Getting on the Computer
After reviewing the manuscript, Zhou Yu'an said, "I think your solution is generally sound. The only point of contention is that some algebraic processes might be meaningless. However, if we consider it from another perspective, meaninglessness can also be meaningful, and meaning can be meaningless. Macroscopic meaninglessness, when applied to the microscopic level, might have profound implications, even becoming a standard. Microscopic meaning, when extended to the macroscopic level, might be worthless. The BSD Conjecture involves a philosophical question, namely the Local-Global Principle. It seems that Ou Ye's understanding has been elevated."
Zhou Yu'an's philosophically insightful comments seemed to open a new door for the three students.
"Hmm... philosophy, I get it." Zhao Tian frowned in thought, then suddenly realized.
"You have a high level of comprehension," Zhou Yu'an said with considerable admiration. He then asked, "Zhao Tian, what do you think philosophy is?"
Zhao Tian suddenly became serious. "Philosophy is like a security guard at the gate of Yenching University."
Zhou Yu'an: "Hmm?"
"The security guard at our school gate has three thought-provoking philosophical sayings: Who are you? Where do you come from? Where are you going?" Zhao Tian was filled with respect; he suddenly understood.
Zhao Tian continued, "I think this is philosophy. Philosophy is everywhere; it's lofty and unattainable, yet it permeates every corner of society. And perhaps the pinnacle of mathematics is philosophy itself. In fact, isn't every mathematical formula a philosophical proposition? That's why the BSD Conjecture is so important; it's not just a mathematical problem, but it has the potential to change the way humanity thinks."
"That's the logic, but your understanding is still at a very basic level." Zhou Yu'an saw several computers in the room. For students, these computers were top-of-the-line, but for scientific research, they were far too rudimentary. "Are you guys planning to use these beat-up computers to verify your Sister Yezi's four-step proof?"
Zhao Tian explained, "Teacher Zhou, these computers are pretty good; Sister Yezi bought them for us out of her own pocket."
"So, Ou Ye's political awareness is too low. Compared to her husband, she's Big Idiot," Zhou Yu'an said helplessly.
"Your Sister Yezi is quite wealthy; everyone in the School of Mathematical Sciences knows that she's the richest woman at Peking University. However, even if she has more money than she can spend, Ou Ye should avoid using her own money to buy research equipment. She made a political mistake. As a full professor and researcher at Peking University, she shouldn't have started a research project on the BSD Conjecture without establishing a project or applying for national research funding."
"To put it bluntly, what Ou Ye is doing gives some excuses to those with ulterior motives. Imagine if Ou Ye had funded the project out of his own pocket, without going through the school or the government, and actually proved the BSD Conjecture, that would be individual heroism, that would be making a mistake."
"We must be clear that every scientific research achievement in public universities and research institutions is obtained with the strong support of the Party and the State."
"Shen Qi did a great job in this regard; he didn't leave any loopholes. Even a basic research project on Diophantine equation worth 20,000 yuan at Shen Qi Research Center would have to go through the National Natural Science Foundation of China." Zhou Yu'an was quite worried about Ou Ye. He asked, "By the way, have you three outstanding students joined the Party?"
"No... I haven't joined the Party." After hearing Zhou Yu'an's words, the three students felt both a sense of political urgency and a vague sense of tension.
Zhou Yu'an shook his head with a wry smile, "Well, Ou Ye, this Non-Party Affiliated Person, is leading three non-partisan students to conduct research on a major mathematical problem without the approval of the Party and the state. That's unacceptable, unacceptable... I strongly suggest that your Strong BSD Conjecture project be approved immediately and that you apply for research funding. Even applying for basic theoretical research funding within Yanda University would be acceptable. I will discuss this with Ou Ye. And you three shouldn't use these old computers anymore. How long will it take to verify anything with these old computers? Starting tomorrow, the three of you will come to the Shen Qi Research Center. I will provide you with the highest-performance Computer Science in the Center Mathematics Department."
"That's great, thank you, Teacher Zhou!" The students felt the warmth of the organization. Teacher Zhou is a veteran Party member, and veteran Party members are indeed highly conscious and thoughtful.
So, under the Party's arrangement, Zhao Tian, Xiao Yun, and Zeng Han came to the Shen Qi Research Center building, where they used the center's high-performance advanced Computer Science to verify the Elliptic Curve set by Ou Ye.
The BSD Conjecture has an inextricable connection with Computer Science.
In the early 1960s, Computer Science were in their early stages of development, with only a handful in the world, mainly housed in a few important universities.
British mathematicians Birch and Swinnerton-Dyer, professors at Cambridge University, used Cambridge EDSAC, one of the most powerful Computer Science in the world at the time, to calculate and deduce possible solutions to polynomial equations.
Two mathematicians navigated the ocean of data, astutely identifying a new pattern from massive amounts of Computer Science data, thus proposing one of the Millennium Prize Problem in the History of Mathematics, the BSD Conjecture.
Throughout the thousands of years of History of Mathematics, most people who propose conjectures are not the ones who prove them.
Many contemporary professional mathematicians admire Euclid the most among the ancient mathematicians. Euclid derived the vast and rigorous Euclidean geometry system using five common-sense axioms.
Birch and Swinnerton-Dale used Computer Science in the 20th century to propose the BSD Conjecture.
Their contribution to proving this conjecture was actually not very effective.
I bet you'll get the certificate, and if you do, you'll be awesome; if you do, I'll be awesome too... that's roughly the pattern.
Of course, there are historical reasons for this as well.
Before 1995, before Andrew Wiles proved Fermat's Last Theorem, the international Mathematics Community had not even figured out whether the BSD Conjecture was meaningful.
Most of the valid contributions to the proof of the BSD Conjecture came after 1995.
The contemporary international Mathematics Community has a profound understanding of the mathematical and even philosophical significance of the BSD Conjecture. This conjecture is certainly meaningful, with far-reaching implications, reaching to the stars and the sea.
The international Mathematics Community eagerly anticipates that one or more outstanding mathematicians will complete the proof of the BSD Conjecture.
Shen Qi is widely recognized by the international Mathematics Community as the most promising mathematician to prove the BSD Conjecture; however, Shen Qi has never formally launched an attempt to prove the BSD Conjecture.
Shen Qi's wife has made substantial research achievements on this conjecture.
Similar to when Birch and Swinnerton-Dale first proposed the BSD Conjecture, Ou Ye's three students adopted a hands-on approach, first using brute force to eliminate Elliptic Curve that did not possess the Kolyvagin theorem, Gross-Zagier theorem, or Shafarevich-Tate group order characteristics.
This operation isn't difficult, it's just quite time-consuming.
After adding the characteristic condition of the Hasse-Weil L-function, Zhao Tian couldn't help but shudder. "Adding just one more basic condition increases the computational load by a factor of 10 to the power of 12... Luckily, Teacher Zhou lent us this high-performance Computer Science, otherwise, even after I graduated with my doctorate, I still wouldn't be able to finish calculating Sister Yezi's manuscript..."