Zhao Tian, Xiaoyun, and Zeng Han went to Yanda People's Hospital to visit Ou Ye.

Ou Ye, who had just woken up, delivered the manuscript to the three students, and this and so did she teach the students face-to-face.

The context of the proof of the strong BSD conjecture sorted out by Ou Ye is very clear, and this proof context adopts the method of reverse pushing.

In the last step, to prove the strong BSD conjecture, we will prove that the sufficient and necessary condition for E(Q) to be an infinite set is that the Taylor polynomial of L(E,s) at s=1 has the following form, L(E,s)=c(s-1)^r+ higher-order terms, where c≠0 and r are the rank of E.

In the penultimate step, to prove the above sentence, you need to count the rational points on the elliptic curve.

In the penultimate step, if you want to count the rational points on the elliptic curve, you need to first demonstrate the rank on the elliptic curve.

In the penultimate step, if you want to demonstrate the rank on the elliptic curve, you can consider adopting the method of group theory.

After the tireless efforts of Ouye and her three students, the team has now reached the penultimate step.

In fact, the penultimate step, which can also be considered a positive first step, takes the longest. If we do the penultimate step in two years, then the next three steps can be completed in two months...... Ha...... Yawning...... "Although Ouye is not in good health, her mathematical ideas are very clear.

Ou Ye just woke up, but yawned again, and the three students said: "Sister Ye, you rest, we know what to do! ”

The three students carefully packed Ou Ye's manuscript and left the People's Hospital to return to Yan University.

The small room at the end of the corridor on the first floor of the academy was the war room of the three students.

The trio first collated Ouye's manuscript into an electronic data model that could be verified by a computer.

This job takes about three days in a row, and each person works no less than 12 hours a day.

Ou Ye's train of thought, the three students were very clear.

Starting from the group theory, Ouye obtained a hypothesis about the rank of the elliptic curve by calculating the rank of a typical elliptic curve.

Whether this hypothesis can be a lemma needs to be verified.

Ou Yee's approach is very traditional, deducing the typical theory from the typical examples, and then putting the typical theory into all the examples to verify its universality.

The apple fell from the tree and hit Newton's head. Newton deduced a theory that apples were affected by the gravitational pull of the Earth. Is this theory only valid for apples, or is it universal? That's what Newton was going to do about universality, and he finally proved the law of gravitation.

Newton was the great light of mankind, but his method of arguing great theories was also very traditional, from simple to complex, and from complex to simple.

In the penultimate step of Ouye's strong BSD conjecture, she completes the construction of a theory from simple to complex, which can only be considered a hypothesis at present.

From the simplicity of complex regression, it is a huge amount of engineering to finally prove that the assumption of the rank of elliptic curves has universality or conditionally limited universality.

This work will be completed by three students: Zhao Tian, Xiaoyun, and Zeng Han.

For example, under the condition of prime number p=5, the elliptic curve y^2=x^3-x has seven solutions, which are (0,0), (1,0), (4,0), (2,1), (3,2), (3,3), (2,4).

This is easy to calculate, and any one of the three of Zhao Tian, Xiaoyun, and Zeng Han can come up with the correct solution within 10 minutes by manually calculating.

However, there are theoretically infinitely many elliptic curves, and most of them involve an infinite number of calculation projects, which cannot be calculated manually by humans, and must rely on computers.

Zhao Tian, Xiao Yun, and Zeng Han will spend three days processing Ou Ye's manuscript into data that can be verified by a computer.

Based on Ouye's manuscript, the elliptic curve is verified by computer, so I don't know how many days it will take, it may be three days, or it may be three or thirty years.

Fortunately, Professor Gong Changwei, the master's supervisor of Ouye, has made an important contribution to the BSD conjecture.

Professor Gong proved the correlation theorem of Kolyvagin's inverse proposition and jointly proved with other mathematicians that at least two-thirds of elliptic curves satisfy the BSD conjecture.

Professor Gong Changwei helped his disciple Ouye eliminate many of the calculation conditions, so Ouye's three students only needed to verify the elliptic curves satisfying the Kolyvagin theorem, the Gross-Zagier theorem, and the Shafarevich-Tate group order.

Zhao Tian, the eldest of the three students, asked his younger brothers and sisters with concern: "Summer vacation is coming soon, have you bought tickets for the two of you to go home?"

Xiaoyun shook his head: "Anyway, my parents are not at home, and I will be a single dog with no one to feed me when I go back, so I decided to stay in the capital this summer to work and study." ”

"Xiaoyun, where have your parents gone?" Zhao Tian asked.

Xiaoyun said while sorting out Ou Ye's manuscripts: "My mother went to Germany as a visiting scholar, and my father went to Africa to help African friends build infrastructure, and I won't see my parents until the Spring Festival next year." ”

Zhao Tian knows that Xiaoyun Xuemei's mother graduated from Fudan with a doctorate and is now a professor at East China Normal University. Xiaoyun Xuemei's father graduated from Mizuki University with a master's degree and is currently an engineer of China Construction Eighth Bureau.

Xiaoyun Xuemei was able to escort Yan University Math Academy when she was in high school, this is not a question of whether she is smart or not, but genetic inheritance.

"It's okay, it's okay, Xiaoyun, if you don't go home during the summer vacation, if you need anything, just tell your brother. "Zhao Tian is an indigenous resident of the imperial capital, and his hometown is Banchengzi Village, Bulaotun Town, Miyun.

Since he is a resident of the imperial capital and a senior, Zhao Tian thinks that he should take care of Xiaoyun's younger sister.

Xiaoyun nodded and said, "Thank you, brother, let's hurry up and deal with the data." ”

Zhao Tian turned to ask the junior brother: "What about you, Zeng Han, you should go home this summer, right?"

Zeng Han concentrated on processing the data and did not look up: "I don't go home, stay in school." ”

"Why? Your parents are also out of the country?"

"No, it's to stay in school anyway. ”

Zeng Han was sixteen years old and sent to Yan University, and he just turned 18 this year. Zeng Han's parents are both doctors, his grandparents, grandparents and grandparents are high-level intellectuals, his parents' two families have a total of six doctors, seven masters, five full professors and researchers, and the average standard for members of the two families at the age of 35 is associate professor and associate researcher.

Zeng Han, who was born in a family of intellectuals, was able to send Yan University at the age of 16, which is also not a question of whether he is smart or not, but genetic inheritance.

Compared with the two juniors and sisters of a famous family, Zhao Tian, who was born in Banchengzi Village, Bulaotun Town, Miyun, is an inspirational senior.

Zhao Tianchang's words are: "I'm not a genius, I haven't participated in the Olympiad." That year, I took a few blind exams and was admitted to the No. 4 Middle School in the capital, and three years later, I was admitted to Yan University. When I was an undergraduate, I was blind for a few waves, with a GPA of 4.0, and was sent to the graduate school of Yan University. ”

This is Zhao Tian's true words, he feels that compared with his younger brothers and sisters, he is an ordinary person. And Xiaoyun and Zeng Han are geniuses in the true sense.

Crunch, the door to the hut opened.

A man came in, he was not tall, energetic, with a high hairline, and his eyes flashed with wisdom, and he was not a mortal at first glance.

"Teacher Zhou, why are you here?" the three students were surprised.

The person who came was Zhou Yu'an, who, along with Shen Qi and Ou Ye, was known as the "Three Masters of the XX Session of the Yan University Academy".

Zhou Yu'an, Shen Qi, and Ou Ye entered the School of Mathematics of Yan University in the same year, and they were classmates, and the three of them went to the Department of Mathematics at Princeton to complete their doctoral studies. Their class of undergraduate students is also considered to be the strongest in the history of Yan University.

Will the latecomers of the Yan University Academy of Mathematics be able to surpass Shen, Ou, and Wednesday Jie of the XX session?

At the moment, it seems to be more difficult.

Shen Qi's achievements alone are almost unsurpassable. Not to mention surpassing, even replication is difficult.

Zhou Yu'an, an IMO gold medalist, winner of the Ramanujan Award, and director of the mathematics department of the Shen Qi Research Center, is the second male god second only to Shen Qi in the hearts of mathematics students at Yan University.

Teacher Zhou's establishment was not in the Academy, he suddenly drove to the Academy, and came to the three students, there must be something.