Arrangement
The Computer Science processor operates at high speed. L(E, s) is Taylor expanded at s=1, and the order of the expansion is equivalent to the Hasselt-Wey rank r(E) of the Elliptic Curve E.
Rational points on Elliptic Curve dance a mysterious dance under the Computer Science's command; seemingly chaotic, they are actually moving to a rhythm.
A simple Elliptic Curve of the form y^2=x^3+ax+b also has infinitely many rational points, and there are infinitely many such Elliptic Curve.
The conditions for a modulo curve were strictly defined by Zhao Tian and two other students, because in 1999, Kazuya Kato proved that all Elliptic Curve over the rational number field are modulo curves.
This is a grand ball between numbers and symbols, where the prime number p makes its appearance. They spin and leap in the ocean of data, counting the number of rational points on certain Elliptic Curve, which is transformed into counting the number of solutions modulo the prime number p.
The Computer Science screen's background is black, as deep as the universe. The dancers in the darkness are a group of white elves. Under the pressure of ordp(L'(E,1)/CE)=ordp(#Sha(E)), the ps are almost out of control. Their breathing becomes rapid, and their dance steps are chaotic and close to madness.
Watching the constantly changing numbers and symbols on the screen, Xiao Yun was quite fascinated. "This is the beauty of mathematics, this is the power of mathematics, the mysteries of the universe are hidden here."
"Hmm." Zeng Han nodded in agreement.
Verification progress: 2%.
Even with high-performance Computer Science, it takes a week to verify the theoretical assumptions of Ou Ye's construction.
In Xiao Yun and Zeng Han's view, the mathematical world composed of a vast number of Elliptic Curve and equations possesses unparalleled beauty and power.
Perhaps because his prefrontal cortex wasn't as developed as his younger schoolmates', Zhao Tian only experienced limited beauty and power, and mostly suffered from headaches caused by complex data processing.
"Don't you guys find it a bit strange that the one who gave Sister Yezi help and support wasn't Professor Shen, but Teacher Zhou Yu'an?" Zhao Tian said, changing the subject while waiting for the data to be processed.
Xiao Yun thought for a moment and said, "Perhaps Professor Shen secretly arranged for Teacher Zhou to do this?"
Zhao Tian shook his head. "That doesn't make sense. Why doesn't Professor Shen step forward himself? Imagine if Professor Shen and Sister Yezi jointly proved the BSD Conjecture, then Sister Yezi would be the Fields Medal winner, because Professor Shen has already won the Fields Medal. The Fields Medal rules are different from the Nobel Prize; you can only win the Fields Medal once."
Zeng Han retorted, "Your logic is flawed. Do you think Sister Yezi needs Professor Shen to help her lie down?"
Zhao Tian waved his hands repeatedly. "Sister Yezi certainly doesn't need Professor Shen to guide her! I'm just curious, why is Professor Shen so uninterested in the BSD Conjecture?"
Xiao Yun said, "Don't try to guess what the big shots are thinking. You might understand when you become a big shot yourself. Personally, I think Professor Shen is actually very concerned about Sister Yezi's BSD research project. The reason he deliberately avoids the BSD Conjecture is that he doesn't want his shadow to be too much associated with Sister Yezi. Let's not speculate about their marital affairs. The Fields Medal has an age limit of 40. Unless there's another special case like Andrew Wiles winning over the age limit, Sister Yezi only has two more chances to win the Fields Medal. She doesn't say anything, but she really longs for it."
Zhao Tian seemed to have realized something significant. "The judging process for the Fields Medal is unpredictable. Professor Shen might be making a strategic move. He got Teacher Zhou involved in the BSD Conjecture project as a double insurance policy? Once we prove the BSD Conjecture, Sister Yezi and Teacher Zhou can join forces to compete for the Fields Medal, securing first place and aiming for second."
Xiao Yun disagreed. "According to the Fields Medal judging convention, if the same conjecture is proven by multiple people, only one person can receive the Fields Medal. For example, Fermat's Last Theorem was actually proven by the academic partners Andrew Wiles and Richard Taylor, but the Fields Medal was ultimately awarded to Andrew Wiles. Richard Taylor can only win the Fields Medal by relying on new projects and new research results."
Zhao Tian's expression shifted uncertainly. "If that's the case, then Teacher Zhou shouldn't have interfered with our BSD project. What if he snatched Sister Yezi's Fields Medal away?"
"If Teacher Zhou was instructed by Professor Shen to get involved in Sister Yezi's BSD Conjecture project, then I think it's very likely that Teacher Zhou is Professor Shen's true love." Xiao Yun suddenly got excited. She felt that her guess might not be unreliable. Teacher Zhou has a car, a house, status, and identity. He's over thirty and still not married. Why is that?
"True love my foot! You girls have been reading too many gay novels, haven't you? How could Teacher Zhou be gay? Even if Teacher Zhou were gay, the upright Professor Shen could never be gay. The country and the people wouldn't allow him to be gay. It's lunchtime. Zeng Han, you stay here. Xiao Yun and I are going out to eat. I'll bring you some takeout." Zhao Tian pulled Xiao Yun away from the center to eat outside.
The weather is getting hotter and hotter, abnormally so.
The capital city experienced several consecutive days with temperatures reaching 40 degrees Celsius. Zhao Tian, Xiao Yun, and Zeng Han lost their desire to go out for meals and ordered takeout for all three meals. Apart from sleeping, the three of them spent all their time in the Computer Science room of Shen Qi Research Center.
The Computer Science ran continuously, accompanied by the humming of the air conditioner.
The computer verification of the BSD Conjecture proof scheme has entered a critical stage. Zhou Yu'an occasionally comes to the Computer Science room to inquire about the situation, while Shen Qi, the director of the Shen Qi Research Center, and Ou Ye, the academic leader of the project, have never been to the Computer Science room.
Ou Ye didn't come to the Computer Science lab because she was hospitalized. Her mind was preoccupied with the Computer Science calculation results, and she communicated with her three students on her phone every day.
Shen Qi hasn't been to the Computer Science lab lately because he hasn't even been to the center. Shen Qi recent haunts include Academician Shen's villa, Yanjing University People's Hospital, and the kindergarten.
The highest outdoor temperature in the capital reached a historic high of 41 degrees Celsius, according to the weather forecast. The meteorological observatory issued a red high-temperature warning, reminding citizens to take precautions against the heat.
The physics team at Shen Qi Research Center measured the highest outdoor temperature at 44 degrees Celsius. This is in the north! What does 44 degrees mean? It's unbearably hot; even dogs would die from the heat.
On these unusually sweltering days, delivery drivers have to pay at least an extra 15 yuan for each order.
Zhao Tian, Xiao Yun, and Zeng Han, the three math enthusiasts, didn't even bother going downstairs to pick up their takeout. The Computer Science room was piled high with all sorts of food, and the open food packaging emitted a complex odor. Various brands of instant coffee were rapidly dwindling at a rate of one packet per hour.
At noon that day, the blazing sun suddenly filled the sky with dark clouds, and lightning bolts more than five meters wide flashed repeatedly, followed by rolling thunder.
Lightning flashed, thunder roared, and torrential rain poured down; the sweltering week of hellish heat finally came to an end.
Raindrops pattered against the glass of the Computer Science room; the Computer Science, which had been working continuously for a week, finally produced their calculation results.
"This is..." Zhao Tian, Xiao Yun, and Zeng Han stared wide-eyed at the screen, their hearts filled with excitement and confusion.