Chapter 32: All of These Relate to Missile Trajectory Optimization

In the tiered lecture hall of the University of Hong Kong, sunlight filtered through the window panes, casting a glow over Lin Ran’s manuscript.

"Ladies and gentlemen, the roll call just now was simply to get to know you all."

On his first night in Hong Kong, Lin Ran had attended a banquet hosted by local elites, and by the next day, he had begun his seminar without a moment’s rest.

After the roll call, combining the surname "Chen" with the photographs of a young Chen Jingrun he had discovered online back in 2020, and noting the man’s starkly incongruous presence among the fifty students in the room, Lin Ran was certain: the person sent by the mainland was Chen Jingrun.

He felt a sense of relief. The mainland authorities had not underestimated him; they had sent a true genius. Lin Ran had suspected as much—if the mainland truly valued him, it was highly probable that they would send Chen Jingrun, as he was the only candidate suitable for this moment.

"Very well, all fifty of you are here. My time in Hong Kong is limited, so before arriving, I took the liberty of asking the University of Hong Kong to prepare a written entrance examination. This was to set a certain threshold, ensuring that everyone could keep up with the coursework. After all, without a baseline, I would be unable to cover the material I intend to present in a progressive manner over these two months. For those without a foundation in mathematics, my lectures will be quite challenging. Now, since you are all talented students with the necessary background, I will skip over the basics of calculus, linear algebra, and differential equations. We shall begin directly with functional analysis and function spaces. Furthermore, I should inform you that the theme of this seminar is: 'On the Extremal Properties of Functional Spaces under Symmetric Group Actions: An Exploration from Harmonic Analysis to Algebraic Geometry'..."

Li Shaoyuan had always considered himself to have a modest talent for mathematics, but he soon found that even as he listened intently, he began to fall behind, eventually losing track of what Professor Lin was talking about entirely. He glanced at his seatmate, who was listening with deep focus. He remembered from the roll call that this fellow was named Chen Dehui.

In Hong Kong during this era, the poor—especially refugees who had fled from the mainland—typically wore cheap, breathable but coarse cotton clothing from local factories, usually in plain, monotonous colors. The wealthy, however, preferred the trendy Hawaiian shirts popular in America, preferably with vibrant patterns. Chen Dehui was wearing a simple cotton short-sleeve shirt, while Li Shaoyuan was dressed in a Hawaiian shirt.

"Hey, can you actually understand what the professor is saying?" Li Shaoyuan whispered.

Chen Jingrun, currently under the alias Chen Dehui, replied in clumsy Cantonese, "Of course."

He then ignored Li Shaoyuan.

Li Shaoyuan poked him with his pen again. "What is Professor Lin talking about?"

"He is using the orthogonality of Fourier series as an example to teach us the concepts of norms and inner products," Chen Jingrun said, as if it were the most obvious thing in the world.

Clearly, functional analysis was a breeze for him; he had long since mastered the fundamental concepts. However, the specific examples and perspectives Lin Ran chose gave him a sense of sudden enlightenment, and he mused to himself that the man was truly a master of his craft. The entire teaching style was like a heavy sword without a sharp edge—sophisticated yet unadorned.

However, even Chen Jingrun could sense the urgency in Lin Ran’s delivery. His lectures were clear, but they were also rapid; once he finished explaining a point, he would press forward without checking if everyone had understood. Chen Jingrun had attended lectures and taught students back in the mainland, but he had never encountered such a style.

Li Shaoyuan, meanwhile, was beginning to doubt his own reality. He found it hard to believe that his seatmate—a man whose clothing and demeanor screamed "poverty"—could actually follow the lecture.

When the class ended, he felt a grudging admiration for the man. "Could you explain it to me? I’m willing to pay you." He reached into his pocket and pulled out a handful of Hong Kong dollars.

Chen Jingrun was tempted. But considering he still had to return home to transcribe these notes, deliver them to a designated drop-off point, and have them sent back to the mainland, he had to refuse. The amount offered was equivalent to a month’s salary back home.

When Li Shaoyuan returned home, his younger sister, Li Huiling—who went by the English name Helen and was also a student at HKU—rushed to take his bag. "Brother, how did it go? Did you manage to get Professor Lin’s autograph for me?"

Li Shaoyuan handed her the inaugural issue of *New Advances in Mathematics*, which contained Lin Ran’s paper proving Fermat’s Last Theorem. "Here, I asked Professor Lin to sign the flyleaf for you."

Li Huiling opened it to see the bold characters "Lin Ran" written across the page and shrieked with excitement. "Thank you, brother! You really are the best! Now those jealous girls will be green with envy! Did you ask him to come to our home for dinner like I told you?"

Li Shaoyuan shook his head. "No. It’s only the first day; what’s the rush?"

Li Shaoyuan and Li Huiling belonged to the Li family—not the Li Ka-shing family, but the family of Li Koon-chun, the founder of the Bank of East Asia. For them, securing a marriage alliance with Lin Ran would be an excellent choice. Old-money families like the Li Koon-chun clan were well aware of the prestige associated with being Professor Horkheimer’s final student, and they understood the influence of the Frankfurt School across America, England, and the entire Western world. Horkheimer himself had publicly acknowledged this student during an interview.

Whether it was Lin Ran himself or the Frankfurt School he was backed by, it was enough to make the old-money families of Hong Kong covetous. That was the weight of his reputation.

However, the seminar’s attendance dwindled: fifty students on the first day, forty-seven on the second, and forty on the third. After a week, only twenty remained.

Li Shaoyuan, despite considering himself a genius, could not keep up. Because he couldn't understand the content, sitting there for a full day was pure torture. By the time Lin Ran reached the study of symmetry and extrema, Li Shaoyuan felt as if he were listening to a foreign language.

Even Chen Jingrun found it strenuous, as the material had reached the core of the calculus of variations. On the surface, it was a study of symmetry and extrema, but at its heart, it was the calculus of variations. Lin Ran used string vibration to frame potential disturbances in aerospace engineering; he used the mathematical laws of nature—symmetry—to frame Noether’s Theorem; he used the motion of a pendulum to draw an analogy to missile trajectories. The students in the room found it all profoundly obscure.

The Hong Kong media reported on the seminar extensively. They did not criticize Lin Ran; instead, they praised him, remarking that a master is a master indeed. When you are prestigious enough, your shortcomings are not seen as failures, but as signs of your immense capability. The world is a strange place.

By the third week, as the lecture moved into extremal problems combining the calculus of variations with group theory, Lin Ran seized an opportunity. When thirteen of the remaining fourteen students went to the restroom, leaving only the man under the alias Chen Dehui sitting at his desk furiously taking notes, Lin Ran leaned over and whispered softly:

"All of this is actually related to the optimization of intercontinental ballistic missiles."