From small town scholar to chief scientist

After confirming the job, everyone began to work day and night.

If there is any reason not to, they will make an appointment with Zhou Yi in advance and ask clearly.

After Yugaoyuan started, it ushered in the annual postgraduate re-examination.

Recruiting talents is a top priority.

The Chongqing High Court has been established for two or three years.

The first batch of masters and the first batch of more powerful doctoral students are about to graduate,
Send real talents to the society.

Most of these graduates will be directly absorbed by Yuzhou, which is Space-Time Technology Company.

Then it flows to other enterprises or establishments.

Zhou Yi is also busy recruiting students, but the number of accepted students is not enough, so they only accept students in the direction of mathematics.

If there is too much, the quality will drop.

There are already more than ten PhDs and masters under my study.

If there are more than a dozen more, they won't win at all, unless they arrange a small guide for them.

But Zhou Yi felt that this was of little significance, just bring a little less.

It is almost enough to accept 3-4 students a year.

The heat on the Internet came and went quickly, and basically everything calmed down.

Regarding all the things about the sixth-generation fighter jet, Zhou Yi can be regarded as letting go of a paragraph, and just wait quietly for the model machine to come out at the end of the year.

Perhaps some technological breakthroughs in the middle can bring some news from time to time.

In Zhou Yi's office,

Maynard came to Zhou Yi's room again.

"Professor Zhou, how is your BSD conjecture research going? Why don't you just choose your achievements and report at the International Congress of Mathematicians?"

Maynard said anxiously.

Although it is said that the Fields Medal cannot be escaped, it is not a problem to delay it all the time.

You have to choose a subject.

Zhou Yi looked at Maynard, said with an awkward smile:

"Don't worry, don't worry, it will be later, it will be done with us this year, don't worry."

I have been busy with the sixth-generation machine these days, so I don't have time to make BSD guesses.

"Oh, Professor Zhou, this is an excellent opportunity."

Maynard said bitterly.

Now the tripartite alliance, the relationship is closer than before,
It can be said that we share weal and woe.

In addition, Maynard's sense of belonging to the Chongqing Higher Court is getting stronger and stronger, so he hurriedly urged Zhou Yi.

Zhouyi said to solve the BSD conjecture, Maynard believed that Zhouyi had this strength,

But the possibility of solving it before the International Congress of Mathematicians is too low.

With all the calculations, there are still more than 4 months.

Zhou Yi said:

"Haha, I also know that this is an opportunity to prove our Chongqing Higher Court, so don't worry."

Seeing that Maynard regarded Yugaoyuan as his home, Zhou Yi smiled without hesitation, and then comforted Maynard.

Not to chill Maynard's heart.

"Trust me, it will be fine!"

Zhou Yi said with certainty.

Maynard had no choice but to say:

"alright."

After Maynard left, Zhou Yi continued to study the BSD conjecture.

The BSD conjecture, in other words, studies the relationship between the arithmetic of elliptic curves and the analytical properties of their L-functions.

Elliptic curves contain rich arithmetic information.

An important property of it is that the points on it form a commutative group whose structure is defined by equations with rational coefficients on the coordinates.

It sounds simple, but it can be transformed into an algebraic problem.

Zhou Yi looked at the articles about the BSD conjecture in recent years,
He kept saying in his mouth:
"There is a nice analogy between the BSD conjecture and the class number formula for number fields: the Shafarevich-Tate group corresponds to the ideal class of number fields;
And the Mordell-Weil group corresponds to the unit multiplicative group of the integer ring of the number field. "

Zhouyi wrote while reading,

For fear of missing out on hard-won inspiration.

Zhou Yi didn't realize that it was time for lunch until he was hungry at noon and made a gurgling sound.

Zhou Yi ordered a rice bowl with shredded pork and green peppers in the cafeteria. While eating, he thought about the morning problems.

The more I think about it, the more feasible it becomes.

When I was about to continue my research in the afternoon, I was disturbed by various trivial matters in the Chongqing Higher Court.

This made Zhou Yi very depressed. In the evening, there were probably various questions about the sixth-generation fighter jets.

If this continues, it is estimated that more than four months will definitely not be enough.

It is definitely impossible for Zhou Yi to ignore the matter of the Chongqing Higher Court.

This is the painstaking effort of many people, and the sixth-generation fighter has just started to do it in the early stage.

Even if the meeting was held for nearly ten days, it was just to straighten out the ideas and methods.

It does not mean that the process is without problems.

The next morning, Zhou Yi held a meeting,
"I'm going to retreat for 3 months to study the BSD conjecture, so all the things about the Yugao Court have been arranged in advance."

In the conference room, there are all the high-level executives of Yugaoyuan, and many things can be settled.

As for the allocation of funds, it has already been allocated, and there is no need to allocate it again.

In one morning, Zhou Yi took care of all the miscellaneous matters of the Chongqing Higher Court.

In the afternoon, more than a dozen apprentices were assigned tasks.

Zhou Yi didn't take care of it in person for three months, but Shen Yiyu and Zhang Dugang took a few students from the Institute of Mathematics in person.
Zhou Yi asked three academicians to help students from the Institute of Physics, Institute of Computer and Artificial Intelligence, and Institute of Geodynamics for three months.

In this way, their talents will not be wasted, and their abilities will be exercised by the way.

After the chores and student issues of Chongqing Higher Court have been properly arranged,

Zhou Yi was relieved, at least he had nothing to worry about.

You just need to talk to General Zhao and Academician Ma about the situation.

Not long after, several people gathered together. After Zhou Yi briefly explained the situation, everyone expressed their understanding.
General Zhao patted his chest and said:

"Professor Zhou, don't worry about retreating, leave the matter of the sixth-generation fighter to us."

Academician Ma also said:
"Professor Zhou, you have already taught and explained by hand, we must have no problem."

Everyone said to Zhou Yi one after another, expressing that Zhou Yi can retreat with peace of mind and don't worry about other things about the fighter.

General Zhao said:
"The sixth-generation machine is important, but the reputation of Yugaoyuan is even more important. We haven't had Professor Zhou in the past few months, and we just slowed down.
But the accumulation of a well-established institution requires too many things. "

The Air Force Institute has all moved here, and General Zhao obviously hopes that the Chongqing Higher Academy will be stronger and more famous.

This plays a vital role in ZZ and many other aspects.

Zhou Yi was still a little worried, and said:

"Well, if there is anything urgent, please inform Xia Xue and let Xia Xue tell me."

Everyone was silent for a while, nodded and said:

"it is good."

After finishing speaking, everyone left slowly.

Zhou Yi tidied up the table, packed all the materials and documents he read into his notebook,
The draft paper written before was also taken home.

Prepare to solve the BSD conjecture in one go.

After returning home, Zhou Yi briefly explained what had happened to Xia Xue,

Xia Xue said softly:
"I will deliver the food to the study on time every day, remember to eat on time."

Zhou Yi said:

"kindness."

After deciding to retreat, Zhou Yi stayed alone in the study.

The previous materials and documents were all projected by Peony,
Zhou Yi looked at the screen while writing and drawing with a pen.

设α和b是整数，4a^3＋27b^2≠0，

Equation E: y2=x^3+ax+b is called an elliptic curve defined on the rational number field Q.

Let E(Q) represent all rational number points on this curve plus a point at infinity, and an addition operation can be introduced on it to make E(Q) a commutative group.

Regarding the elliptic curve, Zhou Yi wrote it on the draft paper casually,

"British mathematician Mordell proved in 1922 that the group E(Q) is finitely generated, thus having a direct sum decomposition E(Q)=E(Q)_f+E(Q)_t."

For several days in a row, Zhou Yi had no progress, which made Zhou Yi a little anxious.

But it is useless to be anxious. Sometimes the inspiration does not come, but there is no way.

Zhou Yi temporarily slowed down his progress and basked in the sun in the yard.

Make a phone call with Maynard every now and then to discuss it.

Maynard is also an expert in the field of number theory, a person who has won the Fields Medal,
Communicate with them more, maybe a little spark can be collided.

On this day, Maynard said to Zhou Yi in the yard of Zhou Yi's house:
"Since you are stuck in Zhou Yi, why don't you study an ancient number theory problem related to BSD, called the congruent number problem."

After Zhou Yi finished listening, he said with a doubtful tone:

"Congruence problem!?"

Maynard said:
"Start with this question, see if you can find a little inspiration?"

Then Maynard briefly introduced and said:

"A positive integer n is called a congruent number, which means that n is the area of ​​a right triangle whose three sides a, b, and c are all rational numbers."

Having said this, Maynard picked up a piece of chalk and wrote on the blackboard in the courtyard,

"Professor Zhou, look here,"

[n=6 and 5 are congruent numbers, because (a, b, c) can take (3, 4, 5) and (3/2, 20/3, 41/6) respectively. 】

Maynard finished writing and continued:
"So it is not difficult to see that for each positive integer m, m^2n is a congruent number if and only if n is a congruent number, so it may be assumed that n is a positive integer without a square factor.

The congruent number problem is to determine all the congruent numbers. "

Zhou Yi also knew what Maynard meant when he heard this, and said:

"That is to say, the remaining positive integers are non-congruent numbers."

Maynard secretly lamented Zhou Yi's terrifying talent, and said:

"That's right, Professor Zhou.

This problem originated in Arabia in the 11th century AD. So far, many congruent and non-congruent numbers have been determined, but the whole problem has not been completely solved. "

Hearing this, there was a gleam in Zhou Yi's eyes, and he said with an extremely confident tone:
"Then we can know instantly that the connection between the same remainder problem and elliptic curves is:
n is a congruent number if and only if the rank of the elliptic curve En:y2=x^3- n^2x≥1, that is, there are infinitely many rational solutions to this equation. "

With a look of shock in Maynard's eyes, he said:

"That's right, Professor Zhou, that's what it means. Maybe you can take a look at the original article by Professor Tian Ye of the Chinese Academy of Sciences.
In 2022, Professor Tian Ye gave a 45-minute report on this problem and the BSD conjecture at the International Conference of Mathematicians. "

Not long after, Zhou Yi directly projected this article.

"Congruent Number Problems and Elliptic Curves" is still a gift for Academician Yang Le's 80th birthday.

Zhou Yi secretly scolded himself for ignoring this article.

You must know that Professor Tian Ye has a good opinion in the field of BSD conjecture.

Maybe one day in the future, the BSD conjecture can be solved, but now Zhou Yi actually chose,
Then I am only sorry for all my colleagues who have studied this conjecture.

It hasn't been researched for so many years, so it's time to solve it by yourself.

"Thank you, Maynard."

Zhou Yi said very solemnly.

Maynard sighed:

"It's just that you got dizzy from being busy with the sixth-generation aircraft before, otherwise it's impossible not to notice."

What the sixth-generation fighter needs and the difficulty of overcoming is no less than a millennium problem.

Zhou Yi was dizzy for a while, and it was reasonable not to know.

Zhou Yi still insisted:

"Thank you, I am sure to solve this problem."

Maynard said:
"Okay, I won't bother you anymore. Academician Sun Song, the academician of Mathematics, will take care of us, and there won't be any major problems."

Zhou Yi said:

"it is good."

After sending Maynard away, Zhou Yi immediately returned to his room and began to retreat, reading Professor Tian Ye's thesis.

While watching, Zhou Yi couldn't help saying:

"This article only proves the weak Goldfeld conjecture of the congruent number problem, and the Goldfeld conjecture has not been fully resolved.

However, Professor Tian Ye has paved the way. If it is combined with Zhou's analytical method, it must be able to completely solve the Goldfeld conjecture. "

Zhou Yi's eyes lit up, and he wrote vigorously in his hand.

The so-called Goldfeld conjecture is that among all positive integers n such that (n)=+1 (respectively, 1) without a square factor, there exists a subset with a density of 1, so that when n is in this subset,
ords=1L(E^(n),s)=0 (respectively,=1).

And the concept definition of density was also written by Professor Tian Ye,

If D is a subset of positive integers and D' is a subset of D, then the density of D' in D refers to the following limit (if this limit exists),

lim_(N to +∞)((#{n∈D′|n
Seeing this, Zhou Yi said:

"If the density of the subset is not required to be 1, but only positive density is required, the weak Goldfeld conjecture can be written immediately."

Among all square-factorless positive integers n such that (n) equals +1 (respectively, 1), there exists a subset of positive densities such that ords=1L(E^(n ), s)=0 (respectively, =1).

The pen in Zhou Yi's hand immediately wrote on the draft paper, without even reading Professor Tian Ye's post.

This is the mathematical foundation that Zhou Yi has accumulated until now, and it can also be said to be a mathematical talent.

Then Zhou Yi read it while writing it himself.

Look at one step and write ten steps,

Zhou Yi basically proved Professor Tian Ye's proof paper by himself.

From afternoon to night, Zhou Yi didn't even have time to eat.

I wrote nearly twenty sheets of A4 paper on scratch paper.

"Professor Yu Tian's proof method is correct, but if combined with Zhou's analysis method, the steps may be shortened.

It's a pity that my Zhou's analytical method hadn't come out yet. It was 19 years when Professor Tian Ye wrote this paper. "

Zhou Yi stretched his waist, and already had a specific idea about the complete Goldfeld conjecture.

Perhaps the Goldfeld conjecture can be completely solved within half a month, and then the BSD conjecture can be solved.

Zhou Yi lamented that Professor Tian Ye's research on the BSD conjecture is so deep that he seems to be picking up a bargain.

There has been no news from Professor Tianye for so long, and I am also disrespectful.

The academic world is so cruel, it is not necessarily whoever comes first can solve these century-old problems,

It depends on luck and talent!
PS: The references here are mainly the papers of Professor Tian Ye, if you are interested, check them out.