For the gossip-starved mathematics community, any research progress on the Riemann Hypothesis will be talked about for a long time.
"Wake up, stop dreaming!"
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
"there is controversy."
"… Why?"
Many things are difficult to discuss clearly in emails. The two agreed to have a video call at 8pm Beijing time the next day.
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
Three years later, Lu Zhou once again met his most proud disciple, who also made him feel the most complicated.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
haven't seen you for a long time
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
He already had a general understanding of Vera's thinking.
"Do you know why you can't find a reason?"
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
Maybe it's something a little further back.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
Generally speaking, when he is stumped by some problem, don't expect him to be very enthusiastic even if his wife comes...
After swallowing, the doctoral student asked in an expectant tone.
"Hey, if only I could have half the IQ of Professor Lu."
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
"Okay, I recommend you eat it while it's hot." Putting the pizza on the table, the doctoral student glanced at the scrap paper in front of his boss and asked curiously, "Well, I saw it this morning. to your topic on Mathoverflow...are you still working on that paper?"
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
So...
"interesting."
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
"Did I see it wrong..."
"Let's get straight to the point... Let me see what your questions are."
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
“Introducing the method of algebraic geometry, the shadow of Grothendieck’s work can be seen in his paper, but it is not particularly obvious.”
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
"… Why?"
"Hey, if only I could have half the IQ of Professor Lu."
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
"… Why?"
"well done."
However, this also depends on the occasion.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
"there is controversy."
"Wake up, stop dreaming!"
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
"Uh-huh, please, please wait a moment..."
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
For the gossip-starved mathematics community, any research progress on the Riemann Hypothesis will be talked about for a long time.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
"Is there any result?"
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
Not only the students in the mathematics department at Berkeley, professors are also talking about this matter.
"Hey, if only I could have half the IQ of Professor Lu."
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
Maybe it's something a little further back.
"Professor, the pizza you ordered has arrived."
"Because the group construction method cannot prove this problem."
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
"Hey, if only I could have half the IQ of Professor Lu."
Although analytic number theory is not a strong field at Berkeley, relatively speaking, it is still more biased towards partial differential equations. However, for a scholar like Terence Tao who is not proficient in almost any field, he will naturally not miss the big news in the mathematics world. .
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
"well done."
In the office of the Department of Mathematics at Berkeley, Terence Tao is sitting in front of a desk piled with draft papers, spinning a ballpoint pen in his hand. He is staring at the densely written paper on the table with his brows furrowed, because he is too focused on it. As for not even hearing the knock on the door behind him.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
"well done."
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
Obviously, Vera, who was studying the Riemann Hypothesis, naturally saw the preprint he posted on Arxiv, and probably took the time to study it, and generated some questions.
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
"there is controversy."
"Professor, the pizza you ordered has arrived."
The chalk wandering on the blackboard gradually stopped, and Vera turned around and smiled shyly.
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
For the gossip-starved mathematics community, any research progress on the Riemann Hypothesis will be talked about for a long time.
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
"Because the group construction method cannot prove this problem."
Without looking up, Terence Tao said casually with his back to him.
Maybe a year ago
Maybe a year ago
haven't seen you for a long time
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
Not only the students in the mathematics department at Berkeley, professors are also talking about this matter.
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
"I'll tell you if there is."
"Just put it aside for me."
At eight o'clock in the evening the next day, the video call was turned on.
Maybe a year ago
…
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
"there is controversy."
…
"Okay, I recommend you eat it while it's hot." Putting the pizza on the table, the doctoral student glanced at the scrap paper in front of his boss and asked curiously, "Well, I saw it this morning. to your topic on Mathoverflow...are you still working on that paper?"
"well done."
I always feel like there will be unnecessary misunderstandings...
Terence Tao: "Yes."
He already had a general understanding of Vera's thinking.
Many things are difficult to discuss clearly in emails. The two agreed to have a video call at 8pm Beijing time the next day.
It seems a little cold.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
After swallowing, the doctoral student asked in an expectant tone.
After being slightly stunned, Vera asked subconsciously.
It is quite difficult to sort these things out.
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
"Uh-huh, please, please wait a moment..."
Or does it really prove to be a problem as he thought
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
"Is there any result?"
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
Maybe it's something a little further back.
“Introducing the method of algebraic geometry, the shadow of Grothendieck’s work can be seen in his paper, but it is not particularly obvious.”
"I'll tell you if there is."
After swallowing, the doctoral student asked in an expectant tone.
"… Why?"
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
"Wake up, stop dreaming!"
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
Generally speaking, when he is stumped by some problem, don't expect him to be very enthusiastic even if his wife comes...
"Uh-huh, please, please wait a moment..."
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
Does your new hair style look great
Not only the students in the mathematics department at Berkeley, professors are also talking about this matter.
After being slightly stunned, Vera asked subconsciously.
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
Does your new hair style look great
The ballpoint pen tapped lightly on the paper, and after pondering for a long time, he uttered a sentence with a solemn expression.
haven't seen you for a long time
However, this also depends on the occasion.
"Uh-huh, please, please wait a moment..."
Does your new hair style look great
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
"The key lies in the selection of algebraic curves on the complex plane... How did he come up with it?"
Generally speaking, when he is stumped by some problem, don't expect him to be very enthusiastic even if his wife comes...
Without looking up, Terence Tao said casually with his back to him.
"Because the group construction method cannot prove this problem."
"Wake up, stop dreaming!"
It is quite difficult to sort these things out.
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
"interesting."
Many things are difficult to discuss clearly in emails. The two agreed to have a video call at 8pm Beijing time the next day.
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
The ballpoint pen tapped lightly on the paper, and after pondering for a long time, he uttered a sentence with a solemn expression.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
Maybe a year ago
“Introducing the method of algebraic geometry, the shadow of Grothendieck’s work can be seen in his paper, but it is not particularly obvious.”
"Okay, I recommend you eat it while it's hot." Putting the pizza on the table, the doctoral student glanced at the scrap paper in front of his boss and asked curiously, "Well, I saw it this morning. to your topic on Mathoverflow...are you still working on that paper?"
"Hey, if only I could have half the IQ of Professor Lu."
haven't seen you for a long time
Three years later, Lu Zhou once again met his most proud disciple, who also made him feel the most complicated.
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
Seeing the rows of calculations on the blackboard, Lu Zhou was slightly stunned. A trace of surprise quickly flashed in his eyes, and then his expression gradually became serious.
"The key lies in the selection of algebraic curves on the complex plane... How did he come up with it?"
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
"there is controversy."
It seems a little cold.
Maybe a year ago
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
The chalk wandering on the blackboard gradually stopped, and Vera turned around and smiled shyly.
"And... can this method really be called proof?"
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
"I'll tell you if there is."
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
Obviously, Vera, who was studying the Riemann Hypothesis, naturally saw the preprint he posted on Arxiv, and probably took the time to study it, and generated some questions.
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
Vera: "...?"
He rarely bothered him for so long.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
He rarely bothered him for so long.
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
The ballpoint pen tapped lightly on the paper, and after pondering for a long time, he uttered a sentence with a solemn expression.
"And... can this method really be called proof?"
On the basis of her own proof method, she gave a Plancherel formula on a type of simply connected nilpotent Lie group through the mapping method of homology groups... In short, she made certain improvements to his group construction method, and then It is used to amplify the value of ε.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
"there is controversy."
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
"Hey, if only I could have half the IQ of Professor Lu."
"… Why?"
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
However, this also depends on the occasion.
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
"… Why?"
"Did I see it wrong..."
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
Vera: "...?"
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
Or does it really prove to be a problem as he thought
He is worthy of being the disciple he taught.
He already had a general understanding of Vera's thinking.
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
So...
…
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
“Introducing the method of algebraic geometry, the shadow of Grothendieck’s work can be seen in his paper, but it is not particularly obvious.”
"Uh-huh, please, please wait a moment..."
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
"The key lies in the selection of algebraic curves on the complex plane... How did he come up with it?"
"Have you heard? The quasi-Riemann Hypothesis has been proven!"
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
Maybe a year ago
Terence Tao: "Yes."
Vera smiled sheepishly: "Although Molina...Ms. Abel asked me not to discuss these issues with you, I still think...it would be better to discuss them with you."
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
Obviously, Vera, who was studying the Riemann Hypothesis, naturally saw the preprint he posted on Arxiv, and probably took the time to study it, and generated some questions.
"Just heard about it. It's unbelievable. No one has been able to move the right boundary of the critical zone even a little bit to the left in a century!"
He is worthy of being the disciple he taught.
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
…
Maybe it's something a little further back.
Or does it really prove to be a problem as he thought
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
"Professor, the pizza you ordered has arrived."
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
Obviously, Vera, who was studying the Riemann Hypothesis, naturally saw the preprint he posted on Arxiv, and probably took the time to study it, and generated some questions.
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
Many things are difficult to discuss clearly in emails. The two agreed to have a video call at 8pm Beijing time the next day.
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
"Hey, if only I could have half the IQ of Professor Lu."
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
Or does it really prove to be a problem as he thought
So...
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
Terence Tao: "Yes."
Three years later, Lu Zhou once again met his most proud disciple, who also made him feel the most complicated.
He already had a general understanding of Vera's thinking.
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
"Did I see it wrong..."
Vera: "...?"
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
Many things are difficult to discuss clearly in emails. The two agreed to have a video call at 8pm Beijing time the next day.
Although separated by a network cable...
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
It seems a little cold.
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
haven't seen you for a long time
At eight o'clock in the evening the next day, the video call was turned on.
Communicating ideas with geniuses is actually a risky thing, because academia only recognizes results and does not recognize where the "idea" comes from.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
So...
"well done."
"there is controversy."
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
What should I say at this time
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
"Just put it aside for me."
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
haven't seen you for a long time
haven't seen you for a long time
What should I say at this time
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
"Is there any result?"
The ballpoint pen tapped lightly on the paper, and after pondering for a long time, he uttered a sentence with a solemn expression.
Maybe it's something a little further back.
After swallowing, the doctoral student asked in an expectant tone.
At eight o'clock in the evening the next day, the video call was turned on.
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
"The key lies in the selection of algebraic curves on the complex plane... How did he come up with it?"
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
He rarely bothered him for so long.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
What should I say at this time
"… Why?"
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
He is worthy of being the disciple he taught.
"Uh-huh, please, please wait a moment..."
He is worthy of being the disciple he taught.
haven't seen you for a long time
The ballpoint pen tapped lightly on the paper, and after pondering for a long time, he uttered a sentence with a solemn expression.
"Uh-huh, please, please wait a moment..."
"Do you know why you can't find a reason?"
Vera smiled sheepishly: "Although Molina...Ms. Abel asked me not to discuss these issues with you, I still think...it would be better to discuss them with you."
Communicating ideas with geniuses is actually a risky thing, because academia only recognizes results and does not recognize where the "idea" comes from.
So...
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
It seems a little cold.
Speaking of which, Lu Zhou couldn't remember clearly when he last received an email from Vera.
"Because the group construction method cannot prove this problem."
So...
"there is controversy."
Does your new hair style look great
After being slightly stunned, Vera asked subconsciously.
Not only the students in the mathematics department at Berkeley, professors are also talking about this matter.
After swallowing, the doctoral student asked in an expectant tone.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
"well done."
I always feel like there will be unnecessary misunderstandings...
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
Vera smiled sheepishly: "Although Molina...Ms. Abel asked me not to discuss these issues with you, I still think...it would be better to discuss them with you."
What should I say at this time
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
"Because the group construction method cannot prove this problem."
"Do you know why you can't find a reason?"
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
After a pause, Vera put on a serious expression and continued.
Although separated by a network cable...
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
"Did I see it wrong..."
"Let's get straight to the point... Let me see what your questions are."
It is quite difficult to sort these things out.
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
Vera, who was sitting on the other side of the computer, was also relieved, and then nodded like a chicken pecking at rice, and whispered.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
He is worthy of being the disciple he taught.
"I'll tell you if there is."
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
"Okay, I recommend you eat it while it's hot." Putting the pizza on the table, the doctoral student glanced at the scrap paper in front of his boss and asked curiously, "Well, I saw it this morning. to your topic on Mathoverflow...are you still working on that paper?"
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
"Professor, the pizza you ordered has arrived."
…
"interesting."
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
"Uh-huh, please, please wait a moment..."
"I'll tell you if there is."
Vera, who was sitting on the other side of the computer, was also relieved, and then nodded like a chicken pecking at rice, and whispered.
For the gossip-starved mathematics community, any research progress on the Riemann Hypothesis will be talked about for a long time.
Without looking up, Terence Tao said casually with his back to him.
…
haven't seen you for a long time
However, this also depends on the occasion.
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
"Uh-huh, please, please wait a moment..."
He rarely bothered him for so long.
After swallowing, the doctoral student asked in an expectant tone.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
It seems a little cold.
After being slightly stunned, Vera asked subconsciously.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
Seeing the rows of calculations on the blackboard, Lu Zhou was slightly stunned. A trace of surprise quickly flashed in his eyes, and then his expression gradually became serious.
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
Maybe a year ago
After swallowing, the doctoral student asked in an expectant tone.
"So... it would be great if I could help you."
I always feel like there will be unnecessary misunderstandings...
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
Does your new hair style look great
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
"Is there any result?"
And while Vera was looking at Lu Zhou in the video with an uneasy look on her face, Lu Zhou, who was also looking at Vera, had a slightly awkward expression on his face at this moment.
After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
Vera: "...?"
He is worthy of being the disciple he taught.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
"well done."
After making a cup of coffee and sitting in the study, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was unexpectedly stiff.
Does your new hair style look great
"Wake up, stop dreaming!"
The chalk wandering on the blackboard gradually stopped, and Vera turned around and smiled shyly.
On the basis of her own proof method, she gave a Plancherel formula on a type of simply connected nilpotent Lie group through the mapping method of homology groups... In short, she made certain improvements to his group construction method, and then It is used to amplify the value of ε.
"Did I see it wrong..."
Maybe a year ago
He is worthy of being the disciple he taught.
"I'll tell you if there is."
"Is there any result?"
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
It is quite difficult to sort these things out.
Maybe a year ago
Although separated by a network cable...
Vera smiled sheepishly: "Although Molina...Ms. Abel asked me not to discuss these issues with you, I still think...it would be better to discuss them with you."
Not only the students in the mathematics department at Berkeley, professors are also talking about this matter.
This is no exception for the Department of Mathematics at the University of Los Angeles at Berkeley, the mecca of mathematics on the West Coast.
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
Communicating ideas with geniuses is actually a risky thing, because academia only recognizes results and does not recognize where the "idea" comes from.
I always feel like there will be unnecessary misunderstandings...
With a regretful expression on his face, Lu Zhou told the truth.
Terence Tao: "Yes."
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
"Let's get straight to the point... Let me see what your questions are."
After coughing slightly, Lu Zhou tried his best to make a formal expression and spoke in a clear voice.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
"Let's get straight to the point... Let me see what your questions are."
Obviously, Vera, who was studying the Riemann Hypothesis, naturally saw the preprint he posted on Arxiv, and probably took the time to study it, and generated some questions.
After a pause, Vera put on a serious expression and continued.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
After being slightly stunned, Vera asked subconsciously.
Her golden hair was combed into a delicate princess braid, and her long skirt with silk edges outlined the beautiful curves of her shoulders. Even Lu Zhou, who couldn't tell the difference between lipstick shades, could tell that she looked like this. It's obviously not everyday makeup, it's obviously carefully dressed up.
Vera: "...?"
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
After a pause, Vera put on a serious expression and continued.
He already had a general understanding of Vera's thinking.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
For the gossip-starved mathematics community, any research progress on the Riemann Hypothesis will be talked about for a long time.
"Is there any result?"
"The key lies in the selection of algebraic curves on the complex plane... How did he come up with it?"
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
"Let's get straight to the point... Let me see what your questions are."
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.
However, this also depends on the occasion.
"Wake up, stop dreaming!"
With a regretful expression on his face, Lu Zhou told the truth.
"The last research in this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."
After swallowing, the doctoral student asked in an expectant tone.
However, the tone of this sentence was not positive. When dealing with this issue, he was rarely as confident as before.
Vera: "...?"
"Wake up, stop dreaming!"
He already had a general understanding of Vera's thinking.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
Although analytic number theory is not a strong field at Berkeley, relatively speaking, it is still more biased towards partial differential equations. However, for a scholar like Terence Tao who is not proficient in almost any field, he will naturally not miss the big news in the mathematics world. .
“Introducing the method of algebraic geometry, the shadow of Grothendieck’s work can be seen in his paper, but it is not particularly obvious.”
On the basis of her own proof method, she gave a Plancherel formula on a type of simply connected nilpotent Lie group through the mapping method of homology groups... In short, she made certain improvements to his group construction method, and then It is used to amplify the value of ε.
Although analytic number theory is not a strong field at Berkeley, relatively speaking, it is still more biased towards partial differential equations. However, for a scholar like Terence Tao who is not proficient in almost any field, he will naturally not miss the big news in the mathematics world. .
"there is controversy."
Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors at Berkeley who can get along well with students.
At eight o'clock in the evening the next day, the video call was turned on.
The chalk wandering on the blackboard gradually stopped, and Vera turned around and smiled shyly.
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
…
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
haven't seen you for a long time
"Wake up, stop dreaming!"
"And... can this method really be called proof?"
"So... it would be great if I could help you."
"Let's get straight to the point... Let me see what your questions are."
Terence Tao: "Yes."
On the basis of her own proof method, she gave a Plancherel formula on a type of simply connected nilpotent Lie group through the mapping method of homology groups... In short, she made certain improvements to his group construction method, and then It is used to amplify the value of ε.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
Leaning on the office chair and staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some trepidation.
"I'll tell you if there is."
Vera's voice was so low that she wasn't sure whether Lu Zhou on the other end of the video really heard the last sentence.
Or does it really prove to be a problem as he thought
"Did I see it wrong..."
After staring at the calculations on the blackboard carefully for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.
"I carefully studied the algebraic curve on the finite field that you introduced when proving that when ε takes infinitesimal values and Re(s)≥1-ε, there are no non-zero trivial points of the ζ function in the region, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) are obtained... ”
With that said, Vera turned to face the blackboard and wrote out lines of calculations in the blank spaces left in the corners.
…
After saying that, the little girl stood up and walked quickly to the side, and dragged a blackboard from the edge of the classroom with hard work written on it.
"Do you know why you can't find a reason?"
After swallowing, the doctoral student asked in an expectant tone.
"Okay." Listening to this cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.
The little girl who seemed to have held back a lot of things to say seemed to not know how to speak now. She just sat there with a nervous look on her face, staring straight at the computer screen without speaking.
The pleasantries and courtesies will make the atmosphere a little stiff. Everyone is engaged in mathematics and going directly to the topic may make the atmosphere a little more relaxed.
"there is controversy."
haven't seen you for a long time
"Do you know why you can't find a reason?"
After being slightly stunned, Vera asked subconsciously.
Or does it really prove to be a problem as he thought
As soon as the preprint of Professor Lu's paper was posted on Arxiv, news about the quasi-Riemann hypothesis being proved spread everywhere. If you sit in any coffee shop, you can hear people excitedly talking about it. Discussing this problem that has lasted for a century.
"well done."
"… Why?"
"And... can this method really be called proof?"
Therefore, let alone some seemingly interesting ideas, sometimes even interim results that are enough to be published in top publications will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to that The words of a scholar who is indifferent to fame and wealth and does not care about status.
"I'll tell you if there is."
"… Why?"
"interesting."
Does your new hair style look great
With a regretful expression on his face, Lu Zhou told the truth.
"Is there any result?"
Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann hypothesis. I tried to summarize the method from the problem itself. .”
Three years later, Lu Zhou once again met his most proud disciple, who also made him feel the most complicated.
"Because the group construction method cannot prove this problem."
"Did I see it wrong..."
Seeing the rows of calculations on the blackboard, Lu Zhou was slightly stunned. A trace of surprise quickly flashed in his eyes, and then his expression gradually became serious.
"This method probably works, but I couldn't continue until I was halfway through. I think if it were you, you would definitely be able to find the reason..."
Vera: "...?"
Sure enough, as these words were spoken, the atmosphere in the video call softened slightly.
The knocking continued for a while, and then the door opened directly, and a tall and thin Asian man walked in carrying a box of pizza. Judging from his skillful movements, he should be the doctor in this office.