NOVEL NEXT Xueba starts with change
Chapter 441 Nott's Mission (4000-word chapter)
Chapter 441 Nott's Mission (4000-word chapter)
"A problem with algebraic geometry?"
Chen Zhou smiled softly and said, "Then you should ask my tutor, as you said just now, he is a master in the field of algebraic geometry."
After speaking, Chen Zhou looked at his watch.
This Senior Nott has already delayed him for more than ten minutes.
If she didn't tell the purpose of the coincidence later, Chen Zhou planned to leave immediately.
When Nott saw Chen Zhou looking at his watch, he naturally understood what Chen Zhou meant.
Without going around the corner, Nott said, "You know the Artin L function, right?"
Chen Zhou frowned slightly: "A Ting L function?"
Nott nodded: "Yes, Artin L function."
"Of course I know that." Chen Zhou said puzzled, "But if your question is related to Arting's L function, then you should ask Professor Arting, I believe he understands his father's work better."
Nott shook his head: "Professor Artin is not suitable for us, and he will not help us."
Chen Zhou was a little confused now. He looked at Nott and said: "Professor A Ting is not suitable for you, so I am suitable for you? If you say that Professor A Ting will not help you, is it true that as a student of Professor A Ting I will help you? Also, what do you mean?"
Facing Chen Zhou's series of questions, Nott didn't feel impolite, but a smile appeared on the corner of his mouth.
She said slowly: "Do you know the two major mathematical problems that Professor Artin's father, Professor Emil Artin, left for future generations?"
Chen Zhou was stunned for a moment, and said softly: "The linear representation of the Artin L function of the Galois group? And given the proof number a, find the frequency that a is the original root of different prime p modules?"
"That's right!" Hearing Chen Zhou's words, Nott's expression became excited, "These two major mathematical problems are not only the mathematical problems left by Professor Emil Artin to future generations, but also crucial problems in the field of algebra. Two important problems!"
Chen Zhou glanced at Nott, but he didn't quite understand why this man was so excited.
Could it be that the senior Nott in front of me really has something to do with the Queen of Algebra?
But isn't this left by Professor Emil Artin?
Chen Zhou couldn't see the answer.
However, Chen Zhou quite agrees with what Nott said.
In particular, the L function really occupies a very important position in modern mathematics.
从欧拉考虑了函数ζ(S)=∑n=1→∞n^(-S)，并证明了其在S=2点的值1+1/2^2+3^2+……=π^2/6开始。
Later, in his famous paper, Riemann proposed that this function satisfies three conditions.
One is that it has the expression ∑n=1→∞n^(-S)=p∏prime1/1-p^(-S).
One is its value in 1-S and S, which has symmetry and satisfies a certain function equation.
The last one is that its ordinary zero points are distributed on the straight line Re(S)=1/2.
The first two are easy to prove with elementary methods, and the third is the famous Riemann hypothesis.
Today, this function is also commonly referred to as the Riemann zeta function.
It is also a special case of a certain class of functions, which are called L functions.
L functions have properties similar to the above three conditions, and their values at special points have expressions similar to Euler.
Don't think that this vague expression looks like elementary algebra.
In fact, its meaning is profound.
As for the reason...
It contains three of the seven million-dollar millennium problems proposed by the Clay Institute of the United States in the early 21st century-the Bayh and Swinton-Dell conjecture, the Hodge conjecture and the Riemann conjecture.
Besides that, there are many other famous conjectures.
In a sense, behind this expression of the L function, a series of extremely magnificent mathematical structures are hidden.
Behind these structures is not only the meaning of the problem itself, but also contains many powerful tools for solving it.
In addition, the L function generally has two kinds of L functions with different origins, namely the Motivic L function and the automorphic L function.
The Artin L function is also included in this.
The Motivic L function originated from algebraic number theory and algebraic geometry.
As we all know, one of the core problems of algebraic number theory is to solve univariate polynomial equations with integer coefficients.
For every prime number p, the case modulo p can be considered and a univariate polynomial equation over a finite field can be obtained.
In principle, it can be easily solved.
And how the solution modulo p is related to the integer solution is an important problem in number theory.
The famous quadratic reciprocity law discovered by Gauss and Euler is the solution of this problem in the special case of quadratic polynomials in one variable.
Later, with the important discovery of class field theory in the early 20th century, this problem was solved for a larger class of univariate polynomial equations.
But this class of equations is not limited by the degree of polynomials, but depends on the intrinsic symmetry of the equations.
More precisely, it depends on its Galois group.
It has to be said that the development of mathematics really depends on some great gods.
Not limited to Gauss Euler Riemann, Galois's revolutionary work in the early 19th century was the introduction of group theory for the first time.
And use group theory to accurately measure the symmetry of polynomials.
Therefore, for the first time, mathematicians can bypass cumbersome calculations and use deeper abstract properties to deal with more specific problems on the surface.
This also marks the beginning of modern algebra.
The complexity of unary polynomials also lies in the complexity of the Galois group.
And field theory deals with the case of commutative Galois groups.
As for the non-commutative case, because it is much more complicated, it has become an important goal of the modern Langlands program.
The Langlands Program was created by Professor Langlands, one of the three reviewers of Chen Zhou's thesis.
It can be said that, to a certain extent, the L function has guided the development of modern algebra.
As a leading algebraist, the two difficult problems left by Professor Emile Artin can indeed be said to be two crucial difficult problems in the field of algebra.
However, how much does this have to do with the current self?
Chen Zhou said: "It is indeed two very important problems, but the solution to these two problems is not so easy. If you are studying them, then I wish you good luck."
Nott ignored Chen Zhou's words, she stared at Chen Zhou and said, "Don't you think solving such a problem is very attractive?"
Chen Zhou frowned and looked at Nott, is this trying to win him over?
Seeing that Chen Zhou did not speak, Nott continued: "Even, based on this, we can solve a series of problems of the L function! A series of problems including the Langlands program!"
Chen Zhou grinned, this senior, maybe she didn't wake up?
The Langlands program? BSD conjecture?Hodge guess?Riemann conjecture?
This series of... questions?
Chen Zhou really wanted to ask her, has she ever solved a mathematical conjecture?
If not, he could tell her some experience.
Mathematical conjectures are really not mathematical imaginations, they just solve a series of problems casually.
It is the crystallization of wisdom of mathematicians, and it needs mathematical inspiration.
It is far from being as simple as talking about it.
"This..." Chen Zhou said hesitantly, "Just do your research, don't count mine."
Nott froze for a moment, then said immediately, "Aren't you interested?"
Chen Zhou shook his head, and said truthfully, "If you are interested, you are interested, but solving difficult problems is not just about being interested."
After all, this series of questions really fascinated Chen Zhou infinitely.
It would be an understatement to say that you are not interested.
I believe that no mathematician in the world is not interested in the Riemann conjecture, the BSD conjecture, or the Hodge conjecture.
Hearing Chen Zhou's words, Nott breathed a sigh of relief silently, this is the person he likes.
After pausing for a moment, Nott said again: "These two major problems are actually not only proposed by Professor Emil Artin alone, nor are they only his own research topics."
"These two major problems are also the research topics of Professors Emile Noether, Richard Brauer and Helmut Hasse."
"Especially Professor Emile Noether, as the Queen of Algebra, she has long been predictive in the research of these two issues!"
Nott's voice slowly turned from flat to excited again.
Especially when it comes to Emile Knott, the queen of algebra, her body seems to be shaking.
After noticing these, Chen Zhou also had his own answer in mind.
It seems that his previous guess was correct.
The senior Nott in front of her has an extraordinary connection with the Queen of Algebra in the history of mathematics.
At the same time, Chen Zhou probably also guessed Nott's intention of chatting with himself for so long.
Sure enough, before Chen Zhou could ask, Nott calmed down by himself: "Sorry, I lost my composure just now. You are probably thinking, what is the relationship between me and Professor Emil Nott?"
"I'm really curious about the relationship between you two. As far as I know, Professor Emile Noether never married?" Chen Zhou nodded, but he didn't hide his thoughts.
Nott heard the words, smiled slightly at the corner of his mouth, and explained: "Emil Nott, she is my great-grandmother."
Chen Zhou didn't realize it at first, but then he understood.
Professor Emile Noether has three younger brothers.
Presumably, the Nott-senpai in front of you is the offspring of someone, right?
Chen Zhou didn't expect that his wild guess when they met for the first time turned out to be right.
Could it be that in the United States, it is so easy to meet a family of mathematics?
My mentor, Professor Artin, yes, now the identity of Senior Nott has also been confirmed.
Chen Zhou thought for a while and said, "So, is that why you want to study these issues?"
Nott nodded, her expression was very heavy: "Since the death of great-grandmother, the Nott family has not produced a famous enough mathematician, but the Nott family has never given up on mathematics. glory."
"From the time I was born, my father told me that the children of the Knott family must regain the glory of mathematics."
"So, our family's mission, or my mission, is to solve these mathematical legacy problems."
"Because of this, I chose the field of algebra for research and study. My supervisor, Professor Michel, and I have been trying to solve these problems."
Speaking of this, Nott's expression changed, and he said firmly: "I also believe that we can finally solve these remaining mathematical problems, and I can also restore the Nott family to the glory of mathematics in the past!"
After Chen Zhou listened, he looked at the delicate girl in front of him, not knowing what to say.
At least, Chen Zhou still admires this courage to shoulder the mission of the family.
Apart from other things, judging from the question Nott asked himself last time, this girl's math talent is not bad.
Although it is not top-notch, nor can it compare to myself, but with such a strong heart, it is enough to achieve certain results in mathematics.
As for the problem she mentioned, it was not just a question of talent.
While Chen Zhou was thinking, Nott said again: "Student Chen Zhou, I solemnly invite you to join my tutor's research group and work with us to study these difficult problems. You don't have to reject me immediately, I hope you are serious. Consider my invitation."
Nott's tone was very sincere, and his eyes were also very sincere.
The freshman dance was not the first time she saw Chen Zhou, she had seen Chen Zhou's report before.
It was also from that report meeting that Nott got to know Chen Zhou.
This young student left a deep impression on her.
That's why there was a consultation about the freshmen's prom later.
It was a question consultation and a test of strength.
After this period of time, Nott heard the evaluations of Chen Zhou from the professors.
She finally made up her mind and invited Chen Zhou.
That's what happened today.
Chen Zhou asked a little puzzled: "Why me? I still think that Professor A Ting can help you more?"
Nott shook his head again and said the same thing: "Professor Artin is not suitable for us, and he will not help us."
Chen Zhou: "Why?"
Nott was silent for a while before he said, "Because of the relationship between Professor Emile Artin and Professor Emil Nott."
Chen Zhou froze for a moment, then said immediately: "Sorry, I didn't mean to pry into the privacy."
Nott laughed softly: "In addition, Professor Artin is an old pedant, you must be more interesting than him. Moreover, as our peers, it must be more convenient for us to communicate."
Chen Zhou also said with a smile: "Academic exchanges, what's interesting, I think these mathematics professors are sometimes quite cute."
Nott was taken aback for a moment, and looked up at Chen Zhou. Does this person really understand, or?
Chen Zhou looked at his watch again, then turned to Nott and said, "I probably can't agree to your invitation. However, if you encounter any problems and need to communicate or give advice, you can send me an email. "
After finishing speaking, leaving Nott with a dull expression on his face, Chen Zhou went straight back to his dormitory.
Looking at Chen Zhou's back, It took a while for Nott to come back to his senses.
Although Chen Zhou rejected her, she didn't intend to just give up.
Just like her, even if she knows her talent in mathematics, she may not be outstanding.
But still resolutely embarked on the path of mathematics.
Chen Zhou is someone she is very optimistic about.
Her intuition told her that Chen Zhou's mathematical talent was extremely terrifying!
Forgot to write yesterday, write today.
Thanks for the 100 starting coins rewarded by book friend Kunlin Yuanshan!
Thanks to book friend Shuyuan for rewarding "Chen Zhou" with 1000 starting coins!
Thanks to book friend Hiroyoshi Inoue for rewarding 100 starting coins!
Thanks to book friends 20200910163430084 for the 100 starting coins!
(End of this chapter)
"A problem with algebraic geometry?"
Chen Zhou smiled softly and said, "Then you should ask my tutor, as you said just now, he is a master in the field of algebraic geometry."
After speaking, Chen Zhou looked at his watch.
This Senior Nott has already delayed him for more than ten minutes.
If she didn't tell the purpose of the coincidence later, Chen Zhou planned to leave immediately.
When Nott saw Chen Zhou looking at his watch, he naturally understood what Chen Zhou meant.
Without going around the corner, Nott said, "You know the Artin L function, right?"
Chen Zhou frowned slightly: "A Ting L function?"
Nott nodded: "Yes, Artin L function."
"Of course I know that." Chen Zhou said puzzled, "But if your question is related to Arting's L function, then you should ask Professor Arting, I believe he understands his father's work better."
Nott shook his head: "Professor Artin is not suitable for us, and he will not help us."
Chen Zhou was a little confused now. He looked at Nott and said: "Professor A Ting is not suitable for you, so I am suitable for you? If you say that Professor A Ting will not help you, is it true that as a student of Professor A Ting I will help you? Also, what do you mean?"
Facing Chen Zhou's series of questions, Nott didn't feel impolite, but a smile appeared on the corner of his mouth.
She said slowly: "Do you know the two major mathematical problems that Professor Artin's father, Professor Emil Artin, left for future generations?"
Chen Zhou was stunned for a moment, and said softly: "The linear representation of the Artin L function of the Galois group? And given the proof number a, find the frequency that a is the original root of different prime p modules?"
"That's right!" Hearing Chen Zhou's words, Nott's expression became excited, "These two major mathematical problems are not only the mathematical problems left by Professor Emil Artin to future generations, but also crucial problems in the field of algebra. Two important problems!"
Chen Zhou glanced at Nott, but he didn't quite understand why this man was so excited.
Could it be that the senior Nott in front of me really has something to do with the Queen of Algebra?
But isn't this left by Professor Emil Artin?
Chen Zhou couldn't see the answer.
However, Chen Zhou quite agrees with what Nott said.
In particular, the L function really occupies a very important position in modern mathematics.
从欧拉考虑了函数ζ(S)=∑n=1→∞n^(-S)，并证明了其在S=2点的值1+1/2^2+3^2+……=π^2/6开始。
Later, in his famous paper, Riemann proposed that this function satisfies three conditions.
One is that it has the expression ∑n=1→∞n^(-S)=p∏prime1/1-p^(-S).
One is its value in 1-S and S, which has symmetry and satisfies a certain function equation.
The last one is that its ordinary zero points are distributed on the straight line Re(S)=1/2.
The first two are easy to prove with elementary methods, and the third is the famous Riemann hypothesis.
Today, this function is also commonly referred to as the Riemann zeta function.
It is also a special case of a certain class of functions, which are called L functions.
L functions have properties similar to the above three conditions, and their values at special points have expressions similar to Euler.
Don't think that this vague expression looks like elementary algebra.
In fact, its meaning is profound.
As for the reason...
It contains three of the seven million-dollar millennium problems proposed by the Clay Institute of the United States in the early 21st century-the Bayh and Swinton-Dell conjecture, the Hodge conjecture and the Riemann conjecture.
Besides that, there are many other famous conjectures.
In a sense, behind this expression of the L function, a series of extremely magnificent mathematical structures are hidden.
Behind these structures is not only the meaning of the problem itself, but also contains many powerful tools for solving it.
In addition, the L function generally has two kinds of L functions with different origins, namely the Motivic L function and the automorphic L function.
The Artin L function is also included in this.
The Motivic L function originated from algebraic number theory and algebraic geometry.
As we all know, one of the core problems of algebraic number theory is to solve univariate polynomial equations with integer coefficients.
For every prime number p, the case modulo p can be considered and a univariate polynomial equation over a finite field can be obtained.
In principle, it can be easily solved.
And how the solution modulo p is related to the integer solution is an important problem in number theory.
The famous quadratic reciprocity law discovered by Gauss and Euler is the solution of this problem in the special case of quadratic polynomials in one variable.
Later, with the important discovery of class field theory in the early 20th century, this problem was solved for a larger class of univariate polynomial equations.
But this class of equations is not limited by the degree of polynomials, but depends on the intrinsic symmetry of the equations.
More precisely, it depends on its Galois group.
It has to be said that the development of mathematics really depends on some great gods.
Not limited to Gauss Euler Riemann, Galois's revolutionary work in the early 19th century was the introduction of group theory for the first time.
And use group theory to accurately measure the symmetry of polynomials.
Therefore, for the first time, mathematicians can bypass cumbersome calculations and use deeper abstract properties to deal with more specific problems on the surface.
This also marks the beginning of modern algebra.
The complexity of unary polynomials also lies in the complexity of the Galois group.
And field theory deals with the case of commutative Galois groups.
As for the non-commutative case, because it is much more complicated, it has become an important goal of the modern Langlands program.
The Langlands Program was created by Professor Langlands, one of the three reviewers of Chen Zhou's thesis.
It can be said that, to a certain extent, the L function has guided the development of modern algebra.
As a leading algebraist, the two difficult problems left by Professor Emile Artin can indeed be said to be two crucial difficult problems in the field of algebra.
However, how much does this have to do with the current self?
Chen Zhou said: "It is indeed two very important problems, but the solution to these two problems is not so easy. If you are studying them, then I wish you good luck."
Nott ignored Chen Zhou's words, she stared at Chen Zhou and said, "Don't you think solving such a problem is very attractive?"
Chen Zhou frowned and looked at Nott, is this trying to win him over?
Seeing that Chen Zhou did not speak, Nott continued: "Even, based on this, we can solve a series of problems of the L function! A series of problems including the Langlands program!"
Chen Zhou grinned, this senior, maybe she didn't wake up?
The Langlands program? BSD conjecture?Hodge guess?Riemann conjecture?
This series of... questions?
Chen Zhou really wanted to ask her, has she ever solved a mathematical conjecture?
If not, he could tell her some experience.
Mathematical conjectures are really not mathematical imaginations, they just solve a series of problems casually.
It is the crystallization of wisdom of mathematicians, and it needs mathematical inspiration.
It is far from being as simple as talking about it.
"This..." Chen Zhou said hesitantly, "Just do your research, don't count mine."
Nott froze for a moment, then said immediately, "Aren't you interested?"
Chen Zhou shook his head, and said truthfully, "If you are interested, you are interested, but solving difficult problems is not just about being interested."
After all, this series of questions really fascinated Chen Zhou infinitely.
It would be an understatement to say that you are not interested.
I believe that no mathematician in the world is not interested in the Riemann conjecture, the BSD conjecture, or the Hodge conjecture.
Hearing Chen Zhou's words, Nott breathed a sigh of relief silently, this is the person he likes.
After pausing for a moment, Nott said again: "These two major problems are actually not only proposed by Professor Emil Artin alone, nor are they only his own research topics."
"These two major problems are also the research topics of Professors Emile Noether, Richard Brauer and Helmut Hasse."
"Especially Professor Emile Noether, as the Queen of Algebra, she has long been predictive in the research of these two issues!"
Nott's voice slowly turned from flat to excited again.
Especially when it comes to Emile Knott, the queen of algebra, her body seems to be shaking.
After noticing these, Chen Zhou also had his own answer in mind.
It seems that his previous guess was correct.
The senior Nott in front of her has an extraordinary connection with the Queen of Algebra in the history of mathematics.
At the same time, Chen Zhou probably also guessed Nott's intention of chatting with himself for so long.
Sure enough, before Chen Zhou could ask, Nott calmed down by himself: "Sorry, I lost my composure just now. You are probably thinking, what is the relationship between me and Professor Emil Nott?"
"I'm really curious about the relationship between you two. As far as I know, Professor Emile Noether never married?" Chen Zhou nodded, but he didn't hide his thoughts.
Nott heard the words, smiled slightly at the corner of his mouth, and explained: "Emil Nott, she is my great-grandmother."
Chen Zhou didn't realize it at first, but then he understood.
Professor Emile Noether has three younger brothers.
Presumably, the Nott-senpai in front of you is the offspring of someone, right?
Chen Zhou didn't expect that his wild guess when they met for the first time turned out to be right.
Could it be that in the United States, it is so easy to meet a family of mathematics?
My mentor, Professor Artin, yes, now the identity of Senior Nott has also been confirmed.
Chen Zhou thought for a while and said, "So, is that why you want to study these issues?"
Nott nodded, her expression was very heavy: "Since the death of great-grandmother, the Nott family has not produced a famous enough mathematician, but the Nott family has never given up on mathematics. glory."
"From the time I was born, my father told me that the children of the Knott family must regain the glory of mathematics."
"So, our family's mission, or my mission, is to solve these mathematical legacy problems."
"Because of this, I chose the field of algebra for research and study. My supervisor, Professor Michel, and I have been trying to solve these problems."
Speaking of this, Nott's expression changed, and he said firmly: "I also believe that we can finally solve these remaining mathematical problems, and I can also restore the Nott family to the glory of mathematics in the past!"
After Chen Zhou listened, he looked at the delicate girl in front of him, not knowing what to say.
At least, Chen Zhou still admires this courage to shoulder the mission of the family.
Apart from other things, judging from the question Nott asked himself last time, this girl's math talent is not bad.
Although it is not top-notch, nor can it compare to myself, but with such a strong heart, it is enough to achieve certain results in mathematics.
As for the problem she mentioned, it was not just a question of talent.
While Chen Zhou was thinking, Nott said again: "Student Chen Zhou, I solemnly invite you to join my tutor's research group and work with us to study these difficult problems. You don't have to reject me immediately, I hope you are serious. Consider my invitation."
Nott's tone was very sincere, and his eyes were also very sincere.
The freshman dance was not the first time she saw Chen Zhou, she had seen Chen Zhou's report before.
It was also from that report meeting that Nott got to know Chen Zhou.
This young student left a deep impression on her.
That's why there was a consultation about the freshmen's prom later.
It was a question consultation and a test of strength.
After this period of time, Nott heard the evaluations of Chen Zhou from the professors.
She finally made up her mind and invited Chen Zhou.
That's what happened today.
Chen Zhou asked a little puzzled: "Why me? I still think that Professor A Ting can help you more?"
Nott shook his head again and said the same thing: "Professor Artin is not suitable for us, and he will not help us."
Chen Zhou: "Why?"
Nott was silent for a while before he said, "Because of the relationship between Professor Emile Artin and Professor Emil Nott."
Chen Zhou froze for a moment, then said immediately: "Sorry, I didn't mean to pry into the privacy."
Nott laughed softly: "In addition, Professor Artin is an old pedant, you must be more interesting than him. Moreover, as our peers, it must be more convenient for us to communicate."
Chen Zhou also said with a smile: "Academic exchanges, what's interesting, I think these mathematics professors are sometimes quite cute."
Nott was taken aback for a moment, and looked up at Chen Zhou. Does this person really understand, or?
Chen Zhou looked at his watch again, then turned to Nott and said, "I probably can't agree to your invitation. However, if you encounter any problems and need to communicate or give advice, you can send me an email. "
After finishing speaking, leaving Nott with a dull expression on his face, Chen Zhou went straight back to his dormitory.
Looking at Chen Zhou's back, It took a while for Nott to come back to his senses.
Although Chen Zhou rejected her, she didn't intend to just give up.
Just like her, even if she knows her talent in mathematics, she may not be outstanding.
But still resolutely embarked on the path of mathematics.
Chen Zhou is someone she is very optimistic about.
Her intuition told her that Chen Zhou's mathematical talent was extremely terrifying!
Forgot to write yesterday, write today.
Thanks for the 100 starting coins rewarded by book friend Kunlin Yuanshan!
Thanks to book friend Shuyuan for rewarding "Chen Zhou" with 1000 starting coins!
Thanks to book friend Hiroyoshi Inoue for rewarding 100 starting coins!
Thanks to book friends 20200910163430084 for the 100 starting coins!
(End of this chapter)
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