How It All Made Sense!

The core part of the "Strong BSD Conjecture Proof" is displayed on the large screen:

analytic rank≥2, Gauss conjecture in quadratic... h(D)>1/55(ln∣D∣)∏(1-2√p/p+1)... L(E, s)∏p(1-ap/p^s+p/p^2s)^-1→L(E, s)=c(s-1)^r+High-Order Items!

Academician Su Wenxie said, "There's one point I can't explain: under the condition of analytic rank ≥ 2, the distribution of rational points on the Elliptic Curve doesn't necessarily follow your proof. You've gone around in circles, and it looks fancy, but it seems to have returned to the original problem, namely that points with rational coordinates do not satisfy the Local-Global Principle. So Professor Ou, I think your solution needs further examination in certain details."

Upon hearing Academician Su's words, the other members of the Tsinghua University Mathematics Team nodded in agreement. Their eyes were fixed intently on Ou Ye, a dance of belief and skepticism, affirmation and denial flying side by side.

Xiao Huang felt a chill run down his spine and a sense of tension; the question posed by Academician Su was both tricky and crucial.

Yes, Teacher Ou, how do you explain that the distribution of rational points on Elliptic Curve absolutely follows your predetermined scheme?

Xiao Huang has certainly studied the "Strong BSD Conjecture Proof," but studying it doesn't necessarily mean he has a thorough understanding of it.

Explaining the Strong BSD Conjecture Proof requires an extremely high level of mathematical ability.

Although Zhao Tian, Xiao Yun, and Zeng Han are the authors of the "Strong BSD Conjecture Proof," these three students cannot fully explain every detail of the paper. Well, they're just lying around doing nothing; they can just sit back and call the experts "666" (a Chinese internet slang term for being awesome).

This mathematics seminar between Yenching University and Tsinghua University seemed to have turned into a graduation defense for Ou Ye's research group.

As students who have participated in graduation defenses know, the examiners initially assume that you will pass the defense and receive your degree and graduation certificate.

Based on this assumption, and according to your graduation thesis, the reviewers will ask several key questions for you to answer and explain.

Normally, as long as students diligently conduct experiments, write their theses conscientiously, and clearly articulate the key issues during the defense, they can graduate smoothly.

Academician Su was like a kind yet strict mentor. He first assumed that the Strong BSD Conjecture Proof was true, and then led his team to explain it. During the explanation process, Academician Su's Team had some doubts.

During a real graduation defense, the reviewers will also have doubts about the student's thesis. The main points of doubt are: Is your data fabricated? Is it plagiarized? Was it ghostwritten?

As for the doubts expressed by Academician Su's Team, Ou Ye's understanding is that they probably just don't understand them.

History of Mathematics, there are numerous examples of established mathematicians who couldn't understand other people's papers.

The paper written by Norwegian mathematical genius Abel was incomprehensible to Gauss and Cauchy, who were contemporaries of his.

Gauss and Cauchy were already established masters at the time, and they indeed couldn't understand Abel's paper.

More than a century later, Abel's paper was proven to be true by the Mathematics Community, Abelian group and Abel geometry became classics in the History of Mathematics, included in textbooks for students to study.

The fact that Gauss and Cauchy in the 19th century couldn't understand Abel's paper cannot be entirely blamed on these two giants. Abel himself also bears some responsibility.

At that time, young Abel was extremely poor, so poor that he couldn't even afford to eat and was hungry all the time.

Abel's original paper contained more than 10,000 words, but due to poverty, he condensed his manuscript into 6 pages, then printed several copies and sent them to authoritative mathematicians such as Gauss and Cauchy.

Gauss and Cauchy couldn't understand Abel's condensed 6-page paper; the bigwigs unanimously thought Abel was talking nonsense.

Some people say that Abel should have just sent his manuscript of over ten thousand words to Gauss or Cauchy, wouldn't that have solved the problem?

But Abel did not do so, for reasons unknown.

Or perhaps it was because at the time, document delivery fees were charged per page, and the delivery fee itself was more expensive.

Poverty makes people withdrawn.

The impoverished Abel died in his early twenties, looking haggard and forlorn.

This illustrates the unwritten rule in the Mathematics Community: if a senior figure declares your paper valid, then it is valid.

If the expert says your paper is utter nonsense, then you should rewrite it.

Going against a powerful figure will never end well.

This rule still applies in the Mathematics Community today.

Fortunately, Ou Ye was not short of money. Her manuscript, which started at 42 pages, was eventually expanded into a 405-page paper. She could afford the printing, publication, and courier fees.

Back then, Abel appeared rather self-conscious when faced with the doubts of powerful figures.

On one hand, it's because he's poor; on the other hand, it might be related to the fact that Abel is Aries.

The wealthy Virgo Ou Ye, stood up and walked to the blackboard in the lecture hall. "Let me explain Academician Su's doubts."

Everyone looked at the blackboard.

Ou Ye picked up the chalk and started writing and drawing.

She first drew a standard Right triangle with sides of length 3, 4, and 5.

This is clearly Pythagoras triangle.

This classic triangle implies a theorem: with hypotenuse d=5, there is no Right triangle with integer side lengths and area of 5.

"This is... a high school student's geometric approach?" Xiao Huang thought to himself. Could explaining the Millennium Prize Problem -level BSD Conjecture require starting with high school mathematics?

The Tsinghua University team was also puzzled; they remained silent and continued to monitor the situation.

Next, Ou Ye drew a Right triangle with side lengths of 3/2, 20/3, and 41/6.

This triangle also implies a theorem: there exists a Right triangle with rational side lengths and an area of 5.

A rational number is the ratio of an integer a to a positive integer b; this is a topic taught in secondary school mathematics.

Can drawing two Right triangle, which even a middle school student could understand, really answer the questions raised by Academician Su's Team?

No, it's not possible.

Ou Ye then shifted her focus, extending the concept from two Right triangle to write an algebraic proof.

Brush!

Academician Su suddenly stood up, his body trembling slightly, his eyes gleaming.

The simpler, the more complex!

The more complex, the simpler!

The BSD Conjecture is buried deep within extremely advanced mathematics, but we can explain BSD Conjecture by starting with some of the most basic mathematical principles.

The endless problem of rational points on Elliptic Curve, when unraveled, surprisingly conforms to the classical geometric framework of ancient Greece!

Two Right triangle, and an algebraic proof.

That's enough!

Academician Su, in a sudden burst of youthful exuberance, rushed to Ou Ye's side, grasped her hand tightly, and exclaimed excitedly, "If I hear the Way in the morning, I can die content in the evening. I understand, I get it! Thank you, Ou Ye!"

"Old Master Su, I should thank you," Ou Ye said sincerely.

"Hahahaha!" Academician Su laughed heartily, then said to his team, "Men, keep working! We need to complete the explanation of the <Strong BSD Conjecture Proof> within two weeks!"

The younger ones looked at each other in bewilderment; the exchange of blows between masters was indeed profound.

Whether the younger ones understand or not, Academician Su certainly does.

Under the guidance of Academician Su, the Tsinghua University Mathematics team is working intensively to advance the interpretation of the Strong BSD Conjecture Proof.

Academician Su and Ou Ye, who had only met a few times before, became close friends despite their age difference.

Shen Qi's nationwide speaking tour has reached his hometown Nangang City.

Nangang City is the cultural, political, commercial, and academic center of South China.

The city has nearly 100 universities, ranking among the top five in the country in terms of the number of universities.

However, Nangang City actually only has two "Double First-Class" universities.

Shen Qi's speeches in Nangang City were mainly arranged at two Double First-Class universities.

At Sun Yat-sen University, Shen Qi held three lectures at this top-tier university: one for students, one for faculty and staff, and the third was a special study session for Party members and cadres.

Universities are doing everything they can to qualify for the "Double First-Class" initiative, which offers numerous benefits, including abundant resources, funding, and preferential policies.

Looking at the world, it is rare to see Fields Medal and Nobel laureates giving lectures at Fields Medal -tier universities, let alone holding Honorary Professor or Visiting Professor professorships at such universities.

The president of Sun Yat-sen University extended an invitation to Shen Qi to become Visiting Professor at the university, Shen Qi declined.

The president of Sun Yat-sen University was quite disappointed. If Shen Qi could become Visiting Professor at their university, it would be a huge honor.

Over the past five years, Yanshan University has had the highest college entrance examination admission scores in the country, with its average admission score exceeding that of Shuimu University by 15 points.

In some provinces, even with a perfect score of 750 on the college entrance exam, students who score 700 still can't get into Peking University.

Especially for science-related majors, particularly mathematics and physics, if students fail to get admitted through the special admissions program and want to be admitted to the Big Mathematics Department through the national college entrance examination, they need to score more than 30 points higher than Yanshan University's minimum admission score.

It's quite absurd to think about it; the students admitted to the Big Mathematics Department and the School of Physics at Yenching University are basically the top science students in their respective provinces' college entrance examinations.

Yenching University's college entrance examination admission scores have been rising year by year, and the qualifications for admission to Yenching University through competitions have become increasingly stringent. Even international students who want to study at Yenching University must undergo extremely rigorous tests.

Previously, it was a battle between two universities in the capital, but now, Yenching University has become the top university in China.

The students recruited by Yanda University are all freaks, abnormally strong.

One reason for this is that Yenching University's overall strength is constantly improving, including core areas such as scientific research and teaching, where it has indeed achieved first place in China and is among the world's best.

On the other hand, it may be related to individuals, such as the influence and appeal of Shen Qi, who works at Yenching University. At least that's what the president of Sun Yat-sen University thinks.

The principal said warmly, "Academician Shen, thank you so much for giving your first lecture in Nangang at our Sun Yat-sen University. I very much hope that you can become a lifetime Honorary Professor at Sun Yat-sen University -sen University, or even Visiting Professor with a term. We have already set up the highest-level chair for you, tentatively named 'Yixian University Chair Professor.' What do you think, Academician Shen?"

Shen Qi smiled and asked, "How many years will you hire me?"

The principal sensed a glimmer of hope for success and said, "I hope it will last ten thousand years."

"Haha!" Shen Qi laughed heartily. He said tactfully, "I do want to contribute to my hometown, but there are many ways to do so."

"I see. Well then, I respect Academician Shen's wishes." The principal could only conclude that Sun Yat-sen University's prestige was not high enough to attract Academician Shen's favor.

Sun Yat-sen University is a centrally administered university at the vice-ministerial level. Shen Qi genuinely wanted to contribute to his hometown. His contribution to Sun Yat-sen University served both the central government and the local community, given that the Sun Yat-sen University's campus is located in Nangang City.

"As a native of Nangang, my dream was to get into Sun Yat-sen University, but things didn't go as planned, and I ended up going to Yenching University." Shen Qi sighed as he looked back on the past. In the eyes of the people of Nangang, the area north of Nangang is the North, and native Nangang people will travel to the North but rarely settle down there.

The claim that people from Nangang eat Fujianese people is a complete rumor.

Cannibalism is a criminal offense. People in Nangang generally understand the law, and they would never dare to eat others.

But the fact remains that most people in Nangang are born and die there.

Shen Qi has lived in the north for many years and started his own family.

Scientists are mobile, and Shen Qi, returning to his hometown, decided to contribute to it. "My major was mathematics, and mathematics is what I care about most. I also care about mathematics at Sun Yat-sen University. Mathematics at Sun Yat-sen University has been developed into a world-class discipline, and I want to do my part for Sun Yat-sen University."