Library activity room.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
…
"… I see."
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
What motive theory studies is a set named capital N consisting of countless n's.
Chen Yang shook his head.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
And if we only use mathematics for daily life, we may not realize this in our lifetime. Many religions and cultures that give numbers special meanings do not actually understand the "language of God."
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
Library activity room.
Standing next to Lu Zhou, Chen Yang thought for a moment and then suddenly asked.
It is both an abstract number and the essence of numbers.
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
In fact, this problem is a huge category.
"Langlands Programme?"
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
As for the motivation theory, it is less famous than the Langlands program.
"Well, I'll leave this piece to you!"
"It's not just the Langlands program," Lu Zhou said seriously, "but also the motive theory. To solve this problem, we must figure out the connection between different cohomology theories."
…
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
(For the part about motivation theory, please refer to Barry Mazur's famous "What is a Motive", which is a popular science paper. It is indeed eye-opening after reading it.)
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
In the paper, this Russian professor from the Institute for Advanced Study in Princeton proposed a very interesting Motive category.
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
In fact, this problem is a huge category.
Lu Zhou nodded and said.
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
…
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
Chen Yang shook his head.
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
"Two months is not enough, half a month... should be enough."
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
"Langlands Programme?"
What he lacks most is the perseverance to stay on the same path.
"Well, I'll leave this piece to you!"
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
"...the so-called motive is the root of all numbers."
"Langlands Programme?"
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
"Langlands Programme?"
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
Here, n is given a special meaning.
A dark premonition made him feel that he was very close to the finish line.
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
Chen Yang shook his head.
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
In fact, this problem is a huge category.
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
Lu Zhou nodded and said.
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
"… I see."
"It doesn't matter. This is not a task that can be completed in a short time. Besides, I'm not particularly anxious." Lu Zhou smiled and continued, "However, my suggestion is that it is best to give it to me within two months. An answer. If you’re not sure, it’s best to tell me in advance. It’s okay for me to do this myself.”
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
Here, n is given a special meaning.
“I need a theory that can carry forward the classical theory of one-dimensional cohomology—that is, the success of the Jacobi variety theory and Abel variety theory of curves—in order to facilitate cohomology in all dimensions.”
“I need a theory that can carry forward the classical theory of one-dimensional cohomology—that is, the success of the Jacobi variety theory and Abel variety theory of curves—in order to facilitate cohomology in all dimensions.”
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
A hint of excitement gradually filled his pupils, and the pen tip in Lu Zhou's hand stopped.
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
Lu Zhou nodded and said.
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
"Based on this theory, we can study the direct sum decomposition in motive theory to associate H(v) with irreducible motive."
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
And if we only use mathematics for daily life, we may not realize this in our lifetime. Many religions and cultures that give numbers special meanings do not actually understand the "language of God."
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
(For the part about motivation theory, please refer to Barry Mazur's famous "What is a Motive", which is a popular science paper. It is indeed eye-opening after reading it.)
It is both an abstract number and the essence of numbers.
It is both an abstract number and the essence of numbers.
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
"Originally, I planned to do this part myself, but there are still important parts worth completing. I plan to complete the grand unified theory within this year, and I will leave this part to you."
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
"It doesn't matter. This is not a task that can be completed in a short time. Besides, I'm not particularly anxious." Lu Zhou smiled and continued, "However, my suggestion is that it is best to give it to me within two months. An answer. If you’re not sure, it’s best to tell me in advance. It’s okay for me to do this myself.”
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
"Two months is not enough, half a month... should be enough."
Lu Zhou nodded and said.
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
And this was exactly what Lu Zhou needed.
"...the so-called motive is the root of all numbers."
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
What he lacks most is the perseverance to stay on the same path.
In the paper, this Russian professor from the Institute for Advanced Study in Princeton proposed a very interesting Motive category.
Lu Zhou nodded and said.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
Lu Zhou nodded and said.
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
…
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
What motive theory studies is a set named capital N consisting of countless n's.
"...the so-called motive is the root of all numbers."
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
"It doesn't matter. This is not a task that can be completed in a short time. Besides, I'm not particularly anxious." Lu Zhou smiled and continued, "However, my suggestion is that it is best to give it to me within two months. An answer. If you’re not sure, it’s best to tell me in advance. It’s okay for me to do this myself.”
In fact, this problem is a huge category.
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
Chen Yang shook his head.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
Standing next to Lu Zhou, Chen Yang thought for a moment and then suddenly asked.
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
"Two months is not enough, half a month... should be enough."
…
Lu Zhou nodded and said.
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
"...the so-called motive is the root of all numbers."
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
"... If you want to solve the problem of the unity of algebra and geometry, you must separate 'numbers' and 'shapes' from their general expression forms and look for the commonalities between them in abstract concepts."
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
What motive theory studies is a set named capital N consisting of countless n's.
Lu Zhou nodded and said.
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
And this was exactly what Lu Zhou needed.
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
What he lacks most is the perseverance to stay on the same path.
"It doesn't matter. This is not a task that can be completed in a short time. Besides, I'm not particularly anxious." Lu Zhou smiled and continued, "However, my suggestion is that it is best to give it to me within two months. An answer. If you’re not sure, it’s best to tell me in advance. It’s okay for me to do this myself.”
"Two months is not enough, half a month... should be enough."
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
"...the so-called motive is the root of all numbers."
As for the motivation theory, it is less famous than the Langlands program.
"Two months is not enough, half a month... should be enough."
"Well, I'll leave this piece to you!"
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
And if we only use mathematics for daily life, we may not realize this in our lifetime. Many religions and cultures that give numbers special meanings do not actually understand the "language of God."
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
"It doesn't matter. This is not a task that can be completed in a short time. Besides, I'm not particularly anxious." Lu Zhou smiled and continued, "However, my suggestion is that it is best to give it to me within two months. An answer. If you’re not sure, it’s best to tell me in advance. It’s okay for me to do this myself.”
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
…
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
What motive theory studies is a set named capital N consisting of countless n's.
…
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
"It's not just the Langlands program," Lu Zhou said seriously, "but also the motive theory. To solve this problem, we must figure out the connection between different cohomology theories."
"Well, I'll leave this piece to you!"
It is both an abstract number and the essence of numbers.
He created a single theory that bridged the gap between algebraic geometry and various cohomology theories.
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
Lu Zhou whispered softly in a voice that only he could hear. While comparing the calculations in the documents, he wrote furiously on the draft paper.
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
Standing next to Lu Zhou, Chen Yang thought for a moment and then suddenly asked.
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
A dark premonition made him feel that he was very close to the finish line.
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
As for the motivation theory, it is less famous than the Langlands program.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
And this was exactly what Lu Zhou needed.
"...the so-called motive is the root of all numbers."
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
Standing next to Lu Zhou, Chen Yang thought for a moment and then suddenly asked.
(For the part about motivation theory, please refer to Barry Mazur's famous "What is a Motive", which is a popular science paper. It is indeed eye-opening after reading it.)
…
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
In the paper, this Russian professor from the Institute for Advanced Study in Princeton proposed a very interesting Motive category.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
In the paper, this Russian professor from the Institute for Advanced Study in Princeton proposed a very interesting Motive category.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
"Originally, I planned to do this part myself, but there are still important parts worth completing. I plan to complete the grand unified theory within this year, and I will leave this part to you."
And this was exactly what Lu Zhou needed.
Lu Zhou nodded and said.
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
And this was exactly what Lu Zhou needed.
"Originally, I planned to do this part myself, but there are still important parts worth completing. I plan to complete the grand unified theory within this year, and I will leave this part to you."
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
"...the so-called motive is the root of all numbers."
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
As for the motivation theory, it is less famous than the Langlands program.
"...the so-called motive is the root of all numbers."
As for the motivation theory, it is less famous than the Langlands program.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
"Two months is not enough, half a month... should be enough."
Lu Zhou whispered softly in a voice that only he could hear. While comparing the calculations in the documents, he wrote furiously on the draft paper.
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
He created a single theory that bridged the gap between algebraic geometry and various cohomology theories.
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
"I understand," Chen Yang nodded, "I will study it carefully when I get back... but I can't guarantee that this problem can be solved in a short time."
A dark premonition made him feel that he was very close to the finish line.
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
To give a popular example, if we call a number n, and n can be represented as 100 in decimal notation, then in fact it can be either 1100100 or 144.
A dark premonition made him feel that he was very close to the finish line.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
Lu Zhou whispered softly in a voice that only he could hear. While comparing the calculations in the documents, he wrote furiously on the draft paper.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
…
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
It is both an abstract number and the essence of numbers.
And if we only use mathematics for daily life, we may not realize this in our lifetime. Many religions and cultures that give numbers special meanings do not actually understand the "language of God."
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
Here, n is given a special meaning.
What motive theory studies is a set named capital N consisting of countless n's.
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
Looking at the whiteboard in front of him, Lu Zhou continued, "From a strategic perspective, we need to find a factor that can relate the two in the abstract form of numbers and shapes. Tactically, we can learn from Kunneth's formula and Poincare duality. Let’s start with the common features of a series of cohomology theories, as well as the application method of L-manifold on the complex plane that I showed you earlier.”
It is both an abstract number and the essence of numbers.
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
Chen Yang shook his head.
What motive theory studies is a set named capital N consisting of countless n's.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
What he lacks most is the perseverance to stay on the same path.
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
“I need a theory that can carry forward the classical theory of one-dimensional cohomology—that is, the success of the Jacobi variety theory and Abel variety theory of curves—in order to facilitate cohomology in all dimensions.”
Different from all human languages "translated" through different base counting methods, this abstract expression method is the language of the universe in the true sense.
The way of expression is different, the only difference is whether we choose binary or octal system to count it. In fact, whether it is 1100100 or 144, they all correspond to the number n, which is just a different form of explanation of n.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
It is both an abstract number and the essence of numbers.
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
Facing Lu Zhou's request, Chen Yang pondered for a while and then spoke.
"It sounds interesting... If my feeling is correct, if this theory can be found, it should be a clue to solving the Hodge conjecture."
At this moment, the paper he was studying was written by the famous algebraic geometer Professor Voevodsky.
Library activity room.
Different from all human languages "translated" through different base counting methods, this abstract expression method is the language of the universe in the true sense.
"Originally, I planned to do this part myself, but there are still important parts worth completing. I plan to complete the grand unified theory within this year, and I will leave this part to you."
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
The unsolved problem in the field of algebraic geometry - Hodge's conjecture, is one of them, and it is also the most famous one.
And if we only use mathematics for daily life, we may not realize this in our lifetime. Many religions and cultures that give numbers special meanings do not actually understand the "language of God."
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
"Based on this theory, we can study the direct sum decomposition in motive theory to associate H(v) with irreducible motive."
He created a single theory that bridged the gap between algebraic geometry and various cohomology theories.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
One might ask what purpose this has except making calculations more cumbersome. However, in fact it is just the opposite. Separating the number itself from its representation is more helpful for people to study the abstract meaning behind it.
Chen Yang shook his head.
And this was exactly what Lu Zhou needed.
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
"Well, I'll leave this piece to you!"
This kind of work does not require subversive thinking or creativity, but can be solved as long as you are willing to work hard.
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
It is both an abstract number and the essence of numbers.
He created a single theory that bridged the gap between algebraic geometry and various cohomology theories.
"Originally, I planned to do this part myself, but there are still important parts worth completing. I plan to complete the grand unified theory within this year, and I will leave this part to you."
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
"...the so-called motive is the root of all numbers."
It is like the main theme of a symphony. Each special cohomology theory can extract its own theme material from it and perform it according to its own key, major key, minor key or even original time signature.
The relationship between the two parties is as inseparable as the Riemann Hypothesis and the generalization of the Riemann Hypothesis on the Dirichlet function.
"Two months is not enough, half a month... should be enough."
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
In addition to laying the theoretical foundation for modern algebraic geometry, Grothendieck also had another great work.
"Well, I'll leave this piece to you!"
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
Among them, Langlands theory, its spiritual core is to establish an essential connection between some seemingly unrelated contents in mathematics. Since many people have heard of it, I will not repeat it again.
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
…
A hint of excitement gradually filled his pupils, and the pen tip in Lu Zhou's hand stopped.
"… I see."
Lu Zhou whispered softly in a voice that only he could hear. While comparing the calculations in the documents, he wrote furiously on the draft paper.
"Two months is not enough, half a month... should be enough."
As he spoke, Lu Zhou turned his attention to Chen Yang, who was standing next to him.
A hint of excitement gradually filled his pupils, and the pen tip in Lu Zhou's hand stopped.
"… I see."
…
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
(For the part about motivation theory, please refer to Barry Mazur's famous "What is a Motive", which is a popular science paper. It is indeed eye-opening after reading it.)
"...all cohomology theories together form a geometric object, and this geometric object can be studied within the framework he developed."
If the problem of "the connection between different cohomology theories" is continuously subdivided, it can even be split into tens of thousands or even millions of unresolved conjectures, or mathematical propositions.
However, what is interesting is that although there are so many extremely difficult conjectures blocking the way, proving the motive theory does not require solving all of these conjectures.
A dark premonition made him feel that he was very close to the finish line.
As the source of all mathematical expressions, N can be mapped to any set of intervals, whether it is [0, 1] or [0, 9], and all mathematical methods about motivation theory are equally applicable to it.
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
“I don’t know whether it can solve the Hodge conjecture, but as a problem of the same type, its solution may inspire research on the Hodge conjecture.”
After Chen Yang left, Lu Zhou returned to the library. He walked to his previous seat and sat down. He opened the stack of unread documents on the table and continued his previous research while calculating with a pen on the draft paper.
This kind of excitement coming from the depths of his soul is simply more pleasant than the first time he witnessed the virtual reality world...
In fact, this has already touched upon the core issue of algebraic geometry, which is the abstract form of numbers.
A hint of excitement gradually filled his pupils, and the pen tip in Lu Zhou's hand stopped.
…
From a macro perspective, the development of algebraic geometry in modern times can be attributed to two general directions, one is the Langlands program and the other is the Motive theory.
Facing the half-written whiteboard, Lu Zhou took back the marker in his hand, took two steps back and looked at the whiteboard and said.
Library activity room.
Library activity room.
(For the part about motivation theory, please refer to Barry Mazur's famous "What is a Motive", which is a popular science paper. It is indeed eye-opening after reading it.)
"... On the surface, we are studying a complex analysis problem, but in fact it is also a problem of partial differential equations, algebraic geometry, and topology."
He created a single theory that bridged the gap between algebraic geometry and various cohomology theories.
It was not a statement made out of confidence, but an affirmation that was almost declarative. The tools used are readily available, and Lu Zhou has even provided possible ideas for solving the problem.
As for the motivation theory, it is less famous than the Langlands program.
A dark premonition made him feel that he was very close to the finish line.
Looking at the expressionless Chen Yang, Lu Zhou nodded and reached out to pat his arm.
"… I see."
"Well, I'll leave this piece to you!"