I Just Want to Be a Quiet Top Student

Compared with Shen Qi Quantum Club, which is full of atmosphere in the second grade, Ouye Computer Club is much more serious.

According to the management regulations of Yanda clubs, every club in the school needs at least one instructor.

The instructor of Ouye Computer Club is Ouye, and most of the funds for club activities are given by Ouye.

It sounds like a computer society, but in fact the headquarters of the Ouye Computer Society is set up in the Number Academy.

A signboard of "Ouye Computer Club" was hung on the door of a room at the end of the corridor on the first floor of the Shuyuan. A young man was playing cards with a big girl in the room.

"Sister Ye Zi gave our company another 20,000 yuan, and she gave a total of 80,000 yuan this year." The young man's name is Zhao Tian, ​​and he is the president of Ouye Computer Club.

"Professor Shen kindly sponsored 2,000, so, their family must be Sister Yezi who holds the financial power." The eldest girl made a "I want it" gesture, indicating that she wants another card. .

"Xiaoyun, it's already 20 o'clock for you, do you want more?" Zhao Tian gave Xiaoyun another card after speaking

This card is the Ace of Hearts, and Xiaoyun got 21 points.

"Blackjack is a non-linear combination game, Sister Ye Zi said it." Xiaoyun smiled sweetly, and said: "Senior, we have to work hard, and the people from Shen Qi Mathematics Club have taken over the mathematics competition and modeling competition for college students again." Professor Shen was very happy, he offered 50,000 yuan to reward Shen Qi Mathematics Society, and even helped the members of Shen Qi Mathematics Society write letters of recommendation to go to Princeton for further study."

"Xiao Yun, don't waver. We are born to be Ye Zi's people, and we will die to be Ye Zi's ghost." Zhao Tian turned over a card for himself, 7 o'clock, and he also got blackjack in this hand: "University student Mathematics competitions and modeling competitions are nothing, if Professor Shen doesn’t help us write recommendation letters, Sister Ye Zi will definitely help. Have you got your Hong Kong and Macau travel permit?”

"It's done." Xiaoyun nodded.

"Okay, proceed as planned." Zhao Tian reshuffled the cards and continued to practice poker with Xiao Yun.

There were three people in this room, and the other boy stood silently in front of the blackboard, like a plant.

Zhao Tian looked at the boy: "Zeng Han, are you going with us?"

Zeng coldly said: "If you want to die, go to the casino. You want to die, but I don't."

"Zeng Han, you know that we went to Macau not for money, but to study math problems." Zhao Tian tried to persuade him that this junior Zeng Han was a math genius.

Zeng Han stared at the blackboard intently, and said, "Just go and die, and I will burn paper money with you every Qingming Festival."

"Hey, you brat!" Zhao Tian dropped the playing cards in his hand, came to Zeng Han's side, and observed Zeng Han's work on the blackboard.

The first is a right triangle with side lengths 3, 4, 5.

It is easy to see that the area of ​​this triangle is 1/2 times base times height = 6.

This is actually a Pythagorean right triangle, which also involves an ancient mathematical problem: given a positive integer d, is there a right triangle whose side length is a rational number and the area is exactly d?

Using high school mathematics knowledge, it can be proved that the necessary and sufficient condition for the existence of a right-angled triangle whose side length is a rational number and whose area is d is that the equation y2=x3-d2x has a rational number solution to x and y≠0.

Using college mathematics knowledge to make a further interpretation, if and only if d is the area of ​​a right-angled triangle whose side length is a rational number, this equation has a rational number solution to x and y. The discriminant of this equation △=-16[4(-d2)3]=64d6, it is not equal to 0, so the image of this equation is an elliptic curve.

Linking high school mathematics knowledge with university mathematics knowledge, that is, to find out which integers d can become the area of ​​a right-angled triangle whose side length is a rational number, is equivalent to the problem of finding a rational point on a certain elliptic curve.

This is the problem that British scholars Birch and Swinnerton-Dell want to solve all their lives. The academic circles call it the BSD conjecture.

"Brother Zeng Han, I really support your research on the BSD conjecture. In fact, Xiaoyun and I are also very interested in the BSD conjecture." Zhao Tian drew an ellipse in the air. Anyway, he has already secured research, and Zhao Tian has enough time to organize the club activities of Ouye Computer Club.

"Oh." Zeng Han snorted expressionlessly.

Xiao Yun, who was a junior in college, leaned over to Zeng Han and said, "Brother Zeng Han is always so serious, why not just smile."

The corner of Zeng Han's mouth moved slightly: "Oh."

"Such a handsome guy is actually a facial paralysis, hey." Xiaoyun sighed, she looked at the mathematical symbols on the blackboard, and said: "BSD conjecture is classified as number theory, but it actually involves many other branches of mathematics. We all know that the necessary and sufficient condition to prove that the elliptic curve has infinitely many rational points is that L(E, 1) = 0, which proves the BSD conjecture. However, it is really difficult."

While talking, Xiaoyun wiped half of the blackboard with a blackboard eraser, and then wrote a stereotyped Q on the blackboard, representing the set of rational numbers.

Xiaoyun wrote more and more, and she said while writing: "E(Q) is an Albertian group. In 1922, Model proved that the group E(Q) is finitely generated. More than 60 years later, Faltings It also proved the Model conjecture, and in a few years, Wiles proved Fermat's last theorem... Connecting these mathematical histories together, we can find that the way that great mathematicians solve number theory problems is often not a number theory method, only one No exception, Professor Shen."

Zhao Tian: "Hey, Xiaoyun, why are you talking about Professor Shen? Professor Shen doesn't love us, but Sister Yezi who loves us."

Xiaoyun showed a nympho smirk: "Because Professor Shen is so handsome."

"Don't interrupt." Zeng Han said dissatisfiedly to Zhao Tian, ​​and said: "Senior sister, I agree with your point of view, to prove the BSD conjecture must use the means of elliptic curve and group theory, Sister Ye Zi also said so. Now The big question is, how is the rank calculated or can it be arbitrarily large? I think we should have clues in that.”

"Well, yes, but it's so difficult." Xiao Yun tilted her head and fell into deep thought.

How the serious research of three undergraduates can prove the BSD conjecture seems a bit overwhelming.

BSD conjectures, one of the millennium problems in mathematics, if it is solved by a few undergraduates from the School of Mathematics of Yanda University, what will happen?

crunch.

The door opened and a person came in. She was beautiful and intelligent, wise and learned, kind and generous, a mother of one child.

"Hello, Miss Ye Zi!"

The three students stood up straight, and the goddess of their club came.

"How are you all?" Ouye smiled, and she said to Zhao Tian: "Xiao Zhao, does anyone in our club want to go to Columbia University for a year exchange? There is a place."

Zhao Tian: "Of course there are, I'll do some statistics later."

Ouye did his master's degree at Columbia University, and then went to Princeton to study for a Ph.D.

Shen Qi's performance at Princeton was too dazzling, which to some extent made Ouye under his aura when he was studying for a Ph.

But Ouye still has a good reputation in Columbia University, and Columbia University also buys her account.

"Okay, thank you for your hard work." Ouye said, she glanced at the blackboard, a little surprised: "Huh? Are you studying the BSD conjecture?"