Xueba starts with change
Chapter 547 Minimal Model Program Question 1
Chapter 547 The first problem of the minimal model program
Office 302 of the Administration Building of Yanda Mathematics Institute.
Students and teaching assistants who used to run away early at noon.
Surprisingly staying in the office at this moment.
What Xu Chenyang said earlier was only before the door of the cubicle was closed.
After the door closed, these people began to chat in low voices again.
"Brother, why do you think Mr. Chen Zhou appeared here?"
"Do you still need to ask? The previous news has not been reported. Mr. Chen Zhou returned to China this time, and he planned to come to Yanda to teach."
"You mean to say that Mr. Chen Zhou is already a member of Yan University?"
"wrong."
"Wrong? What's wrong?"
"Boss Chen Zhou has always been a member of Yan University!"
"Uh... that's right, senior brother is right, Mr. Chen Zhou has never broken contact with Yan University!"
"Senior brother, what do you think Mr. Chen Zhou will teach when he returns to Yan University this time?"
"It should be number theory..."
"Wow, these undergraduates are blessed! I'm so excited to think about learning from the big guy who solved Goldbach's conjecture!"
"That's what I said, but considering the status of Chen Zhou, the Nobel Prize winner in physics, the Institute of Physics will not let such a big boss go..."
"Brother, what do you mean, Mr. Chen Zhou will teach in both the School of Mathematics and the School of Physics? But this is not in line with Yanda's rules, right?"
"You are wrong, brother means, considering the status of Chen Zhou, the Nobel Prize winner in physics!"
"Huh? Sister, I don't quite understand..."
"Stupid! The Nobel laureates and quasi-Philippine award masters still need to conform to the rules of Yanda University? With this status, you can already break the rules and become the rule-makers, right?"
"Oh, I see..."
"Okay, Li Yuxuan, don't think too much, this is all the result of discussions between the school and Mr. Chen Zhou, no matter how we guess, it doesn't make much sense."
"Yes, Li Yuxuan, we are now studying as graduate students with Professor Xu, even if Mr. Chen Zhou goes to teach number theory to undergraduates, it has nothing to do with us."
Li Yuxuan did not agree with what the senior brother and sister said.
He said: "You can't say that. I think people at the level of Mr. Chen Zhou must have many different opinions even if they teach undergraduates."
"As the saying goes, seeing the big from the small, if we have the opportunity, we should go to the class of Mr. Chen Zhou."
Hearing Li Yuxuan's words, his senior brothers and sisters just smiled, but didn't say anything more.
For Li Yuxuan, he has just entered the first year of graduate school, and he still has a lot of time.
You can attend undergraduate classes and learn a lot.
This is the happiness that all undergraduates and graduate students are destined to obtain.
Therefore, they could understand Li Yuxuan's excitement, and were even a little envious.
But they themselves were not so excited.
For those graduate students who are about to graduate, more consideration is the next step.
Maybe Chen Zhou will have many eye-catching explanations in the undergraduate class.
But they don't have that time to go to class.
Unless Chen Zhou also brings doctoral students.
In that case, they might consider applying for Chen Zhou's doctoral degree.
The reason why it is considered is because Yan University only has one Chen Zhou.
But there are more Chen Zhous in foreign colleges and universities.
In the small cubicle, Chen Zhou, who was immersed in writing on the draft paper, was naturally unaware of the small discussions outside the cubicle.
His mind is now full of problems with the minimal model program.
In fact, in the research field of the minimal model program, although two Philippine Prize winners have been born.
However, in terms of overall mathematical research, the minimal model program is still unpopular in the field of mathematical research.
If you count double rational geometry, an unpopular branch of algebraic geometry.
The minimal model program can be said to be the unpopular among the unpopular.
This is also a true portrayal of the minimal model program in the field of mathematics.
Take Chen Zhou himself as an example.
In addition to discussing the research on the minimal model program with Xu Chenyang, a researcher in the field of dual rational geometry.
Probably only Tao Zhexuan, who knows a little bit about everything, can chat a little bit.
Others, including Chen Zhou's mentor, Professor A Ting, a master of algebraic geometry, have done very little research on this thing.
The reason lies in the complexity of the minimal model program itself.
Since the concept of the minimal model program was proposed.
The first problem of the minimal model program and the second problem of the minimal model program have always been in front of mathematicians.
Two problems are two big mountains.
So far no mathematician has been able to cross the past.
However, the solution of these two problems does not actually represent the solution of the minimal model program.
We all know that the minimal model program is a blow down operation or flip operation that generalizes a given algebraic variety.
Then, after a finite number of operations, a geometrically minimal model can be obtained.
This is the minimal model program.
Mathematicians have achieved very good results in the research of one-dimensional, two-dimensional, and three-dimensional smaller model programs.
However, there is not much substantive progress in the research on the minimal model program of high-dimensional algebraic varieties.
As far as the current research is concerned, if you want to study the minimal model program of high-dimensional algebraic varieties.
Then, the two major problems of the minimal model program are the stepping stones, which must be solved first.
This is why it is said that the solution of these two major problems does not represent the solution of the minimal model program.
Of course, although the minimal model program is relatively unpopular, the degree of difficulty is not low.
But its own academic value is also directly proportional to the difficulty.
This can be seen from the two previous Fields Medal winners.
Chen Zhou's current research progress is also in the solution of the first problem of the minimal model program.
However, it was just like Chen Zhou's previous feeling.
His research on this issue was too smooth.
Even the content of his research has been repeatedly verified by himself.
And the correction of the wrong question set.
But still did not find the error.
Generally speaking, if there is no record in the wrong question set, it means that Chen Zhou's research is correct.
Chen Zhou used to relax his mind and continue to study boldly and full of fighting spirit.
But this time it was different, and Chen Zhou couldn't tell why, but it felt too smooth, even if it went smoothly, he felt abnormal.
It was this strange feeling that prompted Chen Zhou to make the decision to find Xu Chenyang.
But now, Chen Zhou just wanted to say, this time is the right time!
There is no problem with his thinking.
There is no problem with the magic skill of verifying the wrong question set.
The problem is, he really is "too smooth"!
To put it simply, Chen Zhou did not find a way to solve the first problem of the minimal model program.
That fleeting inspiration didn't rush into his brain.
The research he has done is just the research he thinks is correct in his thinking.
In other words, his steady progress in research according to the established ideas does not have any problems in itself.
The problem is that his idea is not to solve the first problem of the minimal model program!
This is also the reason why he couldn't find the problem after his own verification, coupled with the verification of the wrong question set.
At this moment, Chen Zhou finally understood.
There are also bugs in the wrong set of questions!
If your research, your calculations, are all right.
Then, you will not get feedback on the wrong set!
This point has also been ignored by Chen Zhou.
Because the previous physics topics and chemical materials science topics can all get feedback.
This also made him subconsciously believe that the research on mathematics topics can also get corresponding feedback.
But it turns out, the math is a bit different...
In the cubicle, Chen Zhou didn't know how long he had been writing.
When he put down his pen, he only saw a dozen sheets of A4 draft paper piled up next to him.
The draft paper is densely packed with what he just wrote.
At this moment, Xu Chenyang is still concentrating on looking at the documents.
Chen Zhou picked up the stack of draft papers and flipped through them in order.
Although Chen Zhou's movements were not large, they still alarmed Xu Chenyang who was buried in the literature.
In fact, Xu Chenyang is also doing two things at once.
Chen Zhou obviously got the fleeting inspiration from his research content.
If it is not guaranteed, the minimal model program is solved.
How could he calmly read the documents?
This is another Philippine award-level research topic!
So, when Chen Zhou reached for the draft paper, he immediately turned his head and looked over.
When he saw that Chen Zhou was still immersed in his own world, he didn't ask immediately.
However, looking at the stack of draft paper in Chen Zhou's hand, he always had a bad feeling.
Let Chen Zhou find inspiration from his own research content.
In the end, the minimal model program was solved, so Xu Chenyang didn't know whether to laugh or cry.
After all, he is also one of the researchers of the minimal model program.
Moreover, he really wants to touch the Fields Medal before he turns 40...
After staring at Chen Zhou for a while, Xu Chenyang withdrew his gaze, intending to wait.
At this time, an email notification popped up on Xu Chenyang's computer.
Xu Chenyang frowned slightly, and didn't open the mailbox immediately to read this email.
Instead, after glancing at Chen Zhou beside him, he lightly slid the mouse to open his mailbox.
After seeing the content of the email, Xu Chenyang subconsciously looked at Chen Zhou again.
If Chen Zhou looked up at this moment, he would definitely notice the way Xu Chenyang looked at him.
It was the kind of complexity that Chen Zhou didn't think much about at first.
However, the current Chen Zhou only has the content on the draft paper in his eyes.
After Xu Chenyang read the email, he closed the mailbox.
Surprisingly, Xu Chenyang did not reply immediately to this planned email.
He wants to wait...
As time passed, Chen Zhou sorted out the content on the draft paper again.
This time the feeling is right!
Without the slightest hesitation, Chen Zhou picked up the pen again, and started the final verification on a new A4 draft paper.
The first problem of the minimal model program is the existence of blow down operation or flip operation for generalizing algebraic varieties.
Chen Zhou has the answer!
Chen Zhou's action naturally attracted Xu Chenyang's attention.
He got up quietly, stood behind Chen Zhou, and put his head on it.
Looking at it, the pupils of Xu Chenyang's eyes gradually became bigger, and the whole person was stunned.
That's right, just as he thought.
Chen Zhou actually got inspiration from his research content!
Now we are moving towards the end of the first problem of the minimal model program!
Chen Zhou didn't realize there was someone behind him, peeping.
He is getting closer and closer to his goal.
Without letting the elder brother wait too long behind him, Chen Zhou habitually clicked on the draft paper.
Then wrote down the answer to the first question of the minimal model program.
"In summary, from formula 14-11, it can be obtained that blow down operation or flip operation for generalizing algebraic varieties exists!"
After writing this sentence, Chen Zhou smiled slightly.
Now, there should be no problem, right?
The over-reliance on wrong question sets is the most serious problem that Chen Zhou discovered this time!
Compared with the minimal model program he was studying, the problem of the wrong set of questions disturbed him even more!
Fortunately, it was discovered in time, otherwise, time would have slipped away invisibly.
It is no exaggeration to say that from Chen Zhou's determination of the research topic of the minimal model program to now, he has been running around in circles, killing time!
Looking at the draft paper in front of him, Chen Zhou said silently in his heart: "Sure enough, only the knowledge in the brain truly belongs to me!"
In fact, Chen Zhou roughly guessed the reason for the problem with the wrong question set this time.
Mathematics is different from physics and chemistry. Mathematics is purer and more abstract.
In other words, there is nothing objectively existing in mathematics.
But physics and chemistry are different, and their topics require experimental verification.
That is, they all exist objectively.
Therefore, the collection of wrong questions will record the mistakes made during this "objective existence" process.
And mathematics, no!
After this incident, Chen Zhou also experienced some subtle changes in his attitude towards the wrong set of questions.
With the use of wrong question sets, Chen Zhou is also more inclined to the application aspect.
Xu Chenyang, who was standing behind Chen Zhou, naturally didn't know what Chen Zhou was thinking.
At this moment, he only felt the content in front of him, the more he looked at it, the more surprised he became!
Swallowing with difficulty, Xu Chenyang asked in disbelief, "You...you solved it?"
The sudden voice from behind not only blew up Chen Zhou's thoughts in an instant.
Even Chen Zhou himself was almost blown away by Xu Chenyang...
Chen Zhou stood up from the chair in an instant: "Damn it, senior brother, can you stop being so scary? You are standing behind you, silent, and suddenly speaking, almost scared me out of my mind..."
Xu Chenyang scratched his head in embarrassment, and said apologetically, "I'm sorry, I... I was so engrossed in watching that I didn't notice this, you... are you okay?"
Chen Zhou looked at Xu Chenyang helplessly: "I'm about to have a heart attack from you..."
Xu Chenyang smiled "hehe" and said "sorry" repeatedly.
In fact, I really can't blame him for this matter, he was really fascinated by it.
When I spoke, I didn't think that much at all.
After a while, seeing that Chen Zhou's mood had calmed down, Xu Chenyang asked a little bit tightly: "Have you completely solved the first problem of the minimal model program?"
Chen Zhou reached out to pick up the stack of draft paper on the table and handed it to Xu Chenyang.
Then, he said very sincerely: "Thank you, big brother..."
Xu Chenyang took the draft paper that Chen Zhou had just finished writing in a daze.
"Really...really solved..."
In Xu Chenyang's heart at the moment, he just wanted to complain.
The inspiration for scientific research is so special!
Thanks to book friend Yan Hongxue for the 100 starting coins!
Thanks for the 100 starting coins rewarded by book friend Kunlin Yuanshan!
Thanks to book friends 20210307203501488 for the 100 starting coins!
(End of this chapter)
Office 302 of the Administration Building of Yanda Mathematics Institute.
Students and teaching assistants who used to run away early at noon.
Surprisingly staying in the office at this moment.
What Xu Chenyang said earlier was only before the door of the cubicle was closed.
After the door closed, these people began to chat in low voices again.
"Brother, why do you think Mr. Chen Zhou appeared here?"
"Do you still need to ask? The previous news has not been reported. Mr. Chen Zhou returned to China this time, and he planned to come to Yanda to teach."
"You mean to say that Mr. Chen Zhou is already a member of Yan University?"
"wrong."
"Wrong? What's wrong?"
"Boss Chen Zhou has always been a member of Yan University!"
"Uh... that's right, senior brother is right, Mr. Chen Zhou has never broken contact with Yan University!"
"Senior brother, what do you think Mr. Chen Zhou will teach when he returns to Yan University this time?"
"It should be number theory..."
"Wow, these undergraduates are blessed! I'm so excited to think about learning from the big guy who solved Goldbach's conjecture!"
"That's what I said, but considering the status of Chen Zhou, the Nobel Prize winner in physics, the Institute of Physics will not let such a big boss go..."
"Brother, what do you mean, Mr. Chen Zhou will teach in both the School of Mathematics and the School of Physics? But this is not in line with Yanda's rules, right?"
"You are wrong, brother means, considering the status of Chen Zhou, the Nobel Prize winner in physics!"
"Huh? Sister, I don't quite understand..."
"Stupid! The Nobel laureates and quasi-Philippine award masters still need to conform to the rules of Yanda University? With this status, you can already break the rules and become the rule-makers, right?"
"Oh, I see..."
"Okay, Li Yuxuan, don't think too much, this is all the result of discussions between the school and Mr. Chen Zhou, no matter how we guess, it doesn't make much sense."
"Yes, Li Yuxuan, we are now studying as graduate students with Professor Xu, even if Mr. Chen Zhou goes to teach number theory to undergraduates, it has nothing to do with us."
Li Yuxuan did not agree with what the senior brother and sister said.
He said: "You can't say that. I think people at the level of Mr. Chen Zhou must have many different opinions even if they teach undergraduates."
"As the saying goes, seeing the big from the small, if we have the opportunity, we should go to the class of Mr. Chen Zhou."
Hearing Li Yuxuan's words, his senior brothers and sisters just smiled, but didn't say anything more.
For Li Yuxuan, he has just entered the first year of graduate school, and he still has a lot of time.
You can attend undergraduate classes and learn a lot.
This is the happiness that all undergraduates and graduate students are destined to obtain.
Therefore, they could understand Li Yuxuan's excitement, and were even a little envious.
But they themselves were not so excited.
For those graduate students who are about to graduate, more consideration is the next step.
Maybe Chen Zhou will have many eye-catching explanations in the undergraduate class.
But they don't have that time to go to class.
Unless Chen Zhou also brings doctoral students.
In that case, they might consider applying for Chen Zhou's doctoral degree.
The reason why it is considered is because Yan University only has one Chen Zhou.
But there are more Chen Zhous in foreign colleges and universities.
In the small cubicle, Chen Zhou, who was immersed in writing on the draft paper, was naturally unaware of the small discussions outside the cubicle.
His mind is now full of problems with the minimal model program.
In fact, in the research field of the minimal model program, although two Philippine Prize winners have been born.
However, in terms of overall mathematical research, the minimal model program is still unpopular in the field of mathematical research.
If you count double rational geometry, an unpopular branch of algebraic geometry.
The minimal model program can be said to be the unpopular among the unpopular.
This is also a true portrayal of the minimal model program in the field of mathematics.
Take Chen Zhou himself as an example.
In addition to discussing the research on the minimal model program with Xu Chenyang, a researcher in the field of dual rational geometry.
Probably only Tao Zhexuan, who knows a little bit about everything, can chat a little bit.
Others, including Chen Zhou's mentor, Professor A Ting, a master of algebraic geometry, have done very little research on this thing.
The reason lies in the complexity of the minimal model program itself.
Since the concept of the minimal model program was proposed.
The first problem of the minimal model program and the second problem of the minimal model program have always been in front of mathematicians.
Two problems are two big mountains.
So far no mathematician has been able to cross the past.
However, the solution of these two problems does not actually represent the solution of the minimal model program.
We all know that the minimal model program is a blow down operation or flip operation that generalizes a given algebraic variety.
Then, after a finite number of operations, a geometrically minimal model can be obtained.
This is the minimal model program.
Mathematicians have achieved very good results in the research of one-dimensional, two-dimensional, and three-dimensional smaller model programs.
However, there is not much substantive progress in the research on the minimal model program of high-dimensional algebraic varieties.
As far as the current research is concerned, if you want to study the minimal model program of high-dimensional algebraic varieties.
Then, the two major problems of the minimal model program are the stepping stones, which must be solved first.
This is why it is said that the solution of these two major problems does not represent the solution of the minimal model program.
Of course, although the minimal model program is relatively unpopular, the degree of difficulty is not low.
But its own academic value is also directly proportional to the difficulty.
This can be seen from the two previous Fields Medal winners.
Chen Zhou's current research progress is also in the solution of the first problem of the minimal model program.
However, it was just like Chen Zhou's previous feeling.
His research on this issue was too smooth.
Even the content of his research has been repeatedly verified by himself.
And the correction of the wrong question set.
But still did not find the error.
Generally speaking, if there is no record in the wrong question set, it means that Chen Zhou's research is correct.
Chen Zhou used to relax his mind and continue to study boldly and full of fighting spirit.
But this time it was different, and Chen Zhou couldn't tell why, but it felt too smooth, even if it went smoothly, he felt abnormal.
It was this strange feeling that prompted Chen Zhou to make the decision to find Xu Chenyang.
But now, Chen Zhou just wanted to say, this time is the right time!
There is no problem with his thinking.
There is no problem with the magic skill of verifying the wrong question set.
The problem is, he really is "too smooth"!
To put it simply, Chen Zhou did not find a way to solve the first problem of the minimal model program.
That fleeting inspiration didn't rush into his brain.
The research he has done is just the research he thinks is correct in his thinking.
In other words, his steady progress in research according to the established ideas does not have any problems in itself.
The problem is that his idea is not to solve the first problem of the minimal model program!
This is also the reason why he couldn't find the problem after his own verification, coupled with the verification of the wrong question set.
At this moment, Chen Zhou finally understood.
There are also bugs in the wrong set of questions!
If your research, your calculations, are all right.
Then, you will not get feedback on the wrong set!
This point has also been ignored by Chen Zhou.
Because the previous physics topics and chemical materials science topics can all get feedback.
This also made him subconsciously believe that the research on mathematics topics can also get corresponding feedback.
But it turns out, the math is a bit different...
In the cubicle, Chen Zhou didn't know how long he had been writing.
When he put down his pen, he only saw a dozen sheets of A4 draft paper piled up next to him.
The draft paper is densely packed with what he just wrote.
At this moment, Xu Chenyang is still concentrating on looking at the documents.
Chen Zhou picked up the stack of draft papers and flipped through them in order.
Although Chen Zhou's movements were not large, they still alarmed Xu Chenyang who was buried in the literature.
In fact, Xu Chenyang is also doing two things at once.
Chen Zhou obviously got the fleeting inspiration from his research content.
If it is not guaranteed, the minimal model program is solved.
How could he calmly read the documents?
This is another Philippine award-level research topic!
So, when Chen Zhou reached for the draft paper, he immediately turned his head and looked over.
When he saw that Chen Zhou was still immersed in his own world, he didn't ask immediately.
However, looking at the stack of draft paper in Chen Zhou's hand, he always had a bad feeling.
Let Chen Zhou find inspiration from his own research content.
In the end, the minimal model program was solved, so Xu Chenyang didn't know whether to laugh or cry.
After all, he is also one of the researchers of the minimal model program.
Moreover, he really wants to touch the Fields Medal before he turns 40...
After staring at Chen Zhou for a while, Xu Chenyang withdrew his gaze, intending to wait.
At this time, an email notification popped up on Xu Chenyang's computer.
Xu Chenyang frowned slightly, and didn't open the mailbox immediately to read this email.
Instead, after glancing at Chen Zhou beside him, he lightly slid the mouse to open his mailbox.
After seeing the content of the email, Xu Chenyang subconsciously looked at Chen Zhou again.
If Chen Zhou looked up at this moment, he would definitely notice the way Xu Chenyang looked at him.
It was the kind of complexity that Chen Zhou didn't think much about at first.
However, the current Chen Zhou only has the content on the draft paper in his eyes.
After Xu Chenyang read the email, he closed the mailbox.
Surprisingly, Xu Chenyang did not reply immediately to this planned email.
He wants to wait...
As time passed, Chen Zhou sorted out the content on the draft paper again.
This time the feeling is right!
Without the slightest hesitation, Chen Zhou picked up the pen again, and started the final verification on a new A4 draft paper.
The first problem of the minimal model program is the existence of blow down operation or flip operation for generalizing algebraic varieties.
Chen Zhou has the answer!
Chen Zhou's action naturally attracted Xu Chenyang's attention.
He got up quietly, stood behind Chen Zhou, and put his head on it.
Looking at it, the pupils of Xu Chenyang's eyes gradually became bigger, and the whole person was stunned.
That's right, just as he thought.
Chen Zhou actually got inspiration from his research content!
Now we are moving towards the end of the first problem of the minimal model program!
Chen Zhou didn't realize there was someone behind him, peeping.
He is getting closer and closer to his goal.
Without letting the elder brother wait too long behind him, Chen Zhou habitually clicked on the draft paper.
Then wrote down the answer to the first question of the minimal model program.
"In summary, from formula 14-11, it can be obtained that blow down operation or flip operation for generalizing algebraic varieties exists!"
After writing this sentence, Chen Zhou smiled slightly.
Now, there should be no problem, right?
The over-reliance on wrong question sets is the most serious problem that Chen Zhou discovered this time!
Compared with the minimal model program he was studying, the problem of the wrong set of questions disturbed him even more!
Fortunately, it was discovered in time, otherwise, time would have slipped away invisibly.
It is no exaggeration to say that from Chen Zhou's determination of the research topic of the minimal model program to now, he has been running around in circles, killing time!
Looking at the draft paper in front of him, Chen Zhou said silently in his heart: "Sure enough, only the knowledge in the brain truly belongs to me!"
In fact, Chen Zhou roughly guessed the reason for the problem with the wrong question set this time.
Mathematics is different from physics and chemistry. Mathematics is purer and more abstract.
In other words, there is nothing objectively existing in mathematics.
But physics and chemistry are different, and their topics require experimental verification.
That is, they all exist objectively.
Therefore, the collection of wrong questions will record the mistakes made during this "objective existence" process.
And mathematics, no!
After this incident, Chen Zhou also experienced some subtle changes in his attitude towards the wrong set of questions.
With the use of wrong question sets, Chen Zhou is also more inclined to the application aspect.
Xu Chenyang, who was standing behind Chen Zhou, naturally didn't know what Chen Zhou was thinking.
At this moment, he only felt the content in front of him, the more he looked at it, the more surprised he became!
Swallowing with difficulty, Xu Chenyang asked in disbelief, "You...you solved it?"
The sudden voice from behind not only blew up Chen Zhou's thoughts in an instant.
Even Chen Zhou himself was almost blown away by Xu Chenyang...
Chen Zhou stood up from the chair in an instant: "Damn it, senior brother, can you stop being so scary? You are standing behind you, silent, and suddenly speaking, almost scared me out of my mind..."
Xu Chenyang scratched his head in embarrassment, and said apologetically, "I'm sorry, I... I was so engrossed in watching that I didn't notice this, you... are you okay?"
Chen Zhou looked at Xu Chenyang helplessly: "I'm about to have a heart attack from you..."
Xu Chenyang smiled "hehe" and said "sorry" repeatedly.
In fact, I really can't blame him for this matter, he was really fascinated by it.
When I spoke, I didn't think that much at all.
After a while, seeing that Chen Zhou's mood had calmed down, Xu Chenyang asked a little bit tightly: "Have you completely solved the first problem of the minimal model program?"
Chen Zhou reached out to pick up the stack of draft paper on the table and handed it to Xu Chenyang.
Then, he said very sincerely: "Thank you, big brother..."
Xu Chenyang took the draft paper that Chen Zhou had just finished writing in a daze.
"Really...really solved..."
In Xu Chenyang's heart at the moment, he just wanted to complain.
The inspiration for scientific research is so special!
Thanks to book friend Yan Hongxue for the 100 starting coins!
Thanks for the 100 starting coins rewarded by book friend Kunlin Yuanshan!
Thanks to book friends 20210307203501488 for the 100 starting coins!
(End of this chapter)
You'll Also Like
-
Hogwarts: Harry brings H3 magic
Chapter 6 minute ago -
Fantasy chat group has a very high level of understanding, Aunt Liu Shen
Chapter 250 21 minute ago -
Zhutian Konoha: Conquer the world from the chat group
Chapter 232 22 minute ago -
Shura White Tiger in Navigation
Chapter 384 1 hours ago -
Villain: I Slapped The God Of War In The Face At The Beginning, And The Female President Helped Me V
Chapter 828 1 hours ago -
You Became A Killing God At The Beginning, Why Did Your Majesty Rebel?
Chapter 730 1 hours ago -
NBA: This Center Is So Stable
Chapter 336 1 hours ago -
King’s Game: Black Bible
Chapter 305 1 hours ago -
Comprehensive comic group chat: Yukino called the police on my father!
Chapter 664 1 hours ago -
My Songwriting Was Rejected, But I Became A Superstar
Chapter 316 1 hours ago