Scholar’s Advanced Technological System

For the mathematical community lacking gossip, any progress in research on Lehman speculation will be talked about for a while.

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

As early as the first time Arxiv was hung in the preprint of Professor Lu's thesis, the news about Junleman's supposition being proven was flying everywhere. Find a cafe to sit in, and you can hear someone talking excitedly about this difficult issue that lasted a century.

“Did you hear that? Jun Lehman's guess proved! ”

“As I've just heard, it's incredible that no one has been able to translate the right border of the critical zone to the left for a century, even a tiny bit! ”

“The last study on this direction directly led to the proof of prime theorem, not knowing what Professor Lu would bring us this time. ”

“Hey, I wish I had half Professor Lu's IQ. ”

“Wake up, stop dreaming! ”

Not just Berkeley students, but professors are arguing about it.

While analytical mathematics is not a powerful direction for Berkeley, and there is a relative preference for differential equations, it is natural not to miss the big news in mathematics for scholars like Tao Zhexuan, who are barely proficient in any field.

The mathematics department office at Berkeley, sitting at a desk full of draft paper, turned Tao Zhexuan with a ballpoint pen in his hand, stared at the paper on the desk with a tight eyebrow, because it was so focused that he didn't even hear the knock behind him.

The knocking continued for a while, and the rear door pushed straight open, and a skinny Asian man came in with a box of pizza. From his skilled moves, it should be the Doctor in this office.

“Professor, your pizza is here. ”

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

“Just put it aside for me. ”

“Okay, although I recommend you eat while it's hot," put the pizza on the table, the doctor took a look at the draft paper in front of the boss and asked curiously, "Well, I saw your topic on Mathoverflow this morning... are you still working on that paper? ”

Tao Zhexuan: “Yes. ”

Pharyngeal spit, the PhD student asked in a tone of anticipation.

“Any results? ”

“If there is, I'll tell you. ”

“All right.” Listen to this cold voice, the Doctor threw up his lower tongue, gave birth to a helpless expression, and walked out the door.

In general, Professor Tao is relatively approachable, and among the many bulls at Berkeley, a minority of them are professors who fight with students.

However, this is also part-time.

Generally, when he gets stuck with something, don't expect him to be passionate even when his wife comes...

“Kind of funny. ”

“The introduction of algebraic geometry can be seen in his thesis in the shadow of Grotendic writings, but it is not particularly evident. ”

“The key is the choice of algebraic curves on the compound plane… how exactly did he come up with this? ”

“And… can this approach really be called proof? ”

Leaning on his office chair, he stared at the dusty ceiling fan on top of his head, and Tao Zhexuan scratched his back head with some brain damage.

He rarely bothers for so long for one thing.

The ballpoint pen lightly lit on the paper, and after a moment of silence, he threw up a sentence in his face.

“Disputed. ”

However, it was not a positive tone, and he was rarely as confident as he used to be when dealing with the issue.

“Am I mistaken...”

Or is it true, as he thinks, that there is a problem?

……

Speaking of which, when was the last time you received Vera's e-mail, the Ark was not quite remembered.

Maybe a year ago?

Probably something a little longer.

Obviously, Lehman's guess of Vera was being studied, and naturally he saw the preprint he hung out on Arxiv, and it should have taken time to study it again, and that raised some questions.

A lot of things are hard to discuss in the mail, and they agreed to make a video call at 8: 00 p.m. the next day.

So…

Three years later, the Ark saw once again his proudest and most complex disciple.

Though across a network...

The next night at exactly 8: 00 p.m., the video call opened.

Made a cup of coffee and sat in the study. The ark was prepared to discuss academic issues, but the atmosphere was somewhat unexpectedly rigid.

Seems to hold up a lot of things to say, little girl, this time like she doesn't know how to talk, just sitting there nervously, staring straight at the computer screen and not talking.

And just as Vera looked at the ark in the video, also looking at Vera's ark, the expression on her face was also slightly awkward.

The golden hair is combed into a fine princess braid, and the long dress with silk edges outlines a good curve on the shoulder. Even an ark that can't tell the difference between the lipstick numbers can tell. This look is obviously not everyday makeup, obviously carefully dressed.

Anyway, what should I say at this time?

Long time no see?

Seems a little cold.

Is your new hairstyle nice?

There is always a feeling that unnecessary misunderstandings will occur...

He coughed gently, and the ark tried to make a formal expression, speaking with a clear voice.

“Get straight to the point… let me see where your questions lie. ”

Cold and condoms can make the atmosphere a little stiff. Everyone is mathematical and goes straight to the point. It might make the atmosphere a little lighter.

Indeed, the atmosphere in the video call softened slightly as the phrase was put out.

Vera sitting at the end of the computer also loosened her mouth and nodded her head immediately after the chicken pecked rice, whispering.

“Mm-hmm, please wait...”

As she said, the little girl got up and quickly walked to one side, and she struggled to drag a blackboard from the side of the classroom with all her heart.

Seeing that line of formula on the blackboard, the ark stunned slightly and quickly flashed a little surprise in his eyes, and his expression grew more serious.

Looking into the contemplative ark, Vera cleared her voice and continued, "This is the algebraic geometry method you used to prove Junior Lehman's guess, and I tried to summarize the method from the question itself. ”

The contents of the blackboard were swiftly viewed and the ark praised the place with a nod and positive review.

“Doing good. ”

He taught his apprentice.

It's not easy to sort these things out.

Vera laughed embarrassingly: "Although Molina... Ms. Abel asked me not to share these questions with you, I still think... it would be better to have a discussion with you. ”

Exchanging this idea with geniuses is actually a risky thing, because academia only recognizes results and not where “IDEA” comes from.

So let's not say it's a somewhat interesting idea, sometimes even if it's staged enough to be on the top of the list, it's not distributed by the author himself… if he's ambitious about higher goals and doesn't belong to that kind of low-profile, unnamed scholar himself.

After a pause, Vera changed her serious expression and continued.

“I have carefully studied the algebraic curves on the finite domains you introduced when demonstrating that there are no non-zero mediocrities of the zeta function in the area where the ε value is infinitely small, Re (s) ≥ 1-ε, and according to the nature of zeta (s) = 2º (1-s) (2π) s-1sin (πs2) zeta (1-s) …”

As she spoke, Vera turned to the blackboard, leaving a blank spot at the corner, and wrote a line of formulas.

Looking at Vera's board book on the blackboard, the ark's eyebrows wrinkled slightly, but quickly loosened up.

He already has a general understanding of Vera's thinking.

On the basis of her own demonstration method, she gave a Plancherel formula on a group of single-connect Power-Zero Lies by mapping the tune group… In short, she made some improvements to his group method and applied it to magnification of ε values.

The chalk swimming on the blackboard slowly stopped, and Vera turned back and smiled.

“This approach may work, but I can't do it in half. I think if it were you, I would definitely find out why...”

“So… I wish I could help you. ”

In the last sentence, Vera's voice was so small that she wasn't sure for herself whether she really heard the ark at the end of the video.

Staring at the formula on the blackboard, he looked carefully for a while, sitting there on the ark, suddenly talking.

“Do you know why you can't find a reason? ”

Slightly stunned, Vera asked subconsciously.

“… why? ”

With an unfortunate expression on his face, the Ark said the truth.

“Because of the cluster approach, there is no proof of this problem. ”

Vera: “…? ”