Compared with the Shen Qi Quantum Society, which is full of middle school atmosphere, the Ouye Computer Club is much more serious.

According to the regulations of Yan University, each club in the school needs at least one instructor.

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

It sounds like a computer club, but in fact, the headquarters of the Ouye Computer Club is set up in the Academy.

At the end of the corridor on the first floor of the courtyard, a sign of "Ouye Computer Club" was hung on the door, and a young man in the room was playing cards with an older girl.

"Sister Ye Zi gave our club 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 the Ouye Computer Club.

"Professor Shen kindly sponsored two thousand, so ah, their family must be Sister Ye Zi who holds the financial power. The big girl made a "I want more" gesture and motioned for another card.

"Xiaoyun, you're 20 o'clock, do you want to?" Zhao Tian said and dealt Xiaoyun another card

The card was the ace of hearts, and Xiaoyun got 21 points.

"21 o'clock is a non-linear combination game, Sister Ye Zi said. Xiao Yun smiled and said, "Senior, let's work hard, the people of Shen Qi Mathematics Club have won the top three in the college students' mathematics competition and modeling competition." Professor Shen was very happy, he took out 50,000 yuan to reward Shen Qi Mathematics Club, and also helped Shen Qi Mathematics Club people write letters of recommendation to study in Princeton. ”

"Xiaoyun, don't be shaken, we are born as Sister Ye's people, and we are Sister Ye's ghosts when we die. Zhao Tian flipped a card for himself, 7 points, and he also got 21 points: "College students' mathematics competitions and modeling competitions are nothing, if Professor Shen doesn't help us write a letter of recommendation, Sister Ye Zi will definitely help." Have you done your Hong Kong and Macau permit?"

"That's it. Xiaoyun nodded.

"Okay, go ahead as planned. Zhao Tian reshuffled the cards and continued to practice poker with Xiaoyun.

There were three people in the room, and the other boy had been standing in front of the blackboard and was silent, like a plant.

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

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

"Zeng Han, you know, we don't go to Macau for money, just to study math problems. Zhao Tian persuaded him hard, this Zeng Han junior is a mathematical genius.

Zeng Han stared at the blackboard intently, and said: "Even if you go to die, every year Qingming, I will burn paper money with you." ”

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

The first is a right-angled triangle with sides of 3, 4, 5.

It is easy to get that the area of this triangle is 1/2 multiplied by base multiplied by high = 6.

This is actually a Pythagorean right triangle, which also involves an old mathematical problem: given a positive integer d, is there a right triangle with a rational number of side lengths and an area exactly d?

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

To take it a step further, if and only if d is the area of a right triangle with a side length of a rational number, the equation has a rational number solution for x and y. The discriminant formula 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 with college mathematics knowledge, that is, finding which integer d can be the area of a right triangle with a side length of a rational number is equivalent to finding rational points on some kind of elliptic curve.

This is the problem that British scholars Birch and Swinnaton-Dyer wanted to solve in their lifetime, and the academic community called it the BSD conjecture.

"Brother Zeng Han, I very much 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, he was a senior in college, and he had already secured the Yan University of Mathematics. Anyway, Zhao Tian has enough time to organize and carry out the club activities of the Ouye Computer Club.

"Oh. Zeng Han snorted expressionlessly.

Xiaoyun, who is in his third year of college, came to Zeng Han's side and said, "Brother Zeng Han is always so serious, laugh." ”

The corners of Zeng Han's mouth moved slightly: "Heh." ”

"Such a handsome guy, he's actually a facial paralysis, hey. Xiaoyun sighed, she looked at the mathematical symbols on the blackboard, and said: "The BSD conjecture is classified as number theory, but it actually involves many other branches of mathematics, and we all know that the sufficient and necessary condition to prove that the elliptic curve has an infinite number of rational points is L(E,1)=0, that is, the BSD conjecture is proved." But it's really hard. ”

As he spoke, Xiao Yun erased half of the blackboard with the blackboard, and then wrote a stereotyped Q on the blackboard, representing the set of rational numbers.

Xiaoyun wrote more and more, and she said as she wrote: "E(Q) is an Albert group, in 1922, Moder proved that the group E(Q) is finitely generated, and more than sixty years later, Faltins proved Model's conjecture, and a few years later, Wiles proved Fermat's theorem...... Connecting these histories of mathematics, we can find that the way great mathematicians solve number theory problems is often not by means of number theory, with the exception of one person, Professor Shen. ”

Zhao Tian: "Hey, Xiaoyun, what are you mentioning Professor Shen to do? Professor Shen doesn't love us, it's Sister Ye Zi who loves us." ”

Xiao Yun smirked like a nymphomaniac: "Because Professor Shen is handsome." ”

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

"Well, yes, but it's hard. Xiao Yun tilted his head and fell into deep thought.

It seems a bit overwhelming to study how three undergraduates can prove the BSD conjecture.

BSD conjectures that if one of the millennial problems of mathematics is solved by a few undergraduates of the School of Mathematics of Yan University, then it will still be done?

Crunch.

The door opened, and in came a woman, beautiful and intelligent, wise and erudite, kind and generous, a mother of a child.

"Sister Ye Zi is good!"

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

"Hello. Ou Ye smiled, and she said to Zhao Tian: "Xiao Zhao, does anyone in our club want to go to Columbia University for an exchange year? ”

Zhao Tian: "Of course there is, I'll count it later." ”

Oye studied at Columbia University and then went to Princeton for his PhD.

Shen Qi's performance in Princeton was too dazzling, and to some extent, Ou Ye was under his aura when he was studying for a PhD at Princeton, so that it overshadowed Ou Ye's own light.

But Ou Ye still has a good reputation in Columbia, and Columbia also buys her account.

"Okay, good work. Ou Ye said, she glanced at the blackboard, a little surprised: "Huh, you guys are working on the BSD conjecture?"