Yi twitched the corner of his mouth.
What the hell.
This is the legendary flipped classroom, right?
But in other people's flipped classrooms, the whole class has to take the class, so here it's just him, right?
Professor Wang, who was standing on the podium, looked at Xiao Yi with a smile and said, "Come on! You see everyone is so enthusiastic, it's hard to refuse such hospitality! I also happen to be a student today, listen to Teacher Xiao's teachings, you can say whatever you want."
Xiao Yi sighed helplessly. He was originally here to experience life, but why did he become the one being experienced?
Okay, just talk!
Get up, leave your seat, and step onto the podium.
Professor Wang sat directly in his seat.
The Ye Cheng people next to them suddenly started sweating profusely, and they sat upright without daring to move.
Xiao Yi, who walked to the podium, felt happy when he saw this scene, but then it was his turn to get entangled.
What are you talking about?
He had never come to class before, so he didn't know where their course progress was.
However, Professor Wang also said that he can talk about whatever he wants.
Hmm...
His eyes lit up and he had an idea.
Since this is a number theory class, why not just teach Goldbach Conjecture?
Coincidentally, he was only a few steps away from solving Ge Guai. All that was left was to sort out the paper, and he took advantage of this class to sort out some of the previous parts.
uh-huh.
Just in time to expose my classmates to these cutting-edge knowledge of mathematics.
Of course, in order to prevent students from not understanding it at the beginning and frightening them, it is best to start with the basics.
The corners of his mouth quirked up.
As his roommates, Ye Cheng and the three of them suddenly felt that life and death were uncertain.
Xiao Yi said, "Then, I will start with a very basic method in number theory."
The word "Sifting Method" was written on the blackboard.
The eyes of the students below suddenly lit up.
They know how awesome Xiao Yi's achievements in screening methods are. After all, it is an achievement that can change the structure of the world's cryptography system.
Even Professor Wang became very interested and began to concentrate his attention.
Only Ye Cheng people became more and more uneasy.
"I don't know if you still remember that in our joint entrance examination, we got the paper Mr. Chen Jingrun about proving Goldbach Conjecture."
"And in that question, we need to use the most basic screening method-Sieve of Eratosthenes."
The students present immediately recalled the question they had taken in the exam. This question was still fresh in their minds.
"Then, let's start from Sieve of Eratosthenes and discuss how the sieving method of Mr. Chen Jingrun was obtained."
"..."
Xiao Yi began to speak.
Although everyone in the class knew what Sieve of Eratosthenes was, the narration of Xiao Yi also brought them different thoughts.
Moreover, as Xiao Yi gradually introduced modern sieving methods, such as Brun's Sieve, Selberg Sieve, etc., it also brought them a lot of inspiration.
Ye Cheng Several people became confused.
Eh?
What about their foreboding feeling?
Brother Xiao Are you really giving a serious lecture?
"... Next, we discuss the sieving method used by Chen Jingrun in the study of Goldbach Conjecture."
"His sieving method is derived from [Large Sieve]. The basic idea is to control the distribution of prime numbers and almost prime numbers by estimating the number of numbers in certain sets - almost prime numbers refer to a number that has exactly two different prime divisors."
"... He constructed an appropriate number set A and defined a sieved set P... and then estimated the number of remaining numbers after excluding multiples of P from A through Large Sieve Inequality..."
As Xiao Yi finished talking about the sieve method used by Chen Jingrun, and the students below were gradually fascinated, he changed his words and said, "However, we need to note that the sieve method alone is not enough for Mr. Chen Jingrun to complete his conclusion. The circle method also needs to be used."
Smiling 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, the key lies in how to further screen the almost prime numbers in the sieved 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 conduct further screening."
Turning around, Xiao Yi started writing on the blackboard.
[|S(A, P)|≤logP|A|...]
Finally, the students below finally realized something was wrong.
What?
Turn 1+2 into 1+1?
Did they hear it correctly?
If it becomes 1+1, doesn't that mean I have proven my guess?
Professor Wang was also confused.
What's going on? Aren't they in class?
Why did it suddenly feel like it was a top mathematics report site?
Watching Xiao Yi simply list 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!
Ye Cheng and the others next to them burst into tears when they saw this.
Sure enough, 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 world, we generally call this method Xiao's expansion."
Xiao Yi said slightly shyly.
Although naming mathematical methods with surnames is relatively common in Scientific Community, it still feels quite stinky to say it - of course, he is still slightly different, because Xiao's expansion is a name called by the mathematical community, not named by himself.
"The principle of Xiao's expansion is combined with Parity Check Classification Sieve. During the use, 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 involved as he talked, which almost helped him become familiar with the entire proof process again.
However, after seeing the increasingly outrageous derivation processes, the students in the classroom finally gave up thinking.
Aren't they here to listen to the class?
How did it become like this?
"Dingling bell~"
Finally, the belated bell finally rang.
Xiao Yi stopped and said, "Since get out of class is over, let's stop here for this class. Let's continue in the next class."
The students below suddenly showed horrified expressions.
Huh?
Still coming?
Professor Wang couldn't sit still at this time, and hurriedly came up and said, "You can stop talking here. I will also teach the students the contents of the book in the next class."
"That's it, okay then."
Xiao Yi could only nod.
Well, that's a pity.
The students finally breathed a sigh of relief at this time.
Okay, okay, next class, I finally don't have to suffer anymore.
For these students of Hua Loo-Keng Class, today's class is a lesson for them, that is, never let Xiao Yi give lectures to them with nothing to do in the future, otherwise, they will only suffer.
Although I couldn't continue to teach everyone, no matter what, Xiao Yi in the second class was able to have a normal class as he wished.
At least I got to experience student life.
After class, Xiao Yi dived into the entrepreneurial base again and started writing his thesis.
The lecture also helped him sort out all the previous processes, which was very convenient for him to complete the final steps of Goldbach Conjecture.
Just like that, four days later.
"... To sum up, we can prove that any even number greater than 2 can be expressed as the sum of two prime numbers."
"Goldbach Conjecture, certified."
"2n is equal to p+q!"
He put down the pen in his hand and rubbed his wrist.
This problem that spanned hundreds of years of history finally came to an end in his hands.
Hilbert He also officially killed two of the three questions involved in the eighth question, and the only one left was Riemann Hypothesis!
It's just that I waited for a long time in my mind, but I never heard the sound of BUFF upgrade.
Xiao Yi shook his head helplessly.
Obviously Goldbach Conjecture cannot be rated as high value.
It can only be said that it is expected, after all, Twin Prime Conjecture is only of medium value.
"Are we really going to prove Riemann Hypothesis?"
This issue can probably only be discussed later.
"Okay, now the question is, where to send the paper?"
Because it has not been long since the Absolute Electronic Computation paper was published, and many people are still discussing it, so he does not plan to put it directly on arxiv, lest it cause too much 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."
He thought so in his mind.
In fact... he simply 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 be when the news that Goldbach Conjecture was proven spread.
"What a happy worry..."
Xiao Yi rubbed his slightly aching head.