The full name of the circle method is "Hardy Littlewood's circle method". It is not only an important tool for studying Goldbach's conjecture, but also an important tool commonly used in analytic number theory.
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
When she saw that line of calculation, she didn't understand it at all.
“That’s it for my report, thank you all for coming!”
The invention of this tool was not about the Goldbach issue. It is now generally accepted in the mathematical community that this concept first appeared when Hardy and Ramanujan were studying the "Asymptotic Analysis of Integer Splits" problem, and then when Hardy and Littlewood collaborated on the Waring problem. , was completed.
"We still have a long way to go to fully prove Goldbach's conjecture."
emmm…
Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.
Vera
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.
"I understand, thank you."
After glancing at his notes, Lu Zhou stood up and asked.
Afraid that she would be embarrassed to ask, Lu Zhou casually said, "Do you have any questions?"
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
For example, Helfgott standing on the podium is the master of circle method theory in today's number theory community.
Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.
"I understand, thank you."
"... The connotation of Goldbach's conjecture is that any even number greater than 2 can be written as the sum of two prime numbers. Let's call it conjecture A."
There was silence in the venue.
“17…”
"... Since an odd number minus an odd prime number is an even number, conjecture A believes that any even number is equal to the sum of two prime numbers. Therefore, conjecture A can be used to deduce conjecture B. Any odd number greater than 9 can be written as the sum of three odd prime numbers. "
At this age, he has not graduated from high school.
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
There was silence in the venue.
Although her English pronunciation is a bit jerky, her voice is very soft and surprisingly pleasant.
At this point in his opening remarks, Helfgott paused and continued.
At this point in his opening remarks, Helfgott paused and continued.
But the reverse is not true.
"That's a good question," Helfgott glanced at Lu Zhou in surprise, turned around and wrote a line of calculations on the whiteboard, then tapped a marker on it, "Do you understand?"
“That’s it for my report, thank you all for coming!”
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
There were whispers in the venue.
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
As for why, this involves a very interesting question in logic and mathematics. It is difficult to describe in elementary mathematics, but to explain it in descriptive language, it is the set composed of "the sum of any odd number greater than 9 and odd prime numbers", which is not equivalent to the set of "any even number", and the intersection All elements are infinite and cannot be proved exhaustively.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
“17…”
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
"May I ask, how old are you this year?"
Probably not
Conjecture A is true, and conjecture B must be true.
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
Conjecture A is true, and conjecture B must be true.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
Helfgott met Lu Zhou's gaze and nodded, indicating that he could stand up and speak.
Conjecture A is true, and conjecture B must be true.
Probably not
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
But the reverse is not true.
"... Since an odd number minus an odd prime number is an even number, conjecture A believes that any even number is equal to the sum of two prime numbers. Therefore, conjecture A can be used to deduce conjecture B. Any odd number greater than 9 can be written as the sum of three odd prime numbers. "
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
Sounds a bit like Hebrew, Russian
As for why, this involves a very interesting question in logic and mathematics. It is difficult to describe in elementary mathematics, but to explain it in descriptive language, it is the set composed of "the sum of any odd number greater than 9 and odd prime numbers", which is not equivalent to the set of "any even number", and the intersection All elements are infinite and cannot be proved exhaustively.
Obviously, the question Lu Zhou asked touched the hearts of many people.
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
Obviously, the question Lu Zhou asked touched the hearts of many people.
"This is the basic proof process. If you have any questions, you can ask them now."
"I am an IMO gold medalist..." Vera smiled sheepishly and said in a somewhat admiring tone, "Of course, it is nothing compared to you who have already solved two mathematical conjectures..."
Nodding politely, Lu Zhou sat back and copied the line of supplementary calculations on the whiteboard into his notebook.
At this age, he has not graduated from high school.
"I understand, thank you."
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
[… When 2||N, there is r3(N)=1/2n(N square/N cubic)∏(1-1/(p-1) square)∏(1+1/(p-1) square) , (1+O(1))]
This distance may be across a river, or it may be two mountains facing each other.
“17…”
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
After a brief opening remarks, Helfgott didn't waste any time and wrote a line of calculations on the whiteboard.
There were whispers in the venue.
“That’s it for my report, thank you all for coming!”
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
[… When 2||N, there is r3(N)=1/2n(N square/N cubic)∏(1-1/(p-1) square)∏(1+1/(p-1) square) , (1+O(1))]
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
"... The connotation of Goldbach's conjecture is that any even number greater than 2 can be written as the sum of two prime numbers. Let's call it conjecture A."
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
"... Since an odd number minus an odd prime number is an even number, conjecture A believes that any even number is equal to the sum of two prime numbers. Therefore, conjecture A can be used to deduce conjecture B. Any odd number greater than 9 can be written as the sum of three odd prime numbers. "
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
He was also not particularly good at communication, but Lu Zhou understood it, so he didn't care and said casually: "It doesn't matter. Besides, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name?"
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
Helfgott nodded slightly and walked towards the audience amid applause.
When studying the twin prime conjecture, Lu Zhou happened to consult that document and even quoted some of its conclusions.
There were whispers in the venue.
More than forty minutes passed. Helfgott stopped the marker in his hand and turned to look at the venue.
When studying the twin prime conjecture, Lu Zhou happened to consult that document and even quoted some of its conclusions.
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
There was silence in the venue.
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
It was precisely because of this that he was deeply impressed by this.
Helfgott met Lu Zhou's gaze and nodded, indicating that he could stand up and speak.
When studying the twin prime conjecture, Lu Zhou happened to consult that document and even quoted some of its conclusions.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
Helfgott nodded slightly and walked towards the audience amid applause.
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
At this point in his opening remarks, Helfgott paused and continued.
It seems that this report meeting is quite interesting.
There are specialties in the art industry, and even a big boss cannot penetrate into someone else's field in an instant. Therefore, papers at general report conferences will be released in advance on the official website of the conference for people to preview and write down the questions they plan to ask in their notes.
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
"We still have a long way to go to fully prove Goldbach's conjecture."
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
"... The connotation of Goldbach's conjecture is that any even number greater than 2 can be written as the sum of two prime numbers. Let's call it conjecture A."
"I'm sorry, can I ask you a question?"
emmm…
Helfgott nodded slightly and walked towards the audience amid applause.
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
There was silence in the venue.
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
Although her English pronunciation is a bit jerky, her voice is very soft and surprisingly pleasant.
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
Because he has never participated in an IMO competition, Lu Zhou is still quite interested. Originally, he planned to chat with the little girl who won the gold medal, but seeing that it was getting late and he happened to have something to do, he put the matter aside, packed up his notes, and walked out of the venue. go.
There are specialties in the art industry, and even a big boss cannot penetrate into someone else's field in an instant. Therefore, papers at general report conferences will be released in advance on the official website of the conference for people to preview and write down the questions they plan to ask in their notes.
Lu Zhou glanced at her in surprise: "Can I go to Berkeley at the age of 17?"
But the reverse is not true.
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
"This is the basic proof process. If you have any questions, you can ask them now."
"I'm sorry, can I ask you a question?"
As for why, this involves a very interesting question in logic and mathematics. It is difficult to describe in elementary mathematics, but to explain it in descriptive language, it is the set composed of "the sum of any odd number greater than 9 and odd prime numbers", which is not equivalent to the set of "any even number", and the intersection All elements are infinite and cannot be proved exhaustively.
There are specialties in the art industry, and even a big boss cannot penetrate into someone else's field in an instant. Therefore, papers at general report conferences will be released in advance on the official website of the conference for people to preview and write down the questions they plan to ask in their notes.
This distance may be across a river, or it may be two mountains facing each other.
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
“17…”
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
"... Since an odd number minus an odd prime number is an even number, conjecture A believes that any even number is equal to the sum of two prime numbers. Therefore, conjecture A can be used to deduce conjecture B. Any odd number greater than 9 can be written as the sum of three odd prime numbers. "
It was precisely because of this that he was deeply impressed by this.
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
“17…”
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
Helfgott nodded slightly and walked towards the audience amid applause.
“17…”
More than forty minutes passed. Helfgott stopped the marker in his hand and turned to look at the venue.
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
"This is the basic proof process. If you have any questions, you can ask them now."
There was silence in the venue.
"That's a good question," Helfgott glanced at Lu Zhou in surprise, turned around and wrote a line of calculations on the whiteboard, then tapped a marker on it, "Do you understand?"
Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
Conjecture A is true, and conjecture B must be true.
"We still have a long way to go to fully prove Goldbach's conjecture."
When studying the twin prime conjecture, Lu Zhou happened to consult that document and even quoted some of its conclusions.
Lu Zhou raised his hand.
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
After a brief opening remarks, Helfgott didn't waste any time and wrote a line of calculations on the whiteboard.
Helfgott met Lu Zhou's gaze and nodded, indicating that he could stand up and speak.
Sounds a bit like Hebrew, Russian
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
emmm…
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
"That's a good question," Helfgott glanced at Lu Zhou in surprise, turned around and wrote a line of calculations on the whiteboard, then tapped a marker on it, "Do you understand?"
After glancing at his notes, Lu Zhou stood up and asked.
Seeing that line of calculations, Lu Zhou looked slightly stunned and nodded.
Although her English pronunciation is a bit jerky, her voice is very soft and surprisingly pleasant.
"May I ask, how old are you this year?"
Seeing that line of calculations, Lu Zhou looked slightly stunned and nodded.
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
The reason why I say she is a little girl is because she looks young and a little shorter than Lu Zhou. She is probably an undergraduate student at the University of California, Berkeley... If she is a graduate student, Lu Zhou will never believe it.
Lu Zhou glanced at her in surprise: "Can I go to Berkeley at the age of 17?"
“That’s it for my report, thank you all for coming!”
“17…”
There were whispers in the venue.
Helfgott nodded slightly and walked towards the audience amid applause.
"I understand, thank you."
“17…”
But the reverse is not true.
This distance may be across a river, or it may be two mountains facing each other.
Obviously, the question Lu Zhou asked touched the hearts of many people.
"I understand, thank you."
After listening to Lu Zhou's explanation, the girl hurriedly took notes in her notebook.
For example, Helfgott standing on the podium is the master of circle method theory in today's number theory community.
After glancing at his notes, Lu Zhou stood up and asked.
"I understand, thank you."
"That's a good question," Helfgott glanced at Lu Zhou in surprise, turned around and wrote a line of calculations on the whiteboard, then tapped a marker on it, "Do you understand?"
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
Afraid that she would be embarrassed to ask, Lu Zhou casually said, "Do you have any questions?"
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
It was precisely because of this that he was deeply impressed by this.
Seeing that line of calculations, Lu Zhou looked slightly stunned and nodded.
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
There was silence in the venue.
"I understand, thank you."
"We still have a long way to go to fully prove Goldbach's conjecture."
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
After listening to Lu Zhou's explanation, the girl hurriedly took notes in her notebook.
But can an undergraduate really understand this kind of lecture
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
The full name of the circle method is "Hardy Littlewood's circle method". It is not only an important tool for studying Goldbach's conjecture, but also an important tool commonly used in analytic number theory.
Nodding politely, Lu Zhou sat back and copied the line of supplementary calculations on the whiteboard into his notebook.
For example, Helfgott standing on the podium is the master of circle method theory in today's number theory community.
This distance may be across a river, or it may be two mountains facing each other.
“That’s it for my report, thank you all for coming!”
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
The reason why I say she is a little girl is because she looks young and a little shorter than Lu Zhou. She is probably an undergraduate student at the University of California, Berkeley... If she is a graduate student, Lu Zhou will never believe it.
But can an undergraduate really understand this kind of lecture
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
The invention of this tool was not about the Goldbach issue. It is now generally accepted in the mathematical community that this concept first appeared when Hardy and Ramanujan were studying the "Asymptotic Analysis of Integer Splits" problem, and then when Hardy and Littlewood collaborated on the Waring problem. , was completed.
But the reverse is not true.
Helfgott met Lu Zhou's gaze and nodded, indicating that he could stand up and speak.
“17…”
"I'm sorry, can I ask you a question?"
"I am an IMO gold medalist..." Vera smiled sheepishly and said in a somewhat admiring tone, "Of course, it is nothing compared to you who have already solved two mathematical conjectures..."
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
There was silence in the venue.
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
Conjecture A is true, and conjecture B must be true.
“17…”
Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.
The speaker was a little girl with slightly pale skin and slightly curly blond hair.
Probably not
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
It can be seen that she is not very good at communicating with people.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
The reason why I say she is a little girl is because she looks young and a little shorter than Lu Zhou. She is probably an undergraduate student at the University of California, Berkeley... If she is a graduate student, Lu Zhou will never believe it.
It was precisely because of this that he was deeply impressed by this.
The full name of the circle method is "Hardy Littlewood's circle method". It is not only an important tool for studying Goldbach's conjecture, but also an important tool commonly used in analytic number theory.
“That’s it for my report, thank you all for coming!”
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
“17…”
Obviously, the question Lu Zhou asked touched the hearts of many people.
Although her English pronunciation is a bit jerky, her voice is very soft and surprisingly pleasant.
He was also not particularly good at communication, but Lu Zhou understood it, so he didn't care and said casually: "It doesn't matter. Besides, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name?"
"May I ask, how old are you this year?"
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
He was also not particularly good at communication, but Lu Zhou understood it, so he didn't care and said casually: "It doesn't matter. Besides, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name?"
When she saw that line of calculation, she didn't understand it at all.
But can an undergraduate really understand this kind of lecture
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
Helfgott met Lu Zhou's gaze and nodded, indicating that he could stand up and speak.
“17…”
The reason why I say she is a little girl is because she looks young and a little shorter than Lu Zhou. She is probably an undergraduate student at the University of California, Berkeley... If she is a graduate student, Lu Zhou will never believe it.
"Are you asking about that expression?" Lu Zhou probably guessed the question she wanted to ask, and explained patiently: "Because in that line of calculation, I(n)=∫｛f(s)/s^(n+ 1)｝ds=2πian, this is a closed-orbit integral, so when you return to the original formula, you can directly apply the residue theorem. The ideas explained by Professor Hergoft may be a bit jumpy, and it is indeed difficult to understand. Please think more about it. .”
When she saw that line of calculation, she didn't understand it at all.
"... The connotation of Goldbach's conjecture is that any even number greater than 2 can be written as the sum of two prime numbers. Let's call it conjecture A."
Obviously, the question Lu Zhou asked touched the hearts of many people.
Because he has never participated in an IMO competition, Lu Zhou is still quite interested. Originally, he planned to chat with the little girl who won the gold medal, but seeing that it was getting late and he happened to have something to do, he put the matter aside, packed up his notes, and walked out of the venue. go.
The reason why I say she is a little girl is because she looks young and a little shorter than Lu Zhou. She is probably an undergraduate student at the University of California, Berkeley... If she is a graduate student, Lu Zhou will never believe it.
The full name of the circle method is "Hardy Littlewood's circle method". It is not only an important tool for studying Goldbach's conjecture, but also an important tool commonly used in analytic number theory.
Seeing that line of calculations, Lu Zhou looked slightly stunned and nodded.
"Are you asking about that expression?" Lu Zhou probably guessed the question she wanted to ask, and explained patiently: "Because in that line of calculation, I(n)=∫｛f(s)/s^(n+ 1)｝ds=2πian, this is a closed-orbit integral, so when you return to the original formula, you can directly apply the residue theorem. The ideas explained by Professor Hergoft may be a bit jumpy, and it is indeed difficult to understand. Please think more about it. .”
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
Probably not
At this point in his opening remarks, Helfgott paused and continued.
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
Seeing that line of calculations, Lu Zhou looked slightly stunned and nodded.
After listening to Lu Zhou's explanation, the girl hurriedly took notes in her notebook.
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
"I'm sorry, can I ask you a question?"
"I understand, thank you."
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
[… When 2||N, there is r3(N)=1/2n(N square/N cubic)∏(1-1/(p-1) square)∏(1+1/(p-1) square) , (1+O(1))]
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
But can an undergraduate really understand this kind of lecture
More than forty minutes passed. Helfgott stopped the marker in his hand and turned to look at the venue.
More than forty minutes passed. Helfgott stopped the marker in his hand and turned to look at the venue.
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
Afraid that she would be embarrassed to ask, Lu Zhou casually said, "Do you have any questions?"
At this point in his opening remarks, Helfgott paused and continued.
Nodding politely, Lu Zhou sat back and copied the line of supplementary calculations on the whiteboard into his notebook.
The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, um... what did you understand just now?"
It seems that this report meeting is quite interesting.
Vera
“17…”
It can be seen that she is not very good at communicating with people.
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
Lu Zhou glanced at her in surprise: "Can I go to Berkeley at the age of 17?"
After a brief opening remarks, Helfgott didn't waste any time and wrote a line of calculations on the whiteboard.
There was silence in the venue.
"That's a good question," Helfgott glanced at Lu Zhou in surprise, turned around and wrote a line of calculations on the whiteboard, then tapped a marker on it, "Do you understand?"
But the reverse is not true.
Probably not
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
It can be seen that she is not very good at communicating with people.
It can be seen that she is not very good at communicating with people.
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
Sounds a bit like Hebrew, Russian
There are specialties in the art industry, and even a big boss cannot penetrate into someone else's field in an instant. Therefore, papers at general report conferences will be released in advance on the official website of the conference for people to preview and write down the questions they plan to ask in their notes.
He was also not particularly good at communication, but Lu Zhou understood it, so he didn't care and said casually: "It doesn't matter. Besides, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name?"
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
"I'm sorry, can I ask you a question?"
“17…”
It can be seen that she is not very good at communicating with people.
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
Afraid that she would be embarrassed to ask, Lu Zhou casually said, "Do you have any questions?"
"This is the basic proof process. If you have any questions, you can ask them now."
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
"I know your name is Lu Zhou. I met you at the opening ceremony." Maybe she suddenly remembered that she hadn't reported her name yet. The girl added sheepishly, "My name is Vera. I study at Berkeley... I am very interested in pure mathematics, especially number theory.”
“17…”
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
Vera
Afraid that she would be embarrassed to ask, Lu Zhou casually said, "Do you have any questions?"
For example, Helfgott standing on the podium is the master of circle method theory in today's number theory community.
After glancing at his notes, Lu Zhou stood up and asked.
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
“17…”
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
Sounds a bit like Hebrew, Russian
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
More than forty minutes passed. Helfgott stopped the marker in his hand and turned to look at the venue.
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
This distance may be across a river, or it may be two mountains facing each other.
Sounds a bit like Hebrew, Russian
emmm…
Conjecture A is true, and conjecture B must be true.
From the way she took notes in detail, Lu Zhou was more convinced of his guess that she was probably studying for an undergraduate degree.
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
Probably not
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
He was also not particularly good at communication, but Lu Zhou understood it, so he didn't care and said casually: "It doesn't matter. Besides, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name?"
The invention of this tool was not about the Goldbach issue. It is now generally accepted in the mathematical community that this concept first appeared when Hardy and Ramanujan were studying the "Asymptotic Analysis of Integer Splits" problem, and then when Hardy and Littlewood collaborated on the Waring problem. , was completed.
As for why, this involves a very interesting question in logic and mathematics. It is difficult to describe in elementary mathematics, but to explain it in descriptive language, it is the set composed of "the sum of any odd number greater than 9 and odd prime numbers", which is not equivalent to the set of "any even number", and the intersection All elements are infinite and cannot be proved exhaustively.
This distance may be across a river, or it may be two mountains facing each other.
There are specialties in the art industry, and even a big boss cannot penetrate into someone else's field in an instant. Therefore, papers at general report conferences will be released in advance on the official website of the conference for people to preview and write down the questions they plan to ask in their notes.
"May I ask, how old are you this year?"
At this point in his opening remarks, Helfgott paused and continued.
"May I ask, how old are you this year?"
The moment he saw this line of calculations, Lu Zhou's eyes lit up slightly.
There were whispers in the venue.
“17…”
After listening to Lu Zhou's explanation, the girl hurriedly took notes in her notebook.
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
There was silence in the venue.
After a brief opening remarks, Helfgott didn't waste any time and wrote a line of calculations on the whiteboard.
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
Lu Zhou subconsciously glanced at her chest. Although it was not perfect, it was indeed a bit shabby.
At this point in his opening remarks, Helfgott paused and continued.
Lu Zhou glanced at her in surprise: "Can I go to Berkeley at the age of 17?"
“17…”
If the lecture does not answer your questions, ask the question during the question-and-answer session. This is the correct way to listen to the academic lecture. It is not just a matter of simply going over to watch the fun and applauding and you have participated.
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
The old man standing in front of the whiteboard said nothing and continued to write with a marker.
Obviously, the question Lu Zhou asked touched the hearts of many people.
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
At this age, he has not graduated from high school.
[… When 2||N, there is r3(N)=1/2n(N square/N cubic)∏(1-1/(p-1) square)∏(1+1/(p-1) square) , (1+O(1))]
Not only Lu Zhou listened very seriously, but other big bosses also listened very seriously and watched.
Just as Lu Zhou was sorting out his notes, someone next to him gently poked him in the arm.
At this point in his opening remarks, Helfgott paused and continued.
"I am an IMO gold medalist..." Vera smiled sheepishly and said in a somewhat admiring tone, "Of course, it is nothing compared to you who have already solved two mathematical conjectures..."
At this point in his opening remarks, Helfgott paused and continued.
Probably not
The invention of this tool was not about the Goldbach issue. It is now generally accepted in the mathematical community that this concept first appeared when Hardy and Ramanujan were studying the "Asymptotic Analysis of Integer Splits" problem, and then when Hardy and Littlewood collaborated on the Waring problem. , was completed.
"I am an IMO gold medalist..." Vera smiled sheepishly and said in a somewhat admiring tone, "Of course, it is nothing compared to you who have already solved two mathematical conjectures..."
Lu Zhou was stunned for a moment and said: "... No, the gold medal in the Olympic Mathematics Competition is already very strong. You can be more confident and don't underestimate yourself. It's surprising that you won the gold medal at the age of 15? Then how old were you? high school-"
After glancing at his notes, Lu Zhou stood up and asked.
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is about the same, and they are all short of the final touch.
Lu Zhou raised his hand.
Lu Zhou raised his hand.
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
After listening to Lu Zhou's explanation, the girl hurriedly took notes in her notebook.
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
There was silence in the venue.
emmm…
"We still have a long way to go to fully prove Goldbach's conjecture."
"And the 'circle method' I'm talking about is the weak conjecture that proves Goldbach's conjecture, that is, conjecture B!"
This line of expression was not just scribbled by the old man. It was one of the many expressions proposed by Hardy and Littlewood, two giants in number theory, in the 1922 paper!
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
Although he mainly studied the sieve method, Mr. Helfgott's method also inspired a lot of his research work. The so-called research work is exactly like this, perfecting one's own theories through exchanges and discussions, and coming up with new ideas through the collision of ideas.
There were whispers in the venue.
Although her English pronunciation is a bit jerky, her voice is very soft and surprisingly pleasant.
"Thank you, no more... I'm sorry, can you give me your email address? I still have many questions to ask... you." Because she was too nervous, this girl who looked a little reckless accidentally bit her tongue, and her face squirmed. turned red.
“That’s it for my report, thank you all for coming!”
At this moment, the last questioner finished speaking. Seeing that no one continued to ask questions, Mr. Helfgott on the stage announced the end of the report meeting.
"We still have a long way to go to fully prove Goldbach's conjecture."
Helfgott nodded slightly and walked towards the audience amid applause.
Regardless of whether the voice sounds good or not, for Lu Zhou, when someone discusses a mathematical problem with him, as long as it is not unreasonable, he will never refuse, so he said generously: "Ask."
"I understand, thank you."
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”
Because he has never participated in an IMO competition, Lu Zhou is still quite interested. Originally, he planned to chat with the little girl who won the gold medal, but seeing that it was getting late and he happened to have something to do, he put the matter aside, packed up his notes, and walked out of the venue. go.
When studying the twin prime conjecture, Lu Zhou happened to consult that document and even quoted some of its conclusions.
"I have questions about the calculation you listed in line 34. In your operation of =∑a(n)z^n+δ(n), you directly get each integer n>0. I guess you may use It’s the Cauchy-Gusa theorem or its corollary the residue theorem. But how do you determine that a function f(s) is a holomorphic function?”