NOVEL NEXT Xueba starts with change
Chapter 454 Mathematician's Feelings (2 in 14000 words)
Chapter 454 Mathematician's Feelings (4000 in [-] [-] words)
Chen Zhou greeted Liu Maosheng and Zeng Zigu, and followed Deligne to a nearby cafe.
in the cafe.
When the waiter asked what he wanted, Chen Zhou only ordered a glass of boiled water.
To be honest, Chen Zhou doesn't like drinking coffee very much, he really isn't used to it.
In contrast, boiled water is the real public drink.
Looking at the young man opposite, Deligne asked softly, "Do you know why I'm looking for you?"
Chen Zhou thought for a while, then said uncertainly, "About the standard conjecture?"
Deligne nodded: "It's related to the teacher's topic."
After receiving an affirmative answer, Chen Zhou became even more puzzled.
I don't seem to be able to help him solve the standard conjecture?
And I don't have the research experience of the standard conjecture, so I can't provide much help.
Could it be that Professor Deligne thinks highly of himself so much that he thinks that the subject he is researching will definitely be solved, so this is to persuade himself to study the standard conjecture?
I'm afraid I'm not kidding myself, right?
Chen Zhou asked himself, he was absolutely inferior to the old man in front of him.
The standard conjecture problem is not only in the present, but also in the future.
At least for now, he is far from capable of solving this problem.
Deligne had been observing Chen Zhou, and after noticing Chen Zhou's puzzled expression, he didn't immediately explain.
Instead, he picked up the coffee and took a sip on his own, and then told a story without haste.
"I remember that as early as 1959, Dwork used the p-adic method to prove the first Weil's conjecture, that is, the zeta function of the finite body solution is a rational function."
"Later, in 1964, my teacher Grothendieck made the I-advance proof of Weil's conjecture more common, and introduced his 'formal system of six operations'."
"Later, the teacher proved the second Weil's conjecture, which is the zeta function of the solution form, which satisfies a certain functional equation."
"It was also during the 60s that finding a way to prove the last Weil's conjecture became the main source of inspiration for the teacher's research and became his obsession."
"The 'Standard Conjecture' was constructed and proposed during this period of time. The teacher always believed that if these standard conjectures could be proved, the entire Weil Conjecture could be proved. And, deeply trapped in this..."
Listening to Deligne's narration, the puzzled expression on Chen Zhou's face has gradually disappeared.
He vaguely guessed the reason for Deligne's unique opening remarks in the lecture.
As Deligne said, the standard conjecture is Grothendieck's last regret.
It is also Deligne's regret that bypasses the standard conjecture and proves Weil's conjecture.
And the reason for this regret, Deligne is telling Chen Zhou.
"Because I was deeply influenced by my teacher, at the beginning of my research on Weil's conjecture, I also revolved around the standard conjecture."
"Until later, I saw Professor Lan Jin's paper, which discussed the theory of classical modular forms that the teacher didn't know."
"And this key concept successfully helped me bypass the standard conjecture and proved Weil's final conjecture."
"This is why some mathematicians later said that in order to prove the final Weil conjecture, more classical material is needed, and this is Grothendieck's blind spot."
"But in fact, this is the biggest misunderstanding of teachers!"
There was a certain strange emotion in Deligne's voice, so that the voice became slightly trembling.
Chen Zhou at this moment is obviously a qualified listener.
At the same time, he was trying to understand Deligne's emotions.
These words of Deligne also made Chen Zhou confirm his guess.
In today's lecture, Deligne did have that opening remark because of Grothendieck.
It was also two years after Grothendieck's death that Deligne used such an occasion to vent some emotions.
However, what Chen Zhou didn't understand was why two years later?
Also, why did the other party say these things to me?
Deligne paused for a moment, restrained his emotions a little, and then continued: "In the teacher's heart, the reason why Weil's conjecture is important is that it is the tip of the iceberg, which can reflect the basic mathematics he wants to discover and develop. structure."
"If the standard conjecture can be proved, this structure can be revealed more deeply. In other words, Weil's conjecture should serve the standard conjecture."
"In the process of proving Weil's conjecture, the standard conjecture must not be bypassed!"
"If I use the Motive theory, the teacher will definitely be very interested. Because it means that the standard conjecture has a new development."
"But I let the tip of the iceberg go, completely out of the standard conjecture..."
Speaking of this, Deligne sighed softly: "That's why, the teacher is not very interested in my flattering proof."
Chen Zhou didn't know how to comfort this mathematician.
But Chen Zhou could clearly hear the cause and effect of this.
Chen Zhou felt that Deligne's lecture today was probably the first step to make up for Grothendieck's regrets, as well as his own.
After a moment of silence, Deligne picked up the coffee and took another sip.
Looking at the young man opposite, Deligne said suddenly: "Do you have any thoughts about today's lecture?"
Chen Zhou thought for a while and said, "Mirnor's conjecture, I think these new research results should be able to promote the solution of Milnor's conjecture, and provide the key to many propositions."
Milnor's conjecture is just a proposition that connects cohomology theory and algebraic K-theory, and also involves quadratic form theory. It is one of the most important problems in algebraic K-theory II for 30 years.
More importantly, if the Milnor conjecture is solved.
Then, the breakthrough of this mathematical theory will be an extremely critical first step in solving the Beilinson-Lichtenbaum conjecture and the Bloch-Garten conjecture.
And these mathematical conjectures are the basic "results" for the establishment of special algebraic diversity obtained by Bellinson, Bloch, Lichtenbaum and others over the years when they studied the standard conjectures .
The reason why this result is in double quotes is because these basic propositions are just conjectures.
But now, Deligne's research seems to make it possible for these conjectures to become theorems.
It also made it possible for Grothendieck's standard conjecture to be further developed.
Although Chen Zhou's answer was not so clear.
If ordinary people were to listen, they might not even know what Chen Zhou was talking about.
However, when Deligne heard Chen Zhou's answer, his eyes lit up immediately.
The look in Chen Zhou's eyes also became a little subtle.
"I originally thought that your research field has always been limited to analytic number theory, and your understanding of algebraic geometry is not deep enough. But your answer exceeded my expectations."
Deligne praised Chen Zhou unabashedly.
However, Chen Zhou explained: "There is probably no mathematician who would not be interested in difficult problems like the standard conjecture. What's more, my tutor is Professor A Ting of Algebraic Geometry."
Deligne nodded with a smile: "I almost forgot, your graduate tutor is Michael Artin."
After a pause, Deligne asked Chen Zhou: "Since you also said that you are interested in the standard conjecture, have you ever thought about switching to this subject?"
Chen Zhou was taken aback by the question. Could this be the ultimate goal of finding himself?
But before Chen Zhou could answer, Deligne said first, "I'm very optimistic about your research in this area, and I also want to believe that you can achieve the same achievements as in analytic number theory."
"Also, I wonder if you are interested in my research group, come and study with me?"
Chen Zhou looked at Deligne with a strange expression, what does this little old man mean?
He told himself a story first, then asked himself what he thought about listening to the lecture, and now he directly invited himself to join his research group.
Could this be the legendary art of throwing bricks to attract jade and attracting people into the group?
"That...Professor Deligne..." Chen Zhou said hesitantly, "I think the current me may not be suitable for the study of the standard conjecture... So, thank you for your kindness..."
Unexpectedly, after hearing this, Deligne just smiled and said: "It doesn't matter, the solution to the standard conjecture will not take a year or two. When you are ready, we can study together again, that's okay."
Chen Zhou was speechless for a moment, it was too...
But then, Deligne continued: "This invitation does not mean that I am the main one, or that you are here to serve my research group. There will be an equal cooperative relationship between the two of us."
Chen Zhou looked up at Deligne, the meaning of these words, or the weight of these words, was a bit too heavy.
Although Chen Zhou has just won the Cole Prize in Number Theory, the highest honor in the number theory field.
But in front of Deligne, he is just a young child who has just started in the world of mathematics.
No matter from which level, he does not have the equality of Deligne as a research collaborator on the subject of the standard conjecture.
It's not that Chen Zhou's ability is not enough at all.
Just because the opponent is Deligne.
Keenly aware of the changes in Chen Zhou, Deligne said softly: "My teacher encountered great technical difficulties when studying the standard conjecture and developing the Motive theory."
"I believe you have also learned from my lectures. In the study of the standard conjecture, the most serious problem is that if you want to achieve the idea of the teacher's Motive theory, you must construct enough algebraic closed chains."
"But it's a pity that even though the teacher has consumed a lot of mind and wisdom, he still can't find the Motive theory in his heart."
"And since then, no one has succeeded..."
Chen Zhou didn't react for a while, he didn't understand why Deligne said such a thing again.
Chen Zhou hesitated and said, "Professor Deligne, your research is approaching this theory, isn't it?"
Deligne shook his head slightly: "Although the mathematics community is not yet convinced of my research results, I understand that this is just the beginning, and it can't even be called close to this theory."
Hearing Deligne's words, Chen Zhou remained silent.
He felt that Deligne was a little pessimistic.
In fact, the importance of this research result is gradually becoming prominent.
Just as Chen Zhou thought just now, the series of propositions foreshadowed by this achievement are not unimportant.
Deligne glanced at the silent Chen Zhou, picked up the cold coffee, and put it down again.
"I have always felt that it might be because of his obsession with the Motive theory and the study of the standard conjecture that the teacher could not solve the Weil conjecture."
"However, Weil's conjecture was solved by me in a flattering way..."
Chen Zhou could clearly hear a hint of sadness in Deligne's voice.
Pursing his lips, Chen Zhou said aloud: "But it is undeniable that the proof of Weil's conjecture is one of the greatest achievements of algebraic geometry in recent decades."
Deligne shook his head: "If I didn't bypass the standard conjecture, I might still be able to accept such a statement. But now, all I have left is regret..."
After a pause, Deligne looked at Chen Zhou, and finally expressed his truest thoughts.
"Chen Zhou, I know it might be presumptuous to say this, but I have to give a reasonable explanation for what I just said."
Chen Zhou nodded slightly, and Deligne continued: "The study of the standard conjecture should require mathematicians to keep trying and finally complete it."
"Just like Fermat's last theorem, after hundreds of years of attempts, it was finally proved by Professor Wiles. The standard conjecture should be the same."
"As the proposer of the standard conjecture, my teacher Grothendieck was the mathematician who first studied the standard conjecture. Unfortunately, he was not able to finally solve this problem that may belong to the future."
When talking about the future, Deligne had a kind of expectation in his eyes.
"I should have been the person closest to the teacher's idea in the study of the standard conjecture, but unfortunately..." Deligne continued, "In order to make up for this regret, I have been obsessed with the study of the standard conjecture in recent years. And achieved the results you know."
"However, in the study of the standard conjecture, I know very well that the solution to this conjecture will not be in my hands. I am just a guide for future generations."
"So, I hope you can follow me, and don't give up the research on the standard conjecture..."
After Deligne finished speaking, Chen Zhou finally understood.
Deligne is looking for the "inheritor" of the standard conjecture.
Chen Zhou felt that this was probably what the inheritor meant.
From Grothendieck to Deligne, this is the same strain.
But after Deligne, he himself did not have a suitable "inheritor".
So, he found Chen Zhou.
Of course, Chen Zhou felt that Deligne's obsession with the standard conjecture mostly came from his desire to make up for his regrets.
And the feelings contained in this heart are all the teacher-student relationship between him and Grothendieck.
From this conversation, Chen Zhou finally understood the feelings of mathematicians.
From the beginning of mathematics to the end of mathematics.
To be honest, Deligne's request was not too difficult for Chen Zhou.
On the road of mathematics, Chen Zhou, who is "determined" to build his own mathematical building, must not get around the standard conjecture, the most important problem in the field of algebraic geometry.
However, Chen Zhou had to figure out one thing.
That is, why him?
In contrast, Schulz, a super genius in the field of algebraic geometry.
Shouldn't it be more appropriate?
Thanks to book friend Kunlin Yuanshan for rewarding Chen Zhou with 100 starting coins!
(End of this chapter)
Chen Zhou greeted Liu Maosheng and Zeng Zigu, and followed Deligne to a nearby cafe.
in the cafe.
When the waiter asked what he wanted, Chen Zhou only ordered a glass of boiled water.
To be honest, Chen Zhou doesn't like drinking coffee very much, he really isn't used to it.
In contrast, boiled water is the real public drink.
Looking at the young man opposite, Deligne asked softly, "Do you know why I'm looking for you?"
Chen Zhou thought for a while, then said uncertainly, "About the standard conjecture?"
Deligne nodded: "It's related to the teacher's topic."
After receiving an affirmative answer, Chen Zhou became even more puzzled.
I don't seem to be able to help him solve the standard conjecture?
And I don't have the research experience of the standard conjecture, so I can't provide much help.
Could it be that Professor Deligne thinks highly of himself so much that he thinks that the subject he is researching will definitely be solved, so this is to persuade himself to study the standard conjecture?
I'm afraid I'm not kidding myself, right?
Chen Zhou asked himself, he was absolutely inferior to the old man in front of him.
The standard conjecture problem is not only in the present, but also in the future.
At least for now, he is far from capable of solving this problem.
Deligne had been observing Chen Zhou, and after noticing Chen Zhou's puzzled expression, he didn't immediately explain.
Instead, he picked up the coffee and took a sip on his own, and then told a story without haste.
"I remember that as early as 1959, Dwork used the p-adic method to prove the first Weil's conjecture, that is, the zeta function of the finite body solution is a rational function."
"Later, in 1964, my teacher Grothendieck made the I-advance proof of Weil's conjecture more common, and introduced his 'formal system of six operations'."
"Later, the teacher proved the second Weil's conjecture, which is the zeta function of the solution form, which satisfies a certain functional equation."
"It was also during the 60s that finding a way to prove the last Weil's conjecture became the main source of inspiration for the teacher's research and became his obsession."
"The 'Standard Conjecture' was constructed and proposed during this period of time. The teacher always believed that if these standard conjectures could be proved, the entire Weil Conjecture could be proved. And, deeply trapped in this..."
Listening to Deligne's narration, the puzzled expression on Chen Zhou's face has gradually disappeared.
He vaguely guessed the reason for Deligne's unique opening remarks in the lecture.
As Deligne said, the standard conjecture is Grothendieck's last regret.
It is also Deligne's regret that bypasses the standard conjecture and proves Weil's conjecture.
And the reason for this regret, Deligne is telling Chen Zhou.
"Because I was deeply influenced by my teacher, at the beginning of my research on Weil's conjecture, I also revolved around the standard conjecture."
"Until later, I saw Professor Lan Jin's paper, which discussed the theory of classical modular forms that the teacher didn't know."
"And this key concept successfully helped me bypass the standard conjecture and proved Weil's final conjecture."
"This is why some mathematicians later said that in order to prove the final Weil conjecture, more classical material is needed, and this is Grothendieck's blind spot."
"But in fact, this is the biggest misunderstanding of teachers!"
There was a certain strange emotion in Deligne's voice, so that the voice became slightly trembling.
Chen Zhou at this moment is obviously a qualified listener.
At the same time, he was trying to understand Deligne's emotions.
These words of Deligne also made Chen Zhou confirm his guess.
In today's lecture, Deligne did have that opening remark because of Grothendieck.
It was also two years after Grothendieck's death that Deligne used such an occasion to vent some emotions.
However, what Chen Zhou didn't understand was why two years later?
Also, why did the other party say these things to me?
Deligne paused for a moment, restrained his emotions a little, and then continued: "In the teacher's heart, the reason why Weil's conjecture is important is that it is the tip of the iceberg, which can reflect the basic mathematics he wants to discover and develop. structure."
"If the standard conjecture can be proved, this structure can be revealed more deeply. In other words, Weil's conjecture should serve the standard conjecture."
"In the process of proving Weil's conjecture, the standard conjecture must not be bypassed!"
"If I use the Motive theory, the teacher will definitely be very interested. Because it means that the standard conjecture has a new development."
"But I let the tip of the iceberg go, completely out of the standard conjecture..."
Speaking of this, Deligne sighed softly: "That's why, the teacher is not very interested in my flattering proof."
Chen Zhou didn't know how to comfort this mathematician.
But Chen Zhou could clearly hear the cause and effect of this.
Chen Zhou felt that Deligne's lecture today was probably the first step to make up for Grothendieck's regrets, as well as his own.
After a moment of silence, Deligne picked up the coffee and took another sip.
Looking at the young man opposite, Deligne said suddenly: "Do you have any thoughts about today's lecture?"
Chen Zhou thought for a while and said, "Mirnor's conjecture, I think these new research results should be able to promote the solution of Milnor's conjecture, and provide the key to many propositions."
Milnor's conjecture is just a proposition that connects cohomology theory and algebraic K-theory, and also involves quadratic form theory. It is one of the most important problems in algebraic K-theory II for 30 years.
More importantly, if the Milnor conjecture is solved.
Then, the breakthrough of this mathematical theory will be an extremely critical first step in solving the Beilinson-Lichtenbaum conjecture and the Bloch-Garten conjecture.
And these mathematical conjectures are the basic "results" for the establishment of special algebraic diversity obtained by Bellinson, Bloch, Lichtenbaum and others over the years when they studied the standard conjectures .
The reason why this result is in double quotes is because these basic propositions are just conjectures.
But now, Deligne's research seems to make it possible for these conjectures to become theorems.
It also made it possible for Grothendieck's standard conjecture to be further developed.
Although Chen Zhou's answer was not so clear.
If ordinary people were to listen, they might not even know what Chen Zhou was talking about.
However, when Deligne heard Chen Zhou's answer, his eyes lit up immediately.
The look in Chen Zhou's eyes also became a little subtle.
"I originally thought that your research field has always been limited to analytic number theory, and your understanding of algebraic geometry is not deep enough. But your answer exceeded my expectations."
Deligne praised Chen Zhou unabashedly.
However, Chen Zhou explained: "There is probably no mathematician who would not be interested in difficult problems like the standard conjecture. What's more, my tutor is Professor A Ting of Algebraic Geometry."
Deligne nodded with a smile: "I almost forgot, your graduate tutor is Michael Artin."
After a pause, Deligne asked Chen Zhou: "Since you also said that you are interested in the standard conjecture, have you ever thought about switching to this subject?"
Chen Zhou was taken aback by the question. Could this be the ultimate goal of finding himself?
But before Chen Zhou could answer, Deligne said first, "I'm very optimistic about your research in this area, and I also want to believe that you can achieve the same achievements as in analytic number theory."
"Also, I wonder if you are interested in my research group, come and study with me?"
Chen Zhou looked at Deligne with a strange expression, what does this little old man mean?
He told himself a story first, then asked himself what he thought about listening to the lecture, and now he directly invited himself to join his research group.
Could this be the legendary art of throwing bricks to attract jade and attracting people into the group?
"That...Professor Deligne..." Chen Zhou said hesitantly, "I think the current me may not be suitable for the study of the standard conjecture... So, thank you for your kindness..."
Unexpectedly, after hearing this, Deligne just smiled and said: "It doesn't matter, the solution to the standard conjecture will not take a year or two. When you are ready, we can study together again, that's okay."
Chen Zhou was speechless for a moment, it was too...
But then, Deligne continued: "This invitation does not mean that I am the main one, or that you are here to serve my research group. There will be an equal cooperative relationship between the two of us."
Chen Zhou looked up at Deligne, the meaning of these words, or the weight of these words, was a bit too heavy.
Although Chen Zhou has just won the Cole Prize in Number Theory, the highest honor in the number theory field.
But in front of Deligne, he is just a young child who has just started in the world of mathematics.
No matter from which level, he does not have the equality of Deligne as a research collaborator on the subject of the standard conjecture.
It's not that Chen Zhou's ability is not enough at all.
Just because the opponent is Deligne.
Keenly aware of the changes in Chen Zhou, Deligne said softly: "My teacher encountered great technical difficulties when studying the standard conjecture and developing the Motive theory."
"I believe you have also learned from my lectures. In the study of the standard conjecture, the most serious problem is that if you want to achieve the idea of the teacher's Motive theory, you must construct enough algebraic closed chains."
"But it's a pity that even though the teacher has consumed a lot of mind and wisdom, he still can't find the Motive theory in his heart."
"And since then, no one has succeeded..."
Chen Zhou didn't react for a while, he didn't understand why Deligne said such a thing again.
Chen Zhou hesitated and said, "Professor Deligne, your research is approaching this theory, isn't it?"
Deligne shook his head slightly: "Although the mathematics community is not yet convinced of my research results, I understand that this is just the beginning, and it can't even be called close to this theory."
Hearing Deligne's words, Chen Zhou remained silent.
He felt that Deligne was a little pessimistic.
In fact, the importance of this research result is gradually becoming prominent.
Just as Chen Zhou thought just now, the series of propositions foreshadowed by this achievement are not unimportant.
Deligne glanced at the silent Chen Zhou, picked up the cold coffee, and put it down again.
"I have always felt that it might be because of his obsession with the Motive theory and the study of the standard conjecture that the teacher could not solve the Weil conjecture."
"However, Weil's conjecture was solved by me in a flattering way..."
Chen Zhou could clearly hear a hint of sadness in Deligne's voice.
Pursing his lips, Chen Zhou said aloud: "But it is undeniable that the proof of Weil's conjecture is one of the greatest achievements of algebraic geometry in recent decades."
Deligne shook his head: "If I didn't bypass the standard conjecture, I might still be able to accept such a statement. But now, all I have left is regret..."
After a pause, Deligne looked at Chen Zhou, and finally expressed his truest thoughts.
"Chen Zhou, I know it might be presumptuous to say this, but I have to give a reasonable explanation for what I just said."
Chen Zhou nodded slightly, and Deligne continued: "The study of the standard conjecture should require mathematicians to keep trying and finally complete it."
"Just like Fermat's last theorem, after hundreds of years of attempts, it was finally proved by Professor Wiles. The standard conjecture should be the same."
"As the proposer of the standard conjecture, my teacher Grothendieck was the mathematician who first studied the standard conjecture. Unfortunately, he was not able to finally solve this problem that may belong to the future."
When talking about the future, Deligne had a kind of expectation in his eyes.
"I should have been the person closest to the teacher's idea in the study of the standard conjecture, but unfortunately..." Deligne continued, "In order to make up for this regret, I have been obsessed with the study of the standard conjecture in recent years. And achieved the results you know."
"However, in the study of the standard conjecture, I know very well that the solution to this conjecture will not be in my hands. I am just a guide for future generations."
"So, I hope you can follow me, and don't give up the research on the standard conjecture..."
After Deligne finished speaking, Chen Zhou finally understood.
Deligne is looking for the "inheritor" of the standard conjecture.
Chen Zhou felt that this was probably what the inheritor meant.
From Grothendieck to Deligne, this is the same strain.
But after Deligne, he himself did not have a suitable "inheritor".
So, he found Chen Zhou.
Of course, Chen Zhou felt that Deligne's obsession with the standard conjecture mostly came from his desire to make up for his regrets.
And the feelings contained in this heart are all the teacher-student relationship between him and Grothendieck.
From this conversation, Chen Zhou finally understood the feelings of mathematicians.
From the beginning of mathematics to the end of mathematics.
To be honest, Deligne's request was not too difficult for Chen Zhou.
On the road of mathematics, Chen Zhou, who is "determined" to build his own mathematical building, must not get around the standard conjecture, the most important problem in the field of algebraic geometry.
However, Chen Zhou had to figure out one thing.
That is, why him?
In contrast, Schulz, a super genius in the field of algebraic geometry.
Shouldn't it be more appropriate?
Thanks to book friend Kunlin Yuanshan for rewarding Chen Zhou with 100 starting coins!
(End of this chapter)
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