The Goddess Had Arrived

Compared to the overly immature Shen Qi Quantum Society, the Ou Ye Computer Society is much more serious.

According to Yenching University's regulations on student association management, each student association on campus must have at least one advisor.

Ou Ye is the advisor of the Ou Ye Computer Society, and he provides most of the club's activity funding.

Although it sounds like a Computer Science club, the headquarters of the Ou Ye Computer Society is actually located in the School of Mathematical Sciences.

At the end of the corridor on the first floor of the Mathematics Department, a room with a sign that read "Ou Ye Computer Society" was located. Inside, a young man was playing cards with a young woman.

"Sister Yezi gave our club another 20,000 yuan, and she gave us a total of 80,000 yuan this year." The young man's Zhao Tian, and he is the president of the Ou Ye Computer Society.

"Professor Shen generously sponsored two thousand, so Sister Yezi must be in charge of the finances in their family." The young woman made a "I want more" gesture, indicating she wanted another card.

"Xiao Yun, it's already 8 PM, do you still want more?" Zhao Tian said, then dealt another card to Xiao Yun.

This card is the Ace of Hearts, Xiao Yun has 21 points.

"Blackjack is a non-linear combinatorics game, as Sister Yezi mentioned," Xiao Yun smiled sweetly. She added, "Senior, we need to work harder! The Shen Qi Math Society swept the top three places in the National Undergraduate Mathematics Competition and the National Undergraduate Mathematical Modeling Competition again. Professor Shen is very happy; he gave the Shen Qi Math Society 50,000 yuan reward and even wrote recommendation letters for its members to study at Princeton."

"Xiao Yun, you mustn't waver! We're Sister Yezi 'Sister Yezi people in life and in death." Zhao Tian flipped over a card for himself, a 7, bringing his total to 21: "The college math competition and modeling competition are nothing. Even if Professor Shen won't write us recommendation letters, Sister Yezi will definitely. Have you applied for your Hong Kong and Macau travel permit yet?"

"It's done," Xiao Yun nodded.

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

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

Zhao Tian looked at the boy and asked, "Zeng Han, are you coming with us?"

Zeng Han replied, "If you want to die, go to the casino. You want to die, but I don't."

"Zeng Han, you know we're not going to Macau for money, we're just here to study mathematical problems," Zhao Tian earnestly advised. This junior of Zeng Han was a mathematical genius.

Zeng Han stared intently at the blackboard and said, "Go ahead and die. Every year during Qingming Festival, I will burn paper money for you."

"Hey, you brat!" Zhao Tian threw down the playing cards in his hand, went over to Zeng Han, and observed Zeng Han's work on the blackboard.

First, there is a Right triangle with side lengths of 3, 4, and 5.

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

This is actually Pythagoras Right triangle, which involves an ancient mathematical problem: given a positive integer d, does there exist a right Right triangle with rational side length and an area of exactly d?

Using high school mathematics, it can be proved that there exists a Right triangle with rational side length and area d, provided that the equation y² = x³ - d²x has rational solutions for x and y ≠ 0.

Using university-level mathematics for further interpretation, this equation has rational solutions for x and y if and only if d is the area of a right Right triangle with rational side lengths. The discriminant of this equation, Δ = -16[4(-d²)³] = 64d⁶, is not equal to 0, so the graph of this equation is an Elliptic Curve.

Connecting high school and university mathematics knowledge—that is, finding which integers d can form the area of a right Right triangle with rational side lengths—is equivalent to finding rational points on a certain Elliptic Curve.

This is the problem that British scholars Birch and Swinnerton-Dyer sought to solve throughout their lives; it is known in academia as the BSD Conjecture.

"Zeng Han, I fully support your research on the BSD Conjecture. Actually, Xiao Yun 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 had already been accepted into the graduate program at Peking University's Big Mathematics Department. Since he had already been accepted into graduate school, Zhao Tian had plenty of time to organize and carry out the club activities of the Ou Ye Computer Society.

"Oh," Zeng Han snorted expressionlessly.

Xiao Yun, a junior in college, sidled up to Zeng Han and said, "Zeng Han, you're always so serious. Give me a smile!"

Zeng Han's lips twitched slightly. "Heh."

"Such a handsome young man, and he's expressionless, sigh." Xiao Yun sighed, looking at the blackboard full of mathematical symbols, and said, "The 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 for Elliptic Curve to have infinitely many rational points is L(E,1)=0, which proves the BSD Conjecture. However, this is really difficult."

As she was talking, Xiao Yun erased half of the blackboard with the eraser, and then wrote a rigid Q on the blackboard to represent the set of rational numbers.

Xiao Yun wrote more and more, saying as she wrote, "E(Q) is an Albe group. In 1922, Model proved that the group E(Q) is finitely generated. More than sixty years later, Faltings proved Mordell Conjecture. A few years later, Wiles proved Fermat's Last Theorem... By connecting these History of Mathematics, we can find that the great mathematicians often solved number theory problems not through number theory methods, with only one exception: Professor Shen."

Zhao Tian: "Hey, Xiao Yun, why are you bringing up Professor Shen again? Professor Shen doesn't love us, it's Sister Yezi who loves us."

Xiao Yun grinned like a lovesick fool. "Because Professor Shen is handsome."

"Don't interrupt," Zeng Han said to Zhao Tian, displeased. She then added, "Senior, I agree with your point. Proving the BSD Conjecture definitely requires Elliptic Curve and Group Theory. Sister Yezi also said so. The biggest problem now is how to calculate the rank, or whether the rank can be arbitrarily large? I think we should find clues in this area."

"Yes, that's right, but it's so difficult." Xiao Yun tilted her head, lost in thought.

It seems a bit presumptuous of three undergraduates to be seriously researching how to prove the BSD Conjecture.

The BSD Conjecture, one of the Millennium Prize Problem in mathematics, what if a few undergraduate students from the Big Mathematics Department of Yenching University could solve it?

Creak.

The door opened, and a woman entered. She was beautiful and intelligent, wise and learned, kind and generous, and a mother.

Hello, Sister Yezi Ye!

Three students stood at attention; their club's goddess had arrived.

"Hello," Ou Ye smiled and said to Zhao Tian, "Xiao Zhao, does anyone in our club want to go on exchange to Columbia University for a year? There's one spot available."

Zhao Tian: "Of course there are. I'll go and tally it up in a bit."

Ou Ye earned her master's degree from Columbia University and then went on to pursue her doctorate at Princeton.

Shen Qi's performance at Princeton was so dazzling that, to some extent, Ou Ye was overshadowed by his brilliance while pursuing her doctorate at Princeton.

But Ou Ye has a good reputation at Columbia University, and the university respects her.

"Okay, thank you for your hard work," Ou Ye said, glancing at the blackboard with a hint of surprise. "Huh? You guys are researching the BSD Conjecture?"