For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.
Lu Zhou: "That's okay, it's just the last question."
"That's it for this class. Just now I happened to have some new ideas... Then, get out of class is over."
"In fact, before the Riemann Hypothesis, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
After a pause, Lu Zhou continued.
"Hiss... wait, this question seems interesting..."
After a pause, Lu Zhou continued.
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"Are you planning to raise a question here?"
"Don't worry, I won't make it too difficult." As he said that, Lu Zhou took out a piece of draft paper from the lesson plan tucked under his elbow, tore off a corner and started writing on it.
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
"In fact, before the Riemann Hypothesis, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."
"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of the prime factors is not considered, then this expression is unique, so the prime number also becomes The basic elements that make up positive integers.”
For example, he knew Schultz, a man whom Faltings called one of the three young scholars most promising to surpass him in the world, who had won three consecutive IMO gold medals.
Lu Zhou: "What else?"
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.
Students: "..."
"...Riemannian zeta function?"
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
"A very excellent number theory class!" Dean Qin came forward with a smile on his face and said with emotion, "Even after listening to it, I have benefited a lot."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
After a pause, Lu Zhou continued.
"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of the prime factors is not considered, then this expression is unique, so the prime number also becomes The basic elements that make up positive integers.”
After muttering something, Dean Qin touched his chin and thought to himself.
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers."
"Are you planning to raise a question here?"
After a pause, Lu Zhou continued.
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
Seeing the students in the classroom gradually getting into the mood, Lu Zhou knew that his class was almost half successful.
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
"...Riemannian zeta function?"
"Hiss... wait, this question seems interesting..."
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
As for when he was asked why he signed up for two more competitions after winning the gold medal, he said it was because he thought it was fun...
Time passed by minute by second, and soon it was time for get out of class to end.
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
Satisfied that he had gradually regained some form, Lu Zhou nodded proudly in his heart.
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
After a pause, Lu Zhou continued.
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
"That's it for this class. Just now I happened to have some new ideas... Then, get out of class is over."
After a pause, Lu Zhou continued.
"Hiss... wait, this question seems interesting..."
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
"I've thought about it." After writing the topic on the paper, Lu Zhou folded the draft paper and gently put it into Dean Qin's hand, "Please pass it to the Chinese Mathematical Society for me. This topic should not be question."
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
"That's it... doesn't look difficult, does it?"
Lu Zhou smiled sheepishly and said.
Of course he had heard of the IMO competition, although he had never had the chance to participate.
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
"Euclide used elementary methods to prove that there are infinitely many prime numbers, and Euler introduced a product formula. These pioneers provided the possibility to analyze the problem of prime numbers. However, until the 1850s, no one had any idea Finding a suitable method to prove the conjecture proposed by Gauss, it was not until a German mathematician published a paper titled "On the Number of Prime Numbers Not Exceeding a Given Value" that the research on π(x) began. A new path has been opened.”
After looking around the silent classroom, Lu Zhou continued.
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
"...Riemannian zeta function?"
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
Time passed by minute by second, and soon it was time for get out of class to end.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
"...Riemannian zeta function?"
"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
For example, he knew Schultz, a man whom Faltings called one of the three young scholars most promising to surpass him in the world, who had won three consecutive IMO gold medals.
"In fact, before the Riemann Hypothesis, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Seeing the students in the classroom gradually getting into the mood, Lu Zhou knew that his class was almost half successful.
[ζ(s)=Σ1/n^s]
For example, he knew Schultz, a man whom Faltings called one of the three young scholars most promising to surpass him in the world, who had won three consecutive IMO gold medals.
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
Lu Zhou: "What else?"
"Don't worry, I won't make it too difficult." As he said that, Lu Zhou took out a piece of draft paper from the lesson plan tucked under his elbow, tore off a corner and started writing on it.
Time passed by minute by second, and soon it was time for get out of class to end.
After a pause, Lu Zhou continued.
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
After looking around the silent classroom, Lu Zhou continued.
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
"Can a competitive student solve this kind of problem?"
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
When he walked outside the classroom, Lu Zhou was about to go back to the office to record down the inspiration he had just had in class, when he was suddenly blocked by Dean Qin who came out of nowhere.
"That's it for this class. Just now I happened to have some new ideas... Then, get out of class is over."
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
"That's it... doesn't look difficult, does it?"
"That's it for this class. Just now I happened to have some new ideas... Then, get out of class is over."
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.
Students: "..."
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
MMP!
[ζ(s)=Σ1/n^s]
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Every year, those who win the gold medal in the IMO competition are all players who are like gods.
Where is it not difficult? !
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
"Are you planning to raise a question here?"
After looking around the silent classroom, Lu Zhou continued.
"Can a competitive student solve this kind of problem?"
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
Dean Qin said with a smile: "Is this appropriate? The last question in the national finals in previous years was also asked by academicians. Not only are you an academician, but you are also a Fields Medal winner. If you are not suitable, then what else? Who would be suitable?”
Lu Zhou: "Aren't you very busy? What's wrong?"
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
"So, we can often get a very beautiful result under the Riemann Hypothesis, but if we can't prove that the Riemann Hypothesis is true, we can't prove that our results are correct."
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
For example, he knew Schultz, a man whom Faltings called one of the three young scholars most promising to surpass him in the world, who had won three consecutive IMO gold medals.
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Of course he had heard of the IMO competition, although he had never had the chance to participate.
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
Lu Zhou glanced at the clock on the wall and saw that it was almost time, so he dropped the chalk in his hand on the multimedia desk.
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
Lu Zhou glanced at the clock on the wall and saw that it was almost time, so he dropped the chalk in his hand on the multimedia desk.
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
"That's it... doesn't look difficult, does it?"
Lu Zhou: "That's okay, it's just the last question."
Students: "..."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
"Can a competitive student solve this kind of problem?"
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
Students: "..."
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
Next, Lu Zhou continued to talk about some research progress on the Riemann Hypothesis, as well as some of its equivalent forms. Although they are all boring stuff, perhaps because of the change in teaching methods, the students obviously listened much more seriously than the previous class.
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
"So, we can often get a very beautiful result under the Riemann Hypothesis, but if we can't prove that the Riemann Hypothesis is true, we can't prove that our results are correct."
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers."
Satisfied that he had gradually regained some form, Lu Zhou nodded proudly in his heart.
Lu Zhou: "Is it appropriate for me to be the proposer?"
When he walked outside the classroom, Lu Zhou was about to go back to the office to record down the inspiration he had just had in class, when he was suddenly blocked by Dean Qin who came out of nowhere.
Lu Zhou: "What else?"
"Can a competitive student solve this kind of problem?"
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Time passed by minute by second, and soon it was time for get out of class to end.
For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.
After muttering something, Dean Qin touched his chin and thought to himself.
"That's it... doesn't look difficult, does it?"
"Euclide used elementary methods to prove that there are infinitely many prime numbers, and Euler introduced a product formula. These pioneers provided the possibility to analyze the problem of prime numbers. However, until the 1850s, no one had any idea Finding a suitable method to prove the conjecture proposed by Gauss, it was not until a German mathematician published a paper titled "On the Number of Prime Numbers Not Exceeding a Given Value" that the research on π(x) began. A new path has been opened.”
"That's it... doesn't look difficult, does it?"
Lu Zhou glanced at the clock on the wall and saw that it was almost time, so he dropped the chalk in his hand on the multimedia desk.
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
"That's it... doesn't look difficult, does it?"
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
"That's it for this class. Just now I happened to have some new ideas... Then, get out of class is over."
Lu Zhou: "That's okay, it's just the last question."
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
"I've thought about it." After writing the topic on the paper, Lu Zhou folded the draft paper and gently put it into Dean Qin's hand, "Please pass it to the Chinese Mathematical Society for me. This topic should not be question."
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
Seeing Lu Zhou take out the draft paper and start writing, Dean Qin was stunned for a moment, and then he couldn't laugh or cry.
"Hiss... wait, this question seems interesting..."
"Hiss... wait, this question seems interesting..."
"Are you planning to raise a question here?"
When he walked outside the classroom, Lu Zhou was about to go back to the office to record down the inspiration he had just had in class, when he was suddenly blocked by Dean Qin who came out of nowhere.
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
Time passed by minute by second, and soon it was time for get out of class to end.
After a pause, Lu Zhou continued.
As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.
"A very excellent number theory class!" Dean Qin came forward with a smile on his face and said with emotion, "Even after listening to it, I have benefited a lot."
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
Lu Zhou smiled sheepishly and said.
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
Seeing Lu Zhou take out the draft paper and start writing, Dean Qin was stunned for a moment, and then he couldn't laugh or cry.
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
Students: "..."
"Can a competitive student solve this kind of problem?"
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
Lu Zhou: "Aren't you very busy? What's wrong?"
Where is it not difficult? !
"Don't worry, I won't make it too difficult." As he said that, Lu Zhou took out a piece of draft paper from the lesson plan tucked under his elbow, tore off a corner and started writing on it.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
After muttering something, Dean Qin touched his chin and thought to himself.
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
Seeing the students in the classroom gradually getting into the mood, Lu Zhou knew that his class was almost half successful.
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
Lu Zhou smiled sheepishly and said.
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
Lu Zhou: "That's okay, it's just the last question."
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
Of course he had heard of the IMO competition, although he had never had the chance to participate.
Lu Zhou smiled sheepishly and said.
Next, Lu Zhou continued to talk about some research progress on the Riemann Hypothesis, as well as some of its equivalent forms. Although they are all boring stuff, perhaps because of the change in teaching methods, the students obviously listened much more seriously than the previous class.
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
Where is it not difficult? !
As for when he was asked why he signed up for two more competitions after winning the gold medal, he said it was because he thought it was fun...
"Are you planning to raise a question here?"
Every year, those who win the gold medal in the IMO competition are all players who are like gods.
"Can a competitive student solve this kind of problem?"
"Can a competitive student solve this kind of problem?"
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
"...Riemannian zeta function?"
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
For example, he knew Schultz, a man whom Faltings called one of the three young scholars most promising to surpass him in the world, who had won three consecutive IMO gold medals.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
As for when he was asked why he signed up for two more competitions after winning the gold medal, he said it was because he thought it was fun...
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
"That's it... doesn't look difficult, does it?"
MMP!
Every year, those who win the gold medal in the IMO competition are all players who are like gods.
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
"So, we can often get a very beautiful result under the Riemann Hypothesis, but if we can't prove that the Riemann Hypothesis is true, we can't prove that our results are correct."
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
Lu Zhou: "What else?"
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
"In fact, before the Riemann Hypothesis, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
Lu Zhou: "Is it appropriate for me to be the proposer?"
"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers not exceeding x. Studying the distribution of prime numbers is a basic task of analytic number theory, and studying the properties of π(x) , is the central problem in analytic number theory."
"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers."
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
Dean Qin said with a smile: "Is this appropriate? The last question in the national finals in previous years was also asked by academicians. Not only are you an academician, but you are also a Fields Medal winner. If you are not suitable, then what else? Who would be suitable?”
Dean Qin said with a smile: "It's like this. Didn't we hold the National High School Mathematics League last month? The top players in each province have been selected. By the national finals of the winter camp in January next year, about 30 people will be selected. Students have entered the national training team. It’s already November, and it’s almost time to prepare for the exam questions.”
Dean Qin said with a smile: "Is this appropriate? The last question in the national finals in previous years was also asked by academicians. Not only are you an academician, but you are also a Fields Medal winner. If you are not suitable, then what else? Who would be suitable?”
Students: "..."
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
Every year, those who win the gold medal in the IMO competition are all players who are like gods.
Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.
"A very excellent number theory class!" Dean Qin came forward with a smile on his face and said with emotion, "Even after listening to it, I have benefited a lot."
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
Lu Zhou: "That's okay, it's just the last question."
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
[ζ(s)=Σ1/n^s]
"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of the prime factors is not considered, then this expression is unique, so the prime number also becomes The basic elements that make up positive integers.”
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
When he walked outside the classroom, Lu Zhou was about to go back to the office to record down the inspiration he had just had in class, when he was suddenly blocked by Dean Qin who came out of nowhere.
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
"A very excellent number theory class!" Dean Qin came forward with a smile on his face and said with emotion, "Even after listening to it, I have benefited a lot."
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
Normally, these things would be obvious to him and he would basically not consider them. Only at this time can he temporarily put aside the research itself and think about the obvious things and why they are obvious.
"Don't worry, I won't make it too difficult." As he said that, Lu Zhou took out a piece of draft paper from the lesson plan tucked under his elbow, tore off a corner and started writing on it.
Dean Qin said understandingly: "Everything has its own sequence, and it is related to national interests. Compared with teaching students, of course your research is more important. Speaking of which, have you been busy recently?"
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
Lu Zhou: "Aren't you very busy? What's wrong?"
Lu Zhou: "That's okay, it's just the last question."
After muttering something, Dean Qin touched his chin and thought to himself.
"In fact, before the Riemann Hypothesis, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."
"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers."
Seeing Lu Zhou take out the draft paper and start writing, Dean Qin was stunned for a moment, and then he couldn't laugh or cry.
Every year, those who win the gold medal in the IMO competition are all players who are like gods.
There was a faint sound of packing up textbooks in the classroom. Lu Zhou tucked the lesson plan under his elbow, nodded to the students who were watching him leave, then turned and walked out of the classroom.
Seeing the students in the classroom gradually getting into the mood, Lu Zhou knew that his class was almost half successful.
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
MMP!
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
"Are you planning to raise a question here?"
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
"That's an award. I'm ashamed to say that I haven't given a class to undergraduates for a while."
Lu Zhou: "Is it appropriate for me to be the proposer?"
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Although the Riemann Hypothesis is a very complex problem, understanding it is not as difficult as most people imagine. The real difficulty is how to solve it...
Students: "..."
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
Lu Zhou: "What else?"
"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of the prime factors is not considered, then this expression is unique, so the prime number also becomes The basic elements that make up positive integers.”
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
Lu Zhou: "What else?"
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.
Dean Qin Khan said: "This is the national finals, so you have to think carefully about it."
"Hiss... wait, this question seems interesting..."
Lu Zhou: "What else?"
MMP!
"Are you planning to raise a question here?"
"Hiss... wait, this question seems interesting..."
After muttering something, Dean Qin touched his chin and thought to himself.
"If anyone can prove the Riemann Hypothesis, he will undoubtedly become the greatest mathematician of this century... I can say this responsibly, even though this century has just begun."
"I've thought about it." After writing the topic on the paper, Lu Zhou folded the draft paper and gently put it into Dean Qin's hand, "Please pass it to the Chinese Mathematical Society for me. This topic should not be question."
"Euclide used elementary methods to prove that there are infinitely many prime numbers, and Euler introduced a product formula. These pioneers provided the possibility to analyze the problem of prime numbers. However, until the 1850s, no one had any idea Finding a suitable method to prove the conjecture proposed by Gauss, it was not until a German mathematician published a paper titled "On the Number of Prime Numbers Not Exceeding a Given Value" that the research on π(x) began. A new path has been opened.”
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
Dean Qin: "This matter is not my responsibility. It is an invitation from our Chinese Mathematical Society. They hope that you will be the proposer of the last question."
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
"...Riemannian zeta function?"
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
"Regarding the problem of π(x), both Gauss and Legendre have done a lot of numerical calculations and conjectured that when x tends to infinity, π(x)~x/lnx. This conjecture was later proved, which is what we call Understand the prime number theorem.”
Lu Zhou: "Aren't you very busy? What's wrong?"
MMP!
Next, Lu Zhou continued to talk about some research progress on the Riemann Hypothesis, as well as some of its equivalent forms. Although they are all boring stuff, perhaps because of the change in teaching methods, the students obviously listened much more seriously than the previous class.
After muttering something, Dean Qin touched his chin and thought to himself.
"... Many people know that the Riemann Hypothesis is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero-point distribution of the Riemann zeta function. But few people know why the Riemann Hypothesis is Being brought up?”
Lu Zhou glanced at the clock on the wall and saw that it was almost time, so he dropped the chalk in his hand on the multimedia desk.
"That's right, there's something I want to ask of you," Dean Qin coughed slightly and said, "Have you heard of the Olympic Mathematics Competition?"
"This is not easy to compare. After all, my achievements are not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain explanation, "But if someone can really prove this conjecture, If so, then his achievements in the field of mathematics will undoubtedly stand at the pinnacle of this era."
MMP!
"Can a competitive student solve this kind of problem?"
"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of the prime factors is not considered, then this expression is unique, so the prime number also becomes The basic elements that make up positive integers.”
Lu Zhou: "Aren't you very busy? What's wrong?"
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
"I've thought about it." After writing the topic on the paper, Lu Zhou folded the draft paper and gently put it into Dean Qin's hand, "Please pass it to the Chinese Mathematical Society for me. This topic should not be question."
"Many people may have already guessed who this great man is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will have an impact on the next century and a half. "
However, at this moment, he suddenly seemed to have thought of something, and his eyes lit up slightly.
Students: "..."
Time passed by minute by second, and soon it was time for get out of class to end.
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
Lu Zhou was stunned for a moment, then he laughed and said, "...You didn't ask me to be the proposer, did you?"
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
"Hiss... wait, this question seems interesting..."
"Well, I'll leave this to you." Suddenly remembering something, Dean Qin quickly added, "By the way, don't make it too difficult. It's pointless if no one can do it. ”
"Professor," at this time, a student couldn't help but raise his hand. After getting a nod from Lu Zhou, he stood up and asked excitedly, "If I can prove the Riemann Hypothesis, how will it compare to you?"
Satisfied that he had gradually regained some form, Lu Zhou nodded proudly in his heart.
"Can a competitive student solve this kind of problem?"
Looking dumbfounded at Lu Zhou's leaving figure, Dean Qin moved his eyes to the draft paper in his hand and silently opened it and took a look.
Looking around mysteriously, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly towards the office.
Students: "..."
Lu Zhou: "I've heard of it, I've heard of it. Do you have any questions?"
Time passed by minute by second, and soon it was time for get out of class to end.
"The reverse is also true. If we can prove that the Riemann Hypothesis is correct, then thousands of mathematical conjectures that exist assuming the Riemann Hypothesis is true will be promoted to theorems!"
"Riemann made further conjectures about the function he proposed in his paper and believed that all non-obvious zero points of ζ(s) are on the critical straight line. Facts have proved that his vision is indeed quite far-sighted. After a lot of calculations, he obtained All non-obvious zero points are on the critical line. Unfortunately, although we know that it is probably correct, we have no way to prove that it is indeed correct."