I Just Want to Be a Quiet Top Student

Chapter 652 4 steps

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

Ou Ye, who had just woke up, delivered the manuscript to the three students, so and so, and so and so, she taught the students face to face.

The context of the strong BSD conjecture proof compiled by Ou Ye is very clear, and this proof context adopts a backward inference method.

The last step is to prove the strong BSD conjecture, that is, to prove this sentence: The necessary and sufficient 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 is the rank of E.

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

The third step from the bottom, if you want to count the rational points on the elliptic curve, you must first demonstrate the rank on the elliptic curve.

The fourth step from the bottom, if you want to prove the rank on the elliptic curve, you can consider the method of group theory.

Through the unremitting efforts of Ou Ye and her three students, the team has achieved the fourth step from the bottom.

“Actually, the fourth to last step can also be considered as the first positive step. It takes the longest time. If we complete the fourth step in two years, then the next three steps can be completed in two months… …Ha…yawn…” Although Ou Yeh is in poor health, her mathematical thinking is very clear.

Ou Ye just woke up, but yawned again and again, the three students said, “Sister Ye Zi, take a rest, we know what to do! You sleep a while, let’s go first.”

The three students carefully installed Ou Ye’s manuscript, then left the People’s Hospital and returned to Yan University.

The small room at the end of the corridor on the first floor of the number courtyard is a war room for three students.

The three first organized Ou Ye’s manuscript into an electronic data model that can be verified by a computer.

This job takes about three people for three consecutive days, and each person will work no less than 12 hours a day.

Ou Ye’s thinking is very clear to the three students.

Ou Ye started from the group theory and obtained a hypothesis about the rank of the elliptic curve by calculating the rank of the typical elliptic curve.

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

The method adopted by Ou Ye is very traditional, inferring the typical theory from typical examples, and then putting the typical theory in all the examples to prove its universality.

The apple fell from the tree and hit Newton’s head. Newton derived a theory that the apple was affected by the gravity of the earth. Is this theory only valid for Apple, or is it universal? This is what Newton will do next to demonstrate the universality. In the end, he proved the law of universal gravitation.

Newton is the great light of mankind, but his method of demonstrating great theories is also very traditional, from simple to complex, and then from complex back to simple.

In the last step of the strong BSD conjecture set by Ou Yeh, she completed the theoretical construction from simple to complex. Of course, it can only be regarded as a hypothesis at present.

From the complex regression to the simplicity, it is a work of enormous amount of engineering to finally prove that the assumption of the rank of the elliptic curve has universality or the universality with conditions.

This job 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. Any one of Zhao Tian, ​​Xiaoyun, and Zeng Han can calculate the correct solution within 10 minutes.

But theoretically there are infinite elliptic curves, and most of them involve an infinite number of check calculations. Humans cannot do manual calculations and must rely on computers.

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

Based on Ou Ye’s manuscript, the elliptic curve is verified by a computer, then 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, Ouye’s master tutor, has made an important contribution to the BSD conjecture.

Professor Gong proved the relevant theorems 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 is equivalent to helping his disciple Ou Ye to eliminate many checking conditions, so the three students of Ou Ye only need to verify the elliptic curve that satisfies the Kolyvagin theorem, the Gross-Zagier theorem, and the order of the Shafarevich-Tate group.

Zhao Tian, ​​the eldest of the three students, asked his junior and junior sisters with concern: “Summer vacation is coming soon. Have you bought tickets to go home?”

Xiaoyun shook his head: “Anyway, my parents are not at home, and I went back to be a single dog with no one to feed, so I decided to stay in the capital for work-study programs this summer.”

“Xiaoyun, where did your parents go?” Zhao Tian asked.

Xiaoyun sorted out Ou Ye’s manuscript while saying: “My mother went to Germany as a visiting scholar, and my dad went to Africa to help African friends build infrastructure. I won’t be able to see my parents until the Spring Festival next year.”

Zhao Tian knows that Xiaoyun Xuemei’s mother graduated from Fudan with a Ph.D. and is currently a professor at East China Normal University. Xiaoyun Xuemei’s father graduated from Shuimu University with a master’s degree and is currently an engineer of the Eighth Engineering Bureau of China Construction.

Xiaoyun school girl can be recommended to Yandashu 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 summer vacation, don’t hesitate to tell me if you need it.” Zhao Tian is an aboriginal in the imperial capital and is born in Banchengzi Village, Bulaotun Town, Miyun.

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

Xiaoyun nodded and said, “Thank you, brother, let’s hurry up and process the data.”

Zhao Tian turned to ask his junior brother: “What about you, Zeng Han, should you go home this summer?”

Zeng Han concentrated on processing the data and did not look up: “I won’t go home, stay at school.”

“Why? Your parents also went abroad?”

“No, it’s just staying in school anyway.”

Zeng Han was recommended to Yan Da at the age of sixteen. He has just turned 18 this year. Zeng Han’s parents are both doctors, his grandparents, grandparents, and grandparents are all senior intellectuals. His parents’ two families have a total of six doctors and seven masters. There are five full professors and researchers, and two family members. When a member is 35 years old, the per capita standard is associate professors and associate researchers.

Zeng Hanneng, who came from a family of intellectuals, recommended to Yanda University at the age of 16. It is also not a question of his intelligence, but genetic inheritance.

Compared with the two schoolmates from famous families, Zhao Tian, ​​who was born in Banchengzi Village, Bulaotun Town, Miyun, is considered an inspirational senior.

Zhao Tianchang said: “I’m not a genius, I have never participated in the Olympiad. That year, I missed a few exams and was admitted to the Capital Fourth Middle School. Three years later, I missed a few exams and passed the Yan University. When I was an undergraduate, I had a few blind spots, with a grade point of 4.0, and I was recommended to graduate students from Yanda University.”

These are the true words of Zhao Tian. He feels that he is an ordinary person compared to his younger brothers and younger sisters. Xiaoyun and Zeng Han are the kind of geniuses in the true sense.

Crunch, the door of the hut opened.

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

“Teacher Zhou why are you here?” The three students were quite surprised.

The visitor is Zhou Yu’an, who, together with Shen Qi and Ou Ye, are called “the XX three outstanding persons of Yandashu Academy”.

Zhou Yu’an, Shen Qi, and Ou Ye enrolled in the Yan-Da University of Mathematics in the same year. The three of them were classmates. The three of them went to the Princeton Department of Mathematics to complete their doctoral studies. The number of undergraduates in their school is also considered to be the strongest in the history of Yan University.

Can the latecomers of Yan Dashu Academy surpass the XX class of Shen, Ou, and Weijie?

currently seems to be more difficult.

Shen Qi’s achievements alone can hardly be surpassed. Not to mention surpassing, even copying is difficult.

IMO gold medalist, Ramanu Gold Medal winner, and director of the Mathematics Room of Shen Qi Research Center, Zhou Yuan, in the hearts of Mathematics students of Yan University, is the second male **** second only to Shen Qi.

Teacher Zhou is not in the school. He suddenly drove to the school and came to the three students. There must be something.