Scholar’s Advanced Technological System

For the mathematical community lacking gossip, any research progress on the Riemann conjecture will be talked about for a while.

This is no exception to the mathematics department of the University of Los Angeles at Berkeley on the West Coast.

As early as the first time that a preprint of Professor Lu's paper was arxiv, the news about the quasi-Riemann's conjecture proved to be flying everywhere. I could find a cafe and sit there. Discussing this difficult problem that lasted a century.

"Have you heard? The Riemann conjecture has been proven!"

"I've just heard it. It's incredible. For a century, no one has been able to translate the right edge of the critical zone to the left, even a little bit!"

"The previous research on this direction directly led to the proof of the prime number theorem. I don't know what Professor Lu will bring us this time."

"Well, if only I could have half the IQ of Professor Lu."

"Wake up, stop dreaming!"

Not only are students from the Department of Mathematics at Berkeley, professors are talking about it.

Although analytic number theory is not a strong direction of Berkeley, it is relatively biased towards partial differential equations, but for scholars like Tao Zhexuan who are not proficient in any field, naturally they will not miss the big news in mathematics. .

At the office of the Department of Mathematics at Berkeley, sitting at a desk full of draft paper, Tao Zhexuan with a ballpoint pen in his hand is staring at the densely packed thesis paper on the table, because it is too focused. I didn't even hear the knock behind the door.

The knock on the door continued for a while, and then the door was pushed open. A thin Asian man took a box of pizza and took a picture. Judging by his skilled movements, it should be a doctor in this office.

"Professor, your pizza has arrived."

Without looking up, Tao Zhexuan said casually with his back to him.

"Just help me aside."

"Okay, although I recommend you eat it while it's hot," put the pizza on the table, the doctoral student glanced at the draft paper in front of the boss and asked curiously, "Well, I'll watch this morning That's your topic on mathoverflow ... are you still working on that paper? "

Tao Zhexuan: "Yes."

Swallowing, the doctoral student asked in anticipation.

"Are there any results?"

"I will tell you if there is."

"Okay." Listening to the cold voice, the doctoral student put out his tongue, gave a helpless expression, and exited the door.

Generally speaking, Professor Tao is more approachable, and among the many bulls at Berkeley, a few professors will be one with the students.

However, this is also occasional.

Generally speaking, when he is stumped by something, even if his wife is here, don't expect him to show how enthusiastic ...

"interesting."

"Introducing the method of algebraic geometry, the shadow of Grothendieck's work can be seen in his dissertation, but it is not particularly obvious."

"The key is to choose the algebraic curve on the complex plane ... how did he come up with it?"

"And ... can this method really be called proof?"

Leaning on the office chair, staring at the dusty ceiling fan above his head, Tao Zhexuan scratched his head with a nerve.

He rarely bothers one thing for so long.

The ball-point pen lightly clicked on the paper, and he groaned for a while before he spit out a word solemnly.

"there is controversy."

However, this sentence is not in a positive tone. When dealing with this problem, he rarely can not be as confident as before.

"Did I read it wrong ..."

Or did he prove to be problematic, as he thought?

...

Speaking of when Lu Wei received the e-mail last time, Lu Zhou didn't remember it well.

Maybe a year ago?

Maybe something longer.

Obviously, Vera, who is studying Riemann's conjecture, naturally saw the preprint he hanged on arxiv, and should have taken the time to research it, and some questions were raised.

Many things are difficult to discuss clearly in the email. The two agreed to make a video call at 8 pm Beijing time the next day.

Because ...

After a lapse of three years, Lu Zhou once again met his disciple who was most proud of him and also most complicated him.

Although separated by a network cable ...

At eight o'clock the next day, the video call opened.

After making a cup of coffee and sitting in the study, Lu Zhou was originally ready to discuss academic issues, but the atmosphere was somewhat unexpectedly stiff.

It seemed that the little girl who had talked a lot about what she was going to say, now it seemed like she didn't know how to speak, and she just sat there nervously, staring at the computer screen without talking.

And just as Willa looked at Lu Zhou in the video with a grimace, she was also looking at Willa's Lu Zhou, and the expression on her face was a bit subtle.

The golden hair was combed into a delicate princess braid, and the long skirt with silk edges outlined the curve of the shoulders, even Lu Zhou, who couldn't tell the difference between the lipstick numbers, could see it. Obviously not daily makeup, obviously well-dressed.

Anything to say at this time?

long time no see?

Seems a bit cold.

Your new hairstyle is great?

I always feel that there will be unnecessary misunderstandings ...

With a slight cough, Lu Zhou tried to make a formal expression, and spoke with a clear voice.

"Go straight to the topic ... let me see what your question is."

On the contrary, the greetings and politeness will make the atmosphere a bit stiff. Everyone is engaged in mathematics and goes directly to the topic. Maybe it will make the atmosphere a little easier.

Sure enough, as the sentence came out, the atmosphere in the video call was slightly softened.

Willa, who was sitting at the computer, was also relieved, and then the chicken nodded like a peck of rice, whispering.

"Huh, please, please wait ..."

With that said, the little girl got up and walked quickly to the side, and laboriously dragged a blackboard full of intentions from the side of the classroom.

Seeing the line of calculations on the blackboard, Lu Zhou froze slightly, a flash of surprise flashed in his eyes, and then his expression gradually became serious.

Looking at Lu Zhou in deep thought, Vera cleared her throat and whispered, "This is the algebraic geometry method you used to prove the quasi-Riemann conjecture. I tried to summarize the method from the problem itself. . "

A quick glance at the contents of the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.

"well done."

It is indeed an apprentice he taught.

It is not easy to sort out these things.

Willa smiled embarrassedly: "Although Molina ... Ms. Abel told me not to talk to you about these issues, I still think ... it would be better to discuss with you."

Communicating this idea with genius is actually a risky thing, because the academic community only recognizes the results and does not recognize where the "idea" comes from.

So let alone some seemingly interesting ideas, sometimes even the staged results that are enough to reach the top issue will be suppressed by the author himself ... if he has ambitions for higher goals, but he does not belong The words of scholars who are indifferent to fame and fancy ~ www.readwn.com ~ paused, Willa changed her serious expression and continued.

"I have carefully studied the algebraic curve on the finite field that you introduced when you proved that when e takes infinitely small values ​​and there is no non-zero trivial point of the z function in the region of re (s) ≥ 1-e, The properties of s) = 2Γ (1-s) (2π) s-1sin (πs / 2) ζ (1-s) are obtained ... "

Speaking of which, Vera turned to face the blackboard, leaving a blank space in the corner and writing a line of calculations.

Looking at Vera's blackboard on the blackboard, Lu Zhou frowned slightly, but soon relaxed.

He had a general idea of ​​Willa's thinking.

On the basis of her own proof method, she gave a formula for a class of single connected nilpotent lie groups through the mapping of homology groups ... In short, he made some improvements to his group construction method, and Used to magnify the value of e.

The chalk walking on the blackboard gradually stopped, and Vera turned around and smiled wryly.

"This method will probably work, but I can't do it halfway through it. I think if you do, you will find the reason ..."

"So ... if only I could help you."

In the last sentence, Vera's voice was very small, so small she wasn't sure if she could actually hear Lu Zhou on the other side of the video.

Staring at the formula on the blackboard for a while, he sat calmly on the land boat, and suddenly said.

"Do you know why you can't find the reason?"

Slightly choked, Willa asked subconsciously.

"……why?"

With a regretful expression on his face, Lu Zhou told the truth.

"Because of the group formation method, this problem cannot be proved."

Vera: "...?"