They're already in university, and the primary school system is only just starting out?

Seeing his serious expression, Gu Ming assumed he had concerns about writing the paper and immediately asked considerately, "Chen Lin, have you... never had any experience with academic paper writing before?"

"Yes," Chen Lin answered honestly.

"It's okay, it's normal!" Gu Ming waved his hand. "I happen to have some free time today, so I'll give you a systematic explanation of what a qualified undergraduate thesis should consist of."

As he spoke, he naturally entered "teaching mode" and began to explain at length.

"First, the title should be concise and clear, summarizing the core content of your entire article."

"Then comes the abstract and keywords. The abstract is a few hundred words that clearly states the research purpose, methods, and conclusions of your paper. The keywords are three to five of the most essential words."

"Next comes the table of contents and the main body. The main body is the core of your paper, and it should include the following sections: introduction, theoretical review, research design, results analysis, conclusions, and future prospects..."

Finally, there are the references, acknowledgments, and appendices.

Gu Ming explained things in a simple and clear way, but Chen Lin, who was a liberal arts student, still felt confused and his head was buzzing when he listened to these unfamiliar professional terms.

However, he still tried his best to remember every point Gu Ming made, and nodded from time to time to show that he was listening attentively.

Gu Ming spoke for over ten minutes straight, then took a sip of water to moisten his throat before summarizing, "That's the general framework. You don't need to rush; you can spend some time brainstorming a topic for your graduation thesis. If you have any preliminary ideas, feel free to come and discuss them with me anytime."

He looked at Chen Lin, his tone softening, full of encouragement: "There's no rush. We can decide on the topic and general direction of our thesis before the semester starts. Normally, according to school regulations, undergraduate students need to write a thesis proposal and defend it. However, your situation is special, and I have absolute confidence in your abilities. Once we discuss and agree, I'll waive the thesis proposal stage for you!"

Hearing Professor Gu's thoughtful and considerate arrangements, Chen Lin felt somewhat embarrassed.

He scratched his head, a hint of embarrassment in his voice: "Um... Professor Gu."

"Um?"

"Actually... I've already decided on the topic." Chen Lin paused, then added, "Moreover, I've almost finished the related theoretical research, as well as the derivation and proof process."

Gu Ming's smile froze instantly.

"?"

A brief silence fell over the meeting room; the air seemed to stand still.

Several seconds passed before Gu Ming seemed to snap out of his petrified state. He blinked and asked incredulously, "You... what's your topic?"

Chen Lin cleared his throat and answered clearly, word by word:

"How to efficiently solve the high-dimensional Monge-Ampère equation numerically to calculate the boundary of the data manifold in a large-scale generative model."

"..."

Gu Ming was stunned again, and he even wondered if there was something wrong with his ears.

He suddenly stood up from the chair, and because of the sudden movement, the chair legs scraped against the ground with a loud "screech".

"The Monge-Ampère equation?!" Gu Ming's voice rose several decibels, his face filled with disbelief. "Chen Lin, do you know that even the world's top applied mathematicians haven't figured out this problem, let alone undergraduates!"

He paced around the table a couple of times, seemingly trying to calm his excitement, before turning around and looking at Chen Lin with an unprecedentedly serious tone, reminding him: "Scientific research isn't like taking an exam or doing a test; it's not something you can solve just by mastering the knowledge! It requires extensive literature review, countless attempts, and even a bit of inspiration and luck!"

Seeing Gu Ming's tense and alarmed appearance, Chen Lin knew that his words had frightened him, so he quickly waved his hand and explained, "Professor Gu, please don't get agitated, that's not what I meant."

He smiled somewhat helplessly: "I didn't say that I had completely solved the problem. I just... just followed the line of thought of my predecessors and pushed the research on this problem forward a little bit."

Hearing Chen Lin's words, Gu Ming breathed a slight sigh of relief, finally returning to his original position.

But then he came to his senses and realized that his first reaction to Chen Lin's bold words was not to deny their possibility one hundred percent and without hesitation!

In other words, just a moment ago, a thought actually flashed through his subconscious: "What if he actually did it?"

He then realized that Chen Lin's almost overwhelming and terrifying talent and unfathomable mathematical level, displayed in the past few days, had unknowingly and completely overturned his understanding of the word "genius" that he had built up over the past twenty years on his academic career.

So much so that now, even when Chen Lin says something as far-fetched as solving a world-class problem, my first subconscious reaction is not to question him, but a complex emotion mixed with shock and anticipation.

Gu Ming took a deep breath, forcibly suppressing the turmoil in his heart, and regained his composure as a professor.

He looked at Chen Lin and sincerely suggested, "Since you already have your own research results, that's perfect. I suggest you don't worry about the formatting for now, and first write a first draft of your research process and conclusions, which is the core part of the paper."

He paused, then added, "After you've finished writing it, send it to me directly. I'll check the content for any problems. If there aren't any, then the rest—the abstract, introduction, references, etc.—are just simple formatting tasks, and I'll guide you through them step by step."

This suggestion was exactly what Chen Lin wanted to hear.

What bothers him most right now are those tedious paper formats and academic formulas, but he is very confident about the core content.

Chen Lin nodded immediately and readily agreed: "Okay, no problem. I'll take about two weeks to write the first draft."

"Two weeks?" Gu Ming's eyes twitched again upon hearing this.

However, this time Gu Ming did not show any surprise. He simply nodded calmly with an encouraging smile on his face: "Okay, there's no rush. Just manage your own pace. Once you're done, send it to my email."

"Okay, thank you, Professor Gu."

……

……

After leaving the Mathematical Sciences office building, Chen Lin did not go straight home, but instead turned and headed towards the library.

The academic atmosphere at Yannan University is still excellent.

Although it's summer vacation and most students have already left campus, the library is still packed with students preparing for postgraduate entrance exams. Rows of seats are crowded with people, and everywhere you look, you see figures engrossed in their studies.

Even when some seats are empty, the tables are piled high with towers of various review materials and professional books, forcefully declaring the "sovereignty" of the place.

Sometimes Chen Lin couldn't help but wonder, what exactly are these people after?

He saw that there was more than one seat, and the dust on the pile of books on it was thick, clearly indicating that the owner had not been there for a long time. However, the seats were still occupied, deterring people who really wanted to sit down and study.

However, Chen Lin did not look for a seat.

He tiptoed into the study area, quickly scanning the crowd, and soon spotted a familiar figure near a window.

Shen Yan was sitting there, her long, smooth black hair casually draped over her shoulders. She lowered her head slightly, staring intently at the laptop screen in front of her, her fair fingers occasionally sliding across the touchpad, as if she were studying some difficult problem.

A smile appeared on Chen Lin's face. He slowed his pace and quietly walked up behind her.

He leaned forward slightly, his gaze landing on Shen Yan's computer screen.

The screen displays a PDF document entirely in English.

Operator spectral theory...

A series of technical terms came into view, but before Chen Lin could take a closer look, the passive effect of "Little Mathematician" in his mind had already been triggered.

Almost instantly, the proof problem about the spectral radius of bounded linear operators that Shen Yan was struggling to figure out became clear in his eyes.

In fact, he even came up with more concise and ingenious proof paths than the method presented in the paper more than once.

He was about to speak, in that casual tone, to give Shen Yan some pointers.

But just as his mouth was slightly open, before he could utter a sound...

Shen Yan, who had been intently staring at the screen, suddenly turned around as if she had eyes in the back of her head.

Her clear, watery eyes met Chen Lin's gaze.

Then, in a soft but clear voice, she slowly said:

"You can explain your thought process to me, but don't just tell me the answer directly."

Upon hearing Shen Yan's words, Chen Lin's prepared "friendly reminder" got stuck in his throat.

He gave an awkward smile and touched his nose.

Good grief, I guess I was predicted.

Shen Yan didn't seem to notice his momentary embarrassment. She simply picked up the thick book from the seat next to her, placed it on a pile of books, and then gestured with her eyes to the empty seat.

Chen Lin didn't stand on ceremony; he pulled out a chair and sat down quietly.

The library was so quiet that you could hear the soft whooshing of the air conditioner vents, mixed with a faint smell of ink and paper from the pages, which calmed your mind without you even realizing it.

He turned his head and lowered his voice, asking, "Are you going to tell me now, or do you want to think about it some more?"

Shen Yan looked at him with her clear eyes almost without hesitation and replied in a soft voice, "Just say it."

She is quite aware of her own abilities.

She's been stuck on this problem for almost an hour, trying all sorts of approaches, but still can't find a breakthrough.

She knew very well that this was no longer a problem that could be solved by spending more time; it was a hard gap in knowledge reserves and thinking.

Instead of wasting time getting bogged down in this, why not just ask the "helper" next to you for advice?

"OK."

Chen Lin nodded and naturally took the ballpoint pen and a piece of draft paper from her hand, which he had written a few lines of deductions on but could not continue.

His pen fell on the paper, not writing any specific calculation steps, but rather lines of concise and clear "hints".

[1. Core Tool: Gelfand-Mazur Theorem]

【2. Auxiliary formula: Spectral radius formula r(T) = lim (n→∞)||T^n||^(1/n)】

[3. Solution/Tip: Try constructing a specific auxiliary operator and using its relationship with the spectral radius of the original operator to complete the proof.]

He wrote only these three lines, then stopped writing and gently pushed the draft paper back to Shen Yan.

Shen Yan whispered "thank you" to him, then lowered her head to study again.

Chen Lin smiled, briefly admiring Shen Yan's beautiful profile as she lowered her head in thought, before going about his own business.

He took his laptop out of his backpack, turned it on, and instantly the whole world was just him.

Instead of rushing to start writing, he first opened his browser and searched for several papers on differential geometry on CNKI and some foreign academic paper websites.

He doesn't need to understand the specific content of these papers.

What he needs to learn is how these mature academic papers organize those cold, abstract mathematical theories into rigorous, clear, and logical language and present them to the reader.

Chen Lin compared the examples he found online with his own 35 pages of draft paper filled with calculations and deductions on the table and carefully reviewed them.

Half an hour later, a clear writing framework had been formed in his mind.

He closed all irrelevant web pages and created a new blank Word document.

He took a deep breath and began typing on the keyboard.

Thanks to his foundation in Chinese Language and Literature, writing a long article was not a difficult task for him. At least in terms of language organization and logical structure, he did not feel completely clueless or inadequate.

Furthermore, the core content of this paper is entirely the result of his research over the past week or so; every formula and every deduction has long been deeply imprinted in his mind.

He had absolute confidence in his calculations and deductions.

Every number and symbol on those thirty-five pages of draft paper was so concise and precise, filled with a pure mathematical beauty.

The only drawback is that this kind of beauty is too slender.

What Chen Lin needs to do now is to enrich its connotation with language, turning it from a pure theory into a paper that can be understood by readers, or at least some readers.

The cursor blinked at the top of the document. After a moment's thought, Chen Lin typed the title of the paper.

[Tentative Title: The "Slicing-Filtering-Convex Hull" Solution of the High-Dimensional Monge-Ampere Equation and Its Theoretical Framework for Manifold Boundary Identification in Generative Model Data]

With the title finalized, he started a new line and began to build the framework of the main text.

[1. Problem Definition and Equation Form...]

2. Numerical Analysis Background and Convergence Criteria

The convergence and stability of high-dimensional MA–SBVP have been established by several pillars: ...

[3. A potential-curvature discriminant for boundary identification: ...]

The keyboard clicks are crisp and rhythmic.

Chen Lin entered a state of focus, and his ideas for the paper became clearer and clearer.