"neither?"
Molina was stunned for a moment, frowned and said, "Sports?"
…
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
Molina was stunned.
"Have you thought about it?"
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
"It's mainly about analytical number theory. I believe that with your ability, you are more than qualified for this job... In addition, I have also prepared a meeting gift for you."
How cool is this.
Just like Fermat's last theorem.
Deligne nodded, not dissatisfied.
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
"Of course, I have to prove it in my own way."
Sitting in his position, it is difficult to be as narrow-minded as the bosses of ordinary doctoral students who use some boring tests to test whether students are "obedient". As he said at the beginning, he offered Lu Zhou two options.
…
When this mathematical method is continuously improved, perfected enough to solve many problems, and perfected enough to change from a toothpick to a Swiss Army knife, its significance may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytic number theory!
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Sitting in his position, it is difficult to be as narrow-minded as the bosses of ordinary doctoral students who use some boring tests to test whether students are "obedient". As he said at the beginning, he offered Lu Zhou two options.
Lu Zhou smiled lightly and said in a relaxed tone.
Including Lu Zhou, everyone benefited a lot from it.
After knocking on the office door, Lu Zhou walked in.
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
…
Lu Zhou felt a little proud in his heart.
Molina curled her lips and said speechlessly: "Of course."
The number of prime factors is 1, so it is naturally a prime number.
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
When he first studied the twin prime conjecture, he also faced similar problems.
…
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Therefore, the 1+1 form is still Goldbach's conjecture itself.
"neither?"
When he first studied the twin prime conjecture, he also faced similar problems.
When Taniyama-Shimura's conjecture was proven, although people could not see the specific prospects yet, everyone knew it because a tool that could solve the problem had appeared. Sure enough, Andrew Wiles finally completed this historic work.
As long as improvements are made, this tool may not be used for Goldbach's conjecture, which is also a prime number problem.
Lu Zhou felt a little proud in his heart.
"It's mainly about analytical number theory. I believe that with your ability, you are more than qualified for this job... In addition, I have also prepared a meeting gift for you."
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
Molina said in a teasing tone, "You mean, people who have studied Goldbach's conjecture have been doing useless work in this century?"
The number of prime factors is 1, so it is naturally a prime number.
do not know why.
Could it be...
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
The number of prime factors is 1, so it is naturally a prime number.
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
At least, I don’t have any hope for Enfa.
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Molina was stunned for a moment, frowned and said, "Sports?"
Lu Zhou: "You know about long jump."
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Sitting in his position, it is difficult to be as narrow-minded as the bosses of ordinary doctoral students who use some boring tests to test whether students are "obedient". As he said at the beginning, he offered Lu Zhou two options.
Molina said in a teasing tone, "You mean, people who have studied Goldbach's conjecture have been doing useless work in this century?"
Lu Zhou: "You know about long jump."
It was not until he was inspired that he tried a completely different proof method and introduced topology theory into the concept of sieve method, which opened the door to a new world.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
Molina curled her lips and said speechlessly: "Of course."
…
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
When this mathematical method is continuously improved, perfected enough to solve many problems, and perfected enough to change from a toothpick to a Swiss Army knife, its significance may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytic number theory!
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
…
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
Including Lu Zhou, everyone benefited a lot from it.
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
Molina was stunned for a moment, frowned and said, "Sports?"
Including Lu Zhou, everyone benefited a lot from it.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Lu Zhou: "You know about long jump."
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
…
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
Molina was stunned.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
do not know why.
A confident smile appeared on Lu Zhou's lips.
"It's mainly about analytical number theory. I believe that with your ability, you are more than qualified for this job... In addition, I have also prepared a meeting gift for you."
It is for the same reason that in last year's year-end speech, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final words to express his views on short-term There is no hope that Bach's conjecture cannot be solved.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
"Have you thought about it?"
"Of course, I have to prove it in my own way."
When this mathematical method is continuously improved, perfected enough to solve many problems, and perfected enough to change from a toothpick to a Swiss Army knife, its significance may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytic number theory!
"I heard from you that your family situation is not good. When I helped you with the admission procedures yesterday, I helped you solve the scholarship problem. You can take this thing to the academic affairs office later, and also take it with you. The tuition issue has been resolved.”
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
do not know why.
Lu Zhou nodded and said.
do not know why.
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
Lu Zhou nodded and said.
"neither?"
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
How cool is this.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
At least, I don’t have any hope for Enfa.
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
At least, I don’t have any hope for Enfa.
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
…
Therefore, the 1+1 form is still Goldbach's conjecture itself.
…
Molina was stunned.
Molina curled her lips and said speechlessly: "Of course."
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
After knocking on the office door, Lu Zhou walked in.
Molina curled her lips and said speechlessly: "Of course."
At least, I don’t have any hope for Enfa.
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
Molina was stunned for a moment, frowned and said, "Sports?"
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Deligne nodded. He did not express surprise at the topic he was studying like Molina did. The ordinary calmness on his face actually surprised Lu Zhou who proposed this proposition.
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Lu Zhou: "You know about long jump."
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
"Have you thought about it?"
Both are indispensable.
The same goes for the circle method.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Just like Fermat's last theorem.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
When Taniyama-Shimura's conjecture was proven, although people could not see the specific prospects yet, everyone knew it because a tool that could solve the problem had appeared. Sure enough, Andrew Wiles finally completed this historic work.
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
But for Goldbach's conjecture, whether it is the grand sieve method or the circle method, it is almost like this.
Molina was stunned for a moment, frowned and said, "Sports?"
Could it be...
But for Goldbach's conjecture, whether it is the grand sieve method or the circle method, it is almost like this.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
At least, I don’t have any hope for Enfa.
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
Lu Zhou felt a little proud in his heart.
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
Previous work has laid a lot of groundwork, but whether it is Chen's theorem from "9+9" to "1+2" or Helfgott's proof of Goldbach's weak conjecture under the odd number condition, there is only one gap left. last step. Even the significance of Chen's theorem is to let other mathematicians understand that the Great Sieve method has been reached to the extreme by Chen Jingrun, and this road is no longer feasible.
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
Molina said in a teasing tone, "You mean, people who have studied Goldbach's conjecture have been doing useless work in this century?"
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
The same goes for the circle method.
Stopping the ballpoint pen in his hand, Professor Deligne looked at Lu Zhou, who was standing opposite the desk, and asked in a relaxed tone.
It was not until he was inspired that he tried a completely different proof method and introduced topology theory into the concept of sieve method, which opened the door to a new world.
After knocking on the office door, Lu Zhou walked in.
There are so many lambda functions to choose from, but no matter how he looks, he can't find the right one.
It is for the same reason that in last year's year-end speech, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final words to express his views on short-term There is no hope that Bach's conjecture cannot be solved.
When he first studied the twin prime conjecture, he also faced similar problems.
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
When he first studied the twin prime conjecture, he also faced similar problems.
Both are indispensable.
At least, I don’t have any hope for Enfa.
"Have you thought about it?"
The same goes for the circle method.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
Including Lu Zhou, everyone benefited a lot from it.
Deligne nodded, not dissatisfied.
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
…
A confident smile appeared on Lu Zhou's lips.
When he first studied the twin prime conjecture, he also faced similar problems.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Lu Zhou: "You know about long jump."
Zhang Yitang's research limited the distance between pairs of prime numbers to 70 million through clever selection of lambda functions. Successors reduced this number to 246 within a year, and then could not make any further progress.
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
"Yes, I plan to continue to complete my own research... I'm sorry, but I may not be able to spare the extra energy to join your project."
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
Molina curled her lips and said speechlessly: "Of course."
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Deligne nodded. He did not express surprise at the topic he was studying like Molina did. The ordinary calmness on his face actually surprised Lu Zhou who proposed this proposition.
When he first studied the twin prime conjecture, he also faced similar problems.
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
There are so many lambda functions to choose from, but no matter how he looks, he can't find the right one.
Lu Zhou answered truthfully: "Goldbach's conjecture."
Deligne nodded, not dissatisfied.
There are so many lambda functions to choose from, but no matter how he looks, he can't find the right one.
Zhang Yitang's research limited the distance between pairs of prime numbers to 70 million through clever selection of lambda functions. Successors reduced this number to 246 within a year, and then could not make any further progress.
Molina said in a teasing tone, "You mean, people who have studied Goldbach's conjecture have been doing useless work in this century?"
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
It was not until he was inspired that he tried a completely different proof method and introduced topology theory into the concept of sieve method, which opened the door to a new world.
Both are indispensable.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
Previous work has laid a lot of groundwork, but whether it is Chen's theorem from "9+9" to "1+2" or Helfgott's proof of Goldbach's weak conjecture under the odd number condition, there is only one gap left. last step. Even the significance of Chen's theorem is to let other mathematicians understand that the Great Sieve method has been reached to the extreme by Chen Jingrun, and this road is no longer feasible.
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
Zhang Yitang's research limited the distance between pairs of prime numbers to 70 million through clever selection of lambda functions. Successors reduced this number to 246 within a year, and then could not make any further progress.
A confident smile appeared on Lu Zhou's lips.
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
do not know why.
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Molina was stunned.
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
"Of course, I have to prove it in my own way."
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
After coming out of the eating club, Lu Zhou did not go to the library for a while after eating as usual, but went to the Institute for Advanced Study in Princeton.
A confident smile appeared on Lu Zhou's lips.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
After knocking on the office door, Lu Zhou walked in.
"Have you thought about it?"
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
Lu Zhou: "You know about long jump."
Therefore, the 1+1 form is still Goldbach's conjecture itself.
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
As long as improvements are made, this tool may not be used for Goldbach's conjecture, which is also a prime number problem.
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
"It's mainly about analytical number theory. I believe that with your ability, you are more than qualified for this job... In addition, I have also prepared a meeting gift for you."
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
"I heard from you that your family situation is not good. When I helped you with the admission procedures yesterday, I helped you solve the scholarship problem. You can take this thing to the academic affairs office later, and also take it with you. The tuition issue has been resolved.”
When this mathematical method is continuously improved, perfected enough to solve many problems, and perfected enough to change from a toothpick to a Swiss Army knife, its significance may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytic number theory!
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
Could it be...
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Sitting in his position, it is difficult to be as narrow-minded as the bosses of ordinary doctoral students who use some boring tests to test whether students are "obedient". As he said at the beginning, he offered Lu Zhou two options.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
Just like Fermat's last theorem.
"I heard from you that your family situation is not good. When I helped you with the admission procedures yesterday, I helped you solve the scholarship problem. You can take this thing to the academic affairs office later, and also take it with you. The tuition issue has been resolved.”
From Goldbach's conjecture, Lu Zhou vaguely saw hope.
How cool is this.
Twisting her long hair around her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?"
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
…
Although he did not make an appointment, according to Professor Delin himself, if nothing unexpected happens, he will be here from 6 to 8 pm every night.
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
On the surface, the group construction method does not seem to have anything to do with Goldbach's conjecture, but fundamentally it evolved from the sieve method and has always been used to solve prime number problems.
Deligne nodded. He did not express surprise at the topic he was studying like Molina did. The ordinary calmness on his face actually surprised Lu Zhou who proposed this proposition.
After knocking on the office door, Lu Zhou walked in.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
After coming out of the eating club, Lu Zhou did not go to the library for a while after eating as usual, but went to the Institute for Advanced Study in Princeton.
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Although he did not make an appointment, according to Professor Delin himself, if nothing unexpected happens, he will be here from 6 to 8 pm every night.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
"neither?"
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
After knocking on the office door, Lu Zhou walked in.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Therefore, the 1+1 form is still Goldbach's conjecture itself.
After coming out of the eating club, Lu Zhou did not go to the library for a while after eating as usual, but went to the Institute for Advanced Study in Princeton.
Stopping the ballpoint pen in his hand, Professor Deligne looked at Lu Zhou, who was standing opposite the desk, and asked in a relaxed tone.
A confident smile appeared on Lu Zhou's lips.
Lu Zhou nodded and said.
do not know why.
When he first studied the twin prime conjecture, he also faced similar problems.
Including Lu Zhou, everyone benefited a lot from it.
Molina curled her lips and said speechlessly: "Of course."
Lu Zhou felt a little proud in his heart.
"Have you thought about it?"
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Lu Zhou answered truthfully: "Goldbach's conjecture."
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Whether it is establishing a theory first and then proving its value, or developing novel theories while studying specific mathematical problems, there are precedents to follow.
Lu Zhou nodded and said.
…
It was not until he was inspired that he tried a completely different proof method and introduced topology theory into the concept of sieve method, which opened the door to a new world.
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
"Yes, I plan to continue to complete my own research... I'm sorry, but I may not be able to spare the extra energy to join your project."
When he first studied the twin prime conjecture, he also faced similar problems.
…
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
The same goes for the circle method.
The same goes for the circle method.
Deligne nodded, not dissatisfied.
It is for the same reason that in last year's year-end speech, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final words to express his views on short-term There is no hope that Bach's conjecture cannot be solved.
A confident smile appeared on Lu Zhou's lips.
Molina was stunned for a moment, frowned and said, "Sports?"
Deligne nodded, not dissatisfied.
Therefore, Lu Zhou gave this weapon of his own a new name, namely "Group Construction Method".
Sitting in his position, it is difficult to be as narrow-minded as the bosses of ordinary doctoral students who use some boring tests to test whether students are "obedient". As he said at the beginning, he offered Lu Zhou two options.
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Therefore, the 1+1 form is still Goldbach's conjecture itself.
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
"The problem of a+b is ultimately a complex formulation of Goldbach's conjecture, that is, every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. And When a=b=1, the problem will eventually return to the original statement, that is, any even number greater than 2 can be written as the sum of two prime numbers."
Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?"
Including Lu Zhou, everyone benefited a lot from it.
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
The number of prime factors is 1, so it is naturally a prime number.
Although this idea was first mentioned by Professor Zellberg in his 1995 paper on the study of Goldbach's conjecture, it was him who improved it and introduced it to the problem of prime number pairs.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
Lu Zhou answered truthfully: "Goldbach's conjecture."
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
After calming down, she looked at Lu Zhou and said in a skeptical tone: "I know you are a genius... Although Goldbach's conjecture is not my research field, if I heard correctly, you are not planning to use this one." Are we going to overturn a century of work and redo it?”
It is for the same reason that in last year's year-end speech, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final words to express his views on short-term There is no hope that Bach's conjecture cannot be solved.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
Deligne nodded. He did not express surprise at the topic he was studying like Molina did. The ordinary calmness on his face actually surprised Lu Zhou who proposed this proposition.
…
There are so many lambda functions to choose from, but no matter how he looks, he can't find the right one.
After knocking on the office door, Lu Zhou walked in.
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
A confident smile appeared on Lu Zhou's lips.
The same goes for the circle method.
Molina curled her lips and said speechlessly: "Of course."
Could it be...
Lu Zhou smiled lightly and said in a relaxed tone.
Zhang Yitang's research limited the distance between pairs of prime numbers to 70 million through clever selection of lambda functions. Successors reduced this number to 246 within a year, and then could not make any further progress.
Lu Zhou answered truthfully: "Goldbach's conjecture."
"Of course not," Lu Zhou shook his head and suddenly asked a question that she didn't expect, "Do you know anything about sports?"
Of course, for a woman who has decided to marry mathematics, the so-called accelerated heartbeat only lasts for a moment...
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
Just like Fermat's last theorem.
do not know why.
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
"Have you thought about it?"
How cool is this.
Just like the "interuniversal Teichmüller theory" and "alien arithmetic holomorphic structure" created by Shinichi Mochizuki, a famous "chuunibyou" in mathematics, when he was studying the ABC conjecture.
Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.
Lu Zhou felt a little proud in his heart.
Lu Zhou felt a little proud in his heart.
As long as improvements are made, this tool may not be used for Goldbach's conjecture, which is also a prime number problem.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
Both are indispensable.
Lu Zhou: "You know about long jump."
Both are indispensable.
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
The solution to a mathematical conjecture requires accumulation of work and a creative genius.
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
Just like Fermat's last theorem.
…
Although he did not make an appointment, according to Professor Delin himself, if nothing unexpected happens, he will be here from 6 to 8 pm every night.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
Molina said in a teasing tone, "You mean, people who have studied Goldbach's conjecture have been doing useless work in this century?"
Lu Zhou nodded: "No problem... If it's a course on number theory or functional analysis, I can still teach some."
Molina curled her lips and said speechlessly: "Of course."
Senior Deligne also believes that he is the "best candidate" to solve this conjecture
How cool is this.
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
But for Goldbach's conjecture, whether it is the grand sieve method or the circle method, it is almost like this.
Stopping the ballpoint pen in his hand, Professor Deligne looked at Lu Zhou, who was standing opposite the desk, and asked in a relaxed tone.
…
Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.
"It's mainly about analytical number theory. I believe that with your ability, you are more than qualified for this job... In addition, I have also prepared a meeting gift for you."
"Of course, in addition to your own research, I also have some non-research work that I need you to do. For example, teaching assistant and the like."
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
Therefore, the 1+1 form is still Goldbach's conjecture itself.
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
"neither?"
Lu Zhou nodded and said.
"Yes, I plan to continue to complete my own research... I'm sorry, but I may not be able to spare the extra energy to join your project."
After knocking on the office door, Lu Zhou walked in.
After a pause, Mr. Deligne reached out and opened the drawer, took out something like a certificate, and placed it on the table. A smile softened on his serious face.
Deligne: "Goldbach's conjecture is an interesting problem. I also studied it when I was young, but I didn't go in depth. I may not be able to provide you with much help. The closest research results in the world are Chen's theorem. and Helfgott’s proof of the weak conjecture, I’m looking forward to your research on something novel based on this.”
"neither?"
Lu Zhou smiled lightly and said, "The a+b proof method started by Brown is equivalent to the run-up before the long jump. Although the run-up time itself is not included in the score, is the run-up useless? By the same token, a+b It is equivalent to a run-up to Goldbach's conjecture. If it were not for it, there would be no great sieve method - an analytic number theory research tool full of illumination and potential. It can even be said that the value of the great sieve method has surpassed Goldbach’s conjecture itself.”
Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
But when thinking about Goldbach's conjecture, his habitual thinking made him selectively ignore his tools.
It is for the same reason that in last year's year-end speech, Helfgott used "We still have a long way to go to fully prove Goldbach's conjecture" as his final words to express his views on short-term There is no hope that Bach's conjecture cannot be solved.
Later, Lu Zhou introduced the knowledge of group theory on this basis and pushed the pairs of prime numbers with a finite distance to infinity. On this basis, he solved the Polignac conjecture. This method has been modified twice. It is beyond recognition and completely deviates from the original appearance of the sifting method.
"I heard from you that your family situation is not good. When I helped you with the admission procedures yesterday, I helped you solve the scholarship problem. You can take this thing to the academic affairs office later, and also take it with you. The tuition issue has been resolved.”
It was not until he was inspired that he tried a completely different proof method and introduced topology theory into the concept of sieve method, which opened the door to a new world.
Deligne nodded, not dissatisfied.
Regardless of whether the Great Sieve method can really cross the final 1+1, it has completed its historical mission and plays an important role in analytic number theory.
When this mathematical method is continuously improved, perfected enough to solve many problems, and perfected enough to change from a toothpick to a Swiss Army knife, its significance may no longer be a simple tool, but gradually evolve into a theoretical framework! And it is the theoretical framework in analytic number theory!
"neither?"
When Taniyama-Shimura's conjecture was proven, although people could not see the specific prospects yet, everyone knew it because a tool that could solve the problem had appeared. Sure enough, Andrew Wiles finally completed this historic work.