Mathematics and physics have combined forces to divide the earth into twenty-four time zones. When teenagers in the Eastern Hemisphere seek spiritual comfort from their loved ones on this night, the sun has just risen in Princeton. Lott Dugan eight o'clock in the morning Walk into his office on time.

Although he could have waited until nine o'clock, but at his age, not only could he not sleep for that long, but he was also unwilling to listen to women's nagging at home. It was better to start his day's work in the office earlier.

At least sitting at his messy desk can bring him an unparalleled sense of accomplishment. But at home, wherever there is a little mess, he can only listen to his wife's endless complaints.

However, Lot Dugan has always had a quirk. No one can move his desk, and he must maintain the messy aesthetic. Because only in this way can he find what he needs at his fingertips. Once the things on the desk become If it is tidy, he will need to spend more time looking for what he exactly needs.

Since the previous new secretary was scolded away for cleaning up his desk, no one has touched his desk in the college except himself. But it is different at home. The office in the study room The table is always neat and tidy, no matter what he says, it doesn't matter.

The elderly wife is different from when she was young. She seems to be suddenly infected with mysophobia, and she cannot tolerate any irregularities in her sight. This also makes the sixty-three-year-old Lot Dugan feel depressed.

Lot Dugan has always felt that his messy desk is like the N-body problem that he has studied all his life. Human beings are still unable to accurately map the motion trajectories of the planets in the solar system, but there are always ways to predict the approximate movement of these planets at a certain time. locations and find them quickly.

The desktop arranged according to his wishes may seem messy, but it is like a nearly perfect coordinate system. Everything will be fixed at a certain coordinate according to his needs. It is not only convenient, but also brings an achievement to Lot Dugan. feel.

After sitting at his desk with satisfaction, Lot Dugan turned on his computer and logged into his personal mailbox first.

I don't know since when, putting private before public has become a principle that every ordinary person in the Federation follows silently, even for people of Lot Dugan's age.

In fact, for people who lived through the 1970s and 1980s, most of them don't like the current federation.

Although the size of the Federation is still so huge and the body still looks strong, it can be clearly felt that something inside is decaying, and as time goes by, the area of ​​decay is growing.

Lot Dugan can sense this even from the soap opera screen.

When he was young, the most popular TV series were "Growing Pains", "Little Britain", "The Rescuers", "Family Matters", "Friends"... and other similar stories that conveyed the positive nature of life.

In this era, the TV series that everyone usually talked about became "Shameless", "Breaking Bad", and "House of Cards"... Of course, he couldn't change these, so he chose to go with the flow.

After checking several emails, he saw an email from Huaxia Yanbei University Tian.

In the past, Lot Dugan was not very fond of China. Including when he went to the capital of China to attend a mathematician conference in 2002, he did not have a very good impression of this country. But this impression began to change the year before last.

In 2022, he was invited to attend the Global Mathematics Forum in a place called Xiaozhou in China, and gave a 60-minute report at the conference. This mathematics conference was initiated by the number theory conference, one of the satellite conferences of the International Congress of Mathematicians, and mainly discussed

Topics in number theory and arithmetic geometry.

That trip to Xiaozhou was also an eye-opener for Lot Dugan.

Before this, Lot Dugan only knew that there were three cities in China: Jingcheng, Linhai, and Zhenguan. He had no impression of other cities at all. However, it was this city that he had never heard of before going there that overturned his understanding of the city.

All perceptions of the country China.

The hotel where the conference is located has an unmanned bar, unmanned robots delivering meals, a well-developed bus system, and even a large screen next to the bus station that broadcasts vehicle information at any time, and there are wireless charging devices on the resting seats next to it.

The streets in the city center are clean and orderly, and some people even asked him to go out for a walk at night.

There are also those high-rise buildings that can be seen everywhere, and the underground transportation system that looks like a future world.

Even that time, he did not return to Princeton directly after the conference, but stayed in China for another week. Accompanied by a doctoral student, he went to three surrounding cities, enjoyed the convenience of high-speed rail, and browsed the scenery of the water town.

I even took a look at the countryside below.

While waiting at the Linhai airport, Lot Dugan only felt that his mind was full of questions - how many truths did those damn media tell and whether this could be considered a developing country? After returning, he naturally paid attention to China.

It has become more numerous, and everything in China is constantly refreshing Lot Dugan's original deep-rooted knowledge.

By the way, during the week he stayed in China, the doctoral student accompanying him was arranged by Tian Yanzhen. So after seeing Tian Yanzhen's email, he clicked on it as soon as possible.

The email was received the morning before yesterday.

However, he had been doing academic exchanges at Columbia University, about a hundred kilometers away, yesterday, and did not log in to his email, so he only saw this email today. "Dear Professor Dugan, hello. Let's meet in person...

Lot Dugan probably read this letter once. It was a letter of recommendation. Whether it was based on his status as the dean of the Princeton School of Mathematics or the editor-in-chief of the Annals of Mathematics, he often received such letters of recommendation.

Familiar professor friends often write him such letters of recommendation. The former mainly recommends students to come to Princeton School of Mathematics for exchange or study, while the latter hopes that the submitted papers will receive certain attention.

Many people outside mathematics may not be aware of the importance of the "Annals of Mathematics" in the international mathematics community. After all, not as many people really pay attention to the development of cutting-edge mathematics as imagined. People are more concerned about visible scientific developments.

Such as brain-computer, such as artificial intelligence, such as autonomous driving...

Therefore, for the public, journals such as "Nature" and "Science" are more likely to arouse people's interest. But if you look at the number of articles published in these journals, you can know how difficult it is to publish in the four top journals.

Last year, there were only 34 papers included in the "Annual Review of Mathematics", while there were 1,017 papers published in "Nature" and 815 papers included in "Science". And last year, Ann.Math had more papers included.

A year, sometimes less than ten papers are collected in a year.

It is well-known and has few accepted papers, so the screening process is naturally very troublesome.

As the editor-in-chief, Lot Dugan knows very well that it is fast for submitted papers to be submitted for review within half a year. If there are some unexpected factors, such as the editor being on vacation, the original reviewer suddenly being shocked, or running away,

And issues such as layout design will further prolong the review time.

Sometimes, for various reasons, mathematicians hope that their papers can be published as soon as possible, so they often send them an email when submitting the paper, hoping to receive special care. Especially when the year of the Mathematicians Conference is approaching.

When he was a mathematician, he would often receive similar emails. Because every four years, the Fields Medal, Nevin Linner Medal, Gauss Medal, Chen Shengshen Medal will be awarded at the World Congress of Mathematicians...

Whether the paper can be published in an authoritative journal in time will sometimes affect the award of the award.

Although some mathematicians are very confident in their papers and will publish them on pre-publication websites such as ArXiver in advance and accept peer review in advance, the problem is that everyone knows that ArXiv is not authoritative. The big boss of the award review committee

It is impossible for us to stare at the results on the pre-publication website

And this year happens to be 2025, and next year will be the year when the World Congress of Mathematicians will be held. So Tian Yanzhen is really not the first to send him a similar email. Everyone hopes that their papers can be published in journals in advance and be selected by the review committee.

The big guys noticed.

So Lot Dugan was used to it.

But what interested him was that the author of the paper Tian Yanzhen specially recommended to him this time had just celebrated his sixteenth birthday. Moreover, the content of the paper still combined Schultz's theory with curves to perform upper bounds.

The derivation of rational points provides a general formula, which is then verified by supercomputing.

This made Lot Dugan decide to take a look at the paper for himself.

If this paper is as creative as Tian Yanzhen said, he would not mind personally serving as the editor of this paper and finding suitable reviewers for this paper. Not only because the content of the paper is very innovative, but also because

The age of the first author Qiao Yu.

Most mathematicians who have achieved a certain status are more interested in young geniuses because they all know the importance of mathematical talent.

In natural subjects such as physics and chemistry, as people get older, they can still rely on their rich experience to continue to shine by guiding students to conduct experiments and find bright spots in complex data, so the research life is generally very long.

But once mathematicians pass a certain age, they will lose their creativity. Mathematics happens to be a subject that requires creative thinking. It does not stick to the laws set by predecessors, but also requires logical autonomy within a perfect framework.

Push the entire discipline forward.

Let’s put it this way, a whimsical idea in mathematics may create a completely different world. But such whimsical ideas are often the patent of young people. Therefore, the Fields Medal is awarded once every four years, and it is only awarded once every four years.

Awarded to scholars under the age of 40.

It would be so imaginative if a sixteen-year-old could really complete such research independently.

So Lot Dugan did not continue to browse his personal emails, but directly logged into the backend of the "Annals of Mathematics" submission system, and through keyword searches, he soon found the paper recommended by Tian Yanzhen.

"Application of Schulz'plete Space Theory and P-Algebra Methods in Deriving Upper Bounds for Rational Points on Curve. The formula directly given in the introduction was enough to attract him. How could it be so simple?

Well, this was indeed a very interesting paper, and Lot Dugan soon became immersed in it.

He read the previous part about the analysis of curves using Schulz's complete spaces very quickly, which was not his area of ​​expertise. Although this part of the work also seemed very creative, based on the understanding of nearly complete spaces,

He does not think this part is the most eye-catching part of the paper.

Because the complexity of Schulz's theory is very high, it is not enough to support the author's ability to derive the formula for the upper bound of the curve's rational number points to such a simple level. Soon Lott Dugan saw the important part - the invariance of geometric constraints.

Derivation of parameters.

What a genius idea!

The genus, homology relationship, modular form, and P-geometric quantization are cleverly combined through the BSD conjecture, from local complexity, radiation to overall complexity, and the constraints of all variables are unified into one geometrically constrained invariant parameter!

Beautiful, simply too beautiful!

Combined with the final supercomputer analysis results of the paper, Lott Dugan also became excited. He picked up his mobile phone and wanted to call Tian Yanzhen to confirm that the main work of this paper was indeed completed by a sixteen-year-old mathematical genius.

.

But I looked at the time and realized that it was already past 11 noon.

This prevented him from dialing the number immediately. Considering the time difference between the two countries, it was already late at night in China. It should be Tian Yanzhen's private time. He planned to put down the phone and directly reply to an email to Tian Yanzhen, but

My heart still feels itchy...

No, this guy wrote him an email recommending the paper first. Even if the call was not polite, the other party would still understand it. After thinking about it, Lot Dugan still made the call.

However, Lot Dugan also thought about it. If the other party didn't answer the phone for thirty seconds, he would stop harassing her today. Thinking about it, it wouldn't be very rude. Fortunately, the call was picked up in less than ten seconds.

"Hello, Professor Dugan, I guess you saw my email, right?"

Lot Dugan could hear the excitement in the other person's tone, which reassured him. The other person was not asleep yet, and he didn't feel that his call had disturbed his life. Maybe Professor Tian was also looking forward to his response.

"Yes, Professor Tian. I'm sorry, I was busy all day at Columbia University yesterday, so I just saw your email this morning. And I just read this paper, and I have to say, especially the ideas proposed in the paper Geometrically constrained invariants are a stroke of genius

So after the Supercomputing Center reviewed the results given in the paper, I decided to personally serve as the editor of this paper. But one thing, Professor Tian, ​​you know, I hope to re-define the main work of this paper. Was it really done independently by Joe Yu, the first author of the paper?"

Lot Dugan, who has taken the initiative to learn about Chinese culture, has become accustomed to respecting Chinese cultural habits and putting his surname in front of his first name when addressing Chinese people. In fact, in recent years, in more and more contexts, people Everyone began to respect this habit subconsciously.

For example, when commenting on international sports events in which Chinese people participate, some international journals began to publish the names of Chinese scientists using the last name followed by a space and then the first name. For example, Qiao Yu. However, this situation is not common because most of them When publishing names in most international academic journals, they still put the first name before the surname. But it is undeniable that this is already a developing trend.

And this method is still used, mainly for the sake of continuity when entering and retrieving. Because it was laid out this way in the past, everyone is used to searching for papers in this way when doing paper retrieval. Changing it rashly will be very troublesome.

"You know? Professor Dugan, I know you will have this question, because when my student proposed to do this proposition, I couldn't believe that he could do it to this extent. But there is no doubt that, This was indeed done independently by him.

I believe you can see from the letter I sent you that I am willing to vouch for him academically. Because we have sufficient evidence to prove this. By the way, maybe you can ask Professor Zhang Shuwen who is currently working at Princeton and the professor at New York University. Professor Robert Green.
To be continued...