From small town academic to chief scientist

After deciding on the job, everyone started working day and night.

If there are any principles that I don’t know, I will make an appointment with Zhouyi in advance and ask clearly.

After the opening of Chongqing High School, the annual postgraduate re-examination was ushered in.

Recruiting talents is a top priority.

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

The first batch of master's students and the first batch of more powerful doctoral students are also about to graduate.

Provide real talents to society.

Most of these graduating students will be directly absorbed by Yuzhou, that is, Spacetime Technology Company.

Then it flows to other enterprises or establishments.

Zhou Yi is also busy recruiting students, but the number of students he accepts is not enough, so he only accepts students majoring in mathematics.

If you carry too much, you won’t be able to carry it, and the quality will decrease.

In total, I have more than ten PhD and master’s degrees currently under study.

If there are more than ten more, they will not be able to win at all, unless they are given small mentors.

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

Accepting 3-4 students a year is enough.

The popularity on the Internet comes and goes quickly, and basically everything has calmed down.

Regarding all things about the sixth-generation fighter jets, Zhou Yi can be regarded as putting aside a paragraph and quietly waiting for the release of the model aircraft at the end of the year.

Perhaps some technological breakthroughs along the way can bring some news from time to time.

In Zhou Yi’s office,

Maynard came to Zhou Yi's room again.

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

Maynard said anxiously.

Although it is said that you cannot run away with the Fields Medal, it is not a problem to keep putting it off.

You have to choose a subject.

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

"No rush, no rush, later, later, we will do it this year, no rush."

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

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

Maynard said earnestly.

Now the tripartite alliance is closer than before.

It can be said that we share weal and woe.

In addition, Maynard's sense of belonging to the Chongqing High Court was getting stronger and stronger, so he rushed Zhou Yi.

Zhou Yi said that he could solve the BSD conjecture. Maynard believed that Zhou Yi had this ability.

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

All things considered, there are still more than 4 months left.

Zhouyi said:

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

Seeing that Maynard regarded Chongqing High Court as his home, Zhou Yi smiled calmly and then comforted Maynard.

Maynard's heart cannot be chilled.

"Believe me, it'll be fine!"

Zhou Yi said with great certainty.

Maynard had no choice but to say:

"Fine."

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 its L-function.

Elliptic curves contain rich arithmetic information.

One of its important properties is that the points on it form a commutative group, and this group structure is defined by the rational coefficient equations on the coordinates.

It sounds simple, but in fact it can be turned into an algebraic problem.

Zhou Yi looked at the articles about BSD conjecture in recent years,

He kept chanting:

"There is a good analogy between the BSD conjecture and the number-like formulas of number fields: the Shafarevich-Tate group corresponds to the ideal group of number fields;

The Mordell-Weil group corresponds to the unit multiplicative group of the integer ring of the number field. "

Zhouyi read and wrote at the same time,

Afraid of missing out on hard-won inspiration.

It wasn't until he got hungry at noon and made a gurgling sound that Zhou Yi realized that it was time to have lunch.

Zhou Yi ordered a green pepper shredded pork rice bowl in the cafeteria, and while eating, he thought about the morning's problems.

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

Just when I was about to continue my research in the afternoon, I was interrupted by various trivial matters at the Chongqing High Court.

This made Zhou Yi very depressed. There may be various questions about the sixth-generation fighter jets tonight.

If this continues, more than four months will definitely not be enough.

It is definitely impossible for Zhou Yi to ignore the affairs of the Chongqing High Court.

This is the hard work of many people, and the sixth-generation fighter jet has just started to be worked on in the early stage.

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

That doesn’t mean the process is problem-free.

The next morning, Zhouyi held a meeting,

"I am going to retreat for three months to study the BSD conjecture, so all the things about the Chongqing High Court have been arranged in advance."

In the conference room, there were all the senior officials of Chongqing High Court, and many things could be agreed upon.

As for the allocation of funds, it has been allocated long ago and no further allocation is needed.

In one morning, Zhou Yi took care of all the chores in the Chongqing High Court.

In the afternoon, more than ten apprentices were assigned tasks.

Zhou Yi did not take care of them personally for three months, so Shen Yiyu and Zhang Dugang took care of several students from the Institute of Mathematics.

Zhou Yi found three academicians to help teach students from the Institute of Physics, the Institute of Computer and Artificial Intelligence, and the Institute of Geodynamics for three months.

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

After the trivial matters and student issues of Chongqing High School are properly arranged,

Zhou Yicai breathed a sigh of relief, at least he didn't have any worries in his heart.

All you need to do is 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 also expressed their understanding.

General Zhao patted his chest and said:

"Professor Zhou, you can rest assured and leave the sixth-generation fighter jets to us."

Academician Ma also said:

"Professor Zhou, you have taught and explained everything step by step. We will definitely have no problem."

Everyone told Zhou Yi one after another, saying that Zhou Yi should be in seclusion with peace of mind and not worry about other things about the fighter.

General Zhao said:

"The sixth-generation machine is important, but the reputation of Chongqing High School is even more important. We have not had Professor Zhou in the past few months, but we are just a little slower.

But the accumulation of a solid academic institution requires too many things. "

The air force station has all moved here, and General Zhao obviously hopes that the Chongqing High Court 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:

"Let's do this. If there is anything urgent, inform Xia Xue and let Xia Xue tell me."

Everyone was silent for a moment, nodded and said:

"good."

After finishing speaking, everyone slowly left.

Zhou Yi cleaned up the table and packed all the materials and documents he read into his notebook.

I also took home all the scratch paper I had written before.

Prepare to solve the BSD conjecture in one go.

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

Xia Xue said softly:

"I will deliver the meals to the study on time every day. Remember to eat on time."

Zhouyi said:

"kindness."

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

All the previous information and documents were projected by Peony.

Zhou Yi looked at the screen while writing and drawing with a pen.

Assume α and b are integers, 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 the rational number points on this curve plus an infinity point. An addition operation can be introduced on it to make E(Q) a commutative group.

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

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

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

But there’s no point in being anxious. Sometimes the inspiration doesn’t come, and there’s just no way around it.

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

Give Maynard a call from time to time and discuss it.

Maynard is also an expert in the field of number theory and a Fields Medal winner.

If you communicate with them more, you might be able to create some sparks.

On this day, Maynard said to Zhou Yi in the yard of Zhou Yi’s house:

"Since Zhou Yi is a little stuck now, why not study an ancient number theory problem related to BSD, called the congruent number problem."

After Zhou Yi listened, he said with a hint of doubt:

"Congruence problem!?"

Maynard said:

"Start with this question and see if you can find some inspiration?"

Then Maynard gave a brief introduction and said:

"A positive integer n is called a congruence number, which means that n is the area of ​​a right triangle whose 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 yard,

"Professor Zhou, look here,"

[n=6 and 5 are congruence numbers, because (a, b, c) can be (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 every positive integer m, m^2n is a congruential number if and only if n is a congruential number, so we might as well assume that n is a positive integer without square factors.

The problem of congruence numbers is to determine all congruence numbers. "

Zhou Yi heard what Maynard meant and said:

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

Maynard secretly sighed at Zhou Yi's terrifying talent and said:

"That's right, Professor Zhou.

This problem originated in Arabia in the 11th century AD. Many congruential and non-congruential numbers have been determined so far, but the entire problem has not been completely solved. "

After hearing this, Zhou Yi's eyes exuded a glimmer of light, and he said with an extremely confident tone:

"Then we can instantly know that the connection between the congruence problem and elliptic curves is:

n is a congruence number if and only if the rank of the elliptic curve En:y2=x^3- n^2x is ≥ 1, that is, this equation has infinite rational solutions. "

Maynard said with a shocked look in his eyes:

"That's right, Professor Zhou, that's what it means. Maybe you can read the original article of Professor Tian Tian of the Chinese Academy of Sciences.

Professor Tian also gave a 45-minute report on this issue and the BSD conjecture at the International Congress of Mathematicians in 2022. "

Not long after, Zhou Yi directly projected this article.

"Congruence Problems and Elliptic Curves" was a gift given to Academician Yang Le on his 80th birthday.

Zhou Yi secretly cursed himself for ignoring this article.

You must know that Professor Tianye has good insights in the field of BSD conjecture.

Maybe the BSD conjecture will be solved one day in the future, but now Zhou Yi has chosen,

Then I can only feel sorry for all the colleagues who are studying this conjecture.

It has not been studied for so many years, so it is time to solve it by ourselves.

"Maynard, thank you."

Zhou Yi said very solemnly.

Maynard lamented:

"It's just that you were so busy with the sixth-generation machine that you fainted, otherwise you wouldn't have noticed it."

What the sixth-generation fighter aircraft requires and the difficulty of overcoming it are no less than a Millennium Problem.

Zhou Yi was so busy that he felt dizzy for a while, which was reasonable.

Zhou Yi still insisted:

"Thank you, I'm sure we can solve this problem."

Maynard said:

"Well, I won't disturb you anymore. Academician Sun Song of Mathematics is taking care of us and there won't be any big problems."

Zhouyi said:

"good."

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

While Zhou Yi was watching, he couldn't help but said:

"This article only proves the weak Goldfeld conjecture of the congruence problem, and the Goldfeld conjecture has not been fully solved.

However, Professor Tian Tian has paved the way. If combined with Zhou's analytical method, the Goldfeld conjecture can be completely solved. "

Zhou Yi's eyes flashed, and he wrote rapidly in his hand.

The so-called Goldfeld conjecture is that among all positive integers n without square factors such that (n) = +1 (respectively, 1), there exists a subset with density 1 such that when n is in this subset,

ords=1L(E^(n), s)=0 (respectively, =1).

The conceptual definition of density was also written by Professor Tian Tian.

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 you do not require the density of the subset to be 1, but only require a positive density, you can immediately write a weak Goldfeld conjecture."

Among all square-free positive integers n such that (n) is equal to +1 (respectively, 1), there exists a subset of positive density such that when n is in this subset, ords=1L(E^(n ), s)=0 (respectively, =1).

Zhou Yi immediately wrote on the draft paper with the pen in his hand, without even looking at Professor Tianye's post.

This is the mathematical foundation accumulated from Zhouyi to the present, and it can also be said to be mathematical talent.

Then Zhou Yi read it and wrote it himself.

Look at one step and write ten steps,

Zhou Yi basically proved this proof paper by Professor Tian.

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

I wrote nearly twenty pieces of A4 paper on the scratch paper.

“Professor Yodo’s proof method is correct, but if combined with Zhou’s analytical method, the steps may be shortened.

It's a pity that my Zhou analysis method has not yet come out. It was in 2019 when Professor Tian Tian wrote this paper. "

Zhou Yi stretched out and already had a specific idea about the complete Goldfeld conjecture.

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

Zhou Yi lamented that Professor Tian Tian’s research on the BSD conjecture was so in-depth that he seemed to be getting a bargain.

There was no news from Professor Tian Tian for so long, and he felt disrespectful.

The academic world is so cruel. It is not necessarily the case that whoever comes first will be able to solve these century-old problems.

It depends on luck and talent!

PS: The references here are mainly the papers of Professor Tianye. If you are interested, check them out.