Chapter 112 - 79: Graduation Thesis First Draft
He paused, then added, "Once you’ve finished writing, send it directly to me. I’ll take a look first to see if there are any problems with the content. If not, then the rest—the abstract, introduction, references, and all that—is just simple formatting work. I can walk you through it step-by-step then."
This proposal was exactly what Chen Lin had been hoping for.
The thing giving him the biggest headache right now was the tedious paper formatting and rigid academic conventions. As for the core content, he was completely confident.
Chen Lin nodded immediately and readily agreed, "Okay, no problem. I’ll spend about two weeks getting the first draft done."
"Two weeks?" Hearing this, the corner of Gu Ming’s eye couldn’t help but twitch again.
This time, however, Gu Ming didn’t show any surprise. He just gave a subtle nod, an encouraging smile on his face. "That’s fine. There’s no rush, so just work at your own pace. When it’s ready, send it directly to my email."
"Okay, thank you, Professor Gu."
...
After leaving the School of Mathematics building, Chen Lin didn’t head straight home. Instead, he turned and walked toward the library.
The academic atmosphere at Yannan University was truly something else.
Even though it was the middle of summer vacation and most students had left campus, the library was still packed to the brim with the grad school entrance exam army. The rows of seats were a sea of bobbing heads; everywhere you looked, there were figures hunched over, studying intently.
Even some of the unoccupied seats had desks piled high with small mountains—towers constructed from various review materials and textbooks—aggressively declaring "sovereignty" over the spot.
Sometimes Chen Lin couldn’t help but wonder, ’What are these people even after?’
He noticed more than one seat where the mountain of books was covered in a thick layer of dust. The owner clearly hadn’t been there in a long time, yet the spot remained claimed, daunting anyone who actually wanted to sit down and study.
But Chen Lin wasn’t looking for a seat.
He walked quietly into the study area, his eyes quickly scanning the crowd. Soon, at a spot by the window, he found a familiar figure.
Shen Yan was sitting there, her long, dark, smooth hair casually draped over her shoulders. Her head was slightly lowered, her expression focused as she stared at the laptop screen in front of her. Her fair fingers would occasionally slide across the trackpad, as if she were wrestling with a difficult problem.
A smile touched Chen Lin’s lips. He lightened his steps, silently walking up behind her.
He leaned forward slightly, his gaze falling on Shen Yan’s computer screen.
Displayed on the screen was a PDF document entirely in English.
Operator spectrum theory...
A series of technical terms entered his vision. Before Chen Lin could get a closer look, the passive effect of "Little Mathematician" had already triggered in his mind.
In an instant, the proof problem concerning the spectral radius of a bounded linear operator, which Shen Yan was struggling with, became crystal clear in his eyes.
He even saw, more than once, pathways to a proof that were more concise and elegant than the method presented in the paper.
He was about to speak up and give Shen Yan a casual hint.
But in the very instant he parted his lips, before any sound could escape...
Shen Yan, who had been focused intently on the screen, suddenly turned her head as if she had eyes in the back of it.
Her eyes, as clear as water, met Chen Lin’s gaze.
Then, in a soft but clear voice, she said slowly,
"You can explain the approach to me, but don’t just tell me the answer."
Hearing Shen Yan’s words, the "friendly tip" Chen Lin had prepared got stuck in his throat.
He gave an awkward smile and rubbed his nose.
’Man, she read me like a book.’
Shen Yan didn’t seem to notice his momentary awkwardness. She just naturally picked up the thick book on the seat next to her, placed it on a nearby pile, and then gestured with her eyes toward the now-empty chair.
Chen Lin didn’t stand on ceremony. He pulled out the chair and sat down without a sound.
The library was so quiet you could hear the faint WHIR of the air conditioning vents, mixed with the faint scent of ink and paper from the book pages, which had a naturally calming effect.
He turned his head and asked in a low voice, "Should I explain it now, or do you want to think about it a little longer?"
Shen Yan barely hesitated. Her clear eyes looked at him, and she replied in a whisper, "Just tell me."
She was well aware of her own limits.
She had been stuck on this problem for nearly an hour, trying every possible approach without finding a breakthrough.
She knew very well that this was no longer a problem that could be solved with a little more time. It was a hard gap in her knowledge base and way of thinking.
Rather than waste time getting bogged down on it, she might as well just ask the "human cheat code" sitting next to her.
"Alright."
Chen Lin nodded, naturally taking the gel pen and a sheet of scratch paper from her side—a sheet where she had written a few lines of deduction before getting stuck.
His pen tip touched the paper, but he didn’t write out any specific calculation steps. Instead, he wrote a few concise, clear "hints."
[1. Core Tool: Gelfand-Mazur Theorem]
[2. Auxiliary Formula: Spectral radius formula r(T) = lim (n→∞) ||T^n||^(1/n)]
[3. Key Insight: Try to construct a specific auxiliary operator and use its relationship with the spectral radius of the original operator to complete the proof.]
He only wrote those three lines before stopping and gently pushing the scratch paper back in front of Shen Yan.
Shen Yan whispered a "thank you" to him, then lowered her head to study it again.
Chen Lin smiled. After briefly admiring the lovely view of Shen Yan’s profile as she pondered, he turned to his own work.
He took his laptop out of his backpack, turned it on, and in an instant, the world narrowed to just himself.
He didn’t rush to start writing. First, he opened his browser and searched for several papers in the field of Differential Geometry on CNKI and other foreign academic journal websites.
He didn’t need to understand the specific content of these papers.
What he needed to learn was how these polished academic papers organized cold, abstract mathematical theories into rigorous, clear, and logical language to present to the reader.
Chen Lin compared the examples he found online, then laid out his thirty-five pages of scratch paper filled with calculations and deductions on the desk and looked them over carefully.
Half an hour later, a clear writing framework had already formed in his mind.
He closed all irrelevant web pages and created a new, blank Word document.
Taking a deep breath, his fingers began to tap on the keyboard.
Thanks to the foundation he had built in the Department of Chinese Language and Literature, writing a long article was not a difficult task for him. At least when it came to organizing language and logical structure, he didn’t feel completely clueless or powerless.
Furthermore, the core content of this paper was the complete result of his research over the past week or so. Every formula, every deduction, was already deeply imprinted in his mind.
He had absolute confidence in his calculations and deductions.
Every number, every symbol on those thirty-five pages of scratch paper was concise and precise, the lines filled with a kind of pure mathematical beauty.
The only flaw was that this beauty was too skeletal.
And what Chen Lin had to do now was to enrich its substance with language, transforming it from pure theory into a paper that could be understood by readers—well, at least some readers.
The cursor blinked at the top of the document. After a moment of thought, Chen Lin typed out the title of the paper.
[Title (provisional): A "Slice-Filter-Convex Hull" Solution for High-Dimensional Monge-Ampère Equations and its Theoretical Framework for Boundary Identification of Data Manifolds in Generative Models]
With the title decided, he started a new line and began to build the skeleton of the main text.
[1. Problem Formulation and Equation Form...]
[2. Numerical-Analytical Background and Convergence BenchmarksThe convergence and stability of high-dimensional MA-SBVP have several pillars: ...]
[3. A "Potential-Curvature" Discriminant for Boundary Identification: ...]
The sound of the keyboard was crisp and rhythmic.
Chen Lin entered a state of focus, the ideas for his paper growing clearer and clearer.