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

Pan's voice echoed in the conference room, and Chen Lin could sense his professionalism and meticulousness.

But for Chen Lin, the non-mathematical content in the design plan was too unfamiliar, and he could hardly understand it.

He was completely baffled by some of the technical terms used in engineering and materials.

He even started to miss Sun Yu a little.

In the previous two consultations, it was all thanks to Sun Yu, the translator, who diligently translated the complex engineering problems into pure mathematical language that he could understand.

Now that this intermediary is gone, he can only pretend to listen attentively with boredom, but in reality his mind is wandering and he begins to secretly observe the people in the conference room.

The conference room was quite large, and besides General Manager Peng and himself, there were more than a dozen engineers sitting there.

There were a few young people who looked like they had just graduated less than two years ago. They still had a bit of a student vibe on their faces, sat up straight, and had curiosity and a hint of nervousness in their eyes.

There were also a few around thirty years old, with faint dark circles under their eyes, slightly loose shirt collars, and an air of weariness unique to those repeatedly battered by projects and KPIs.

The remaining two or three are around Pan's age. Hmm, their generally receding hairlines, gleaming with wisdom, reveal their wealth of experience and exude an aura of strength!

"...The above is the background situation we are currently facing in our project."

It took Engineer Pan a full fifteen minutes to finally finish introducing the project. He put down the laser pointer and looked at General Manager Peng.

Mr. Peng understood immediately and smiled as he continued, "Chen Lin may not be very familiar with the specific details of the engineering design. Sun Yu also reported to me before that Chen Lin's habit is to have our engineers abstract the problems encountered in the plan into simple mathematical models and problems."

His gaze shifted and landed on Engineer Pan.

Engineer Pan nodded immediately and waved to a young employee sitting in the corner: "Xiao Ji, come here."

He then introduced Chen Lin: "This is Xiao Ji, a new recruit we made two years ago. He's a graduate student from a 985 university majoring in mathematics, and he has a very solid foundation in mathematics."

The young man named "Xiao Ji" immediately stood up. He looked only a few years older than Chen Lin, wore half-rimmed glasses, and appeared quite refined. He nervously adjusted his glasses, took a deep breath, and continued the conversation.

From the moment he opened his mouth, you could tell he was quite capable.

"Chen, our current solution for this project treats the caisson as a rigid body, mainly considering its six degrees of freedom motion under wave action, including sway, pitch, heave, roll, pitch, and bow roll. The wave load calculation adopts a method combining the Morrison equation based on linear potential flow theory and diffraction/radiation theory."

"To accurately solve the dynamic response of the caisson under wave action, it is necessary to establish fluid-structure interaction equations. This involves solving the coupled system of the Laplace equation describing the velocity potential of the fluid and the Newton-Euler equation describing the rigid body motion of the caisson."

"Our team currently uses industry-standard software, employing the three-dimensional frequency domain boundary element method, or BEM, to solve for hydrodynamic coefficients, such as added mass, radiation damping, wave excitation force, and torque. These coefficients are then substituted into the rigid body motion equations to solve for the motion response amplitude operators for each degree of freedom."

"The problem we encountered," Xiao Ji said, speaking slowly but clearly, "was that, under specific design wave conditions, the caisson's pitch response amplitude calculated using software differed significantly from the team's prediction based on simplified empirical formulas and model test data."

As soon as he finished speaking, the oldest engineer with the thinnest hair added, "The software results are too large. This means that with this design, the caisson's rotation angle may be too large, affecting its stability and the safety of the superstructure. We need your help to provide a new, computationally efficient, and numerically stable method to verify or replace the core calculation process for solving the hydrodynamic coefficients in the existing commercial software, especially focusing on the coupling effect of the pitch degree of freedom."

Okay, I understand now.

As Chen Lin listened to Xiao Ji and the old engineer's explanations, and combined this with the rows of mathematical formulas and parameters marked next to the structural diagrams on the projection screen, the title of "Little Mathematician" was instantly and passively activated.

Those concepts—Laplace's equation, boundary element method, coupling effect—were crystal clear in his mind, and all the logical chains automatically connected and reorganized. Almost the instant the other person finished speaking, a completely new solution had already fully materialized in his mind.

"I understand." Chen Lin nodded and gestured for Engineer Pan to switch the projection screen back to the page introducing the calculation scheme.

He looked at the screen and asked, "I didn't bring any paper or pen, so I need to use yours."

"I've had the administration prepare everything." As if he had expected this, General Manager Peng gestured directly to his assistant waiting outside the door.

Soon, a stack of pristine white A4 draft paper and several different colored pens were presented to Chen Lin. At the same time, a staff member skillfully switched the projector's signal source to a high-definition camera pointed at the white paper beside Chen Lin.

In this way, everyone in the conference room could see the formula derivation and calculation process he wrote on the draft paper.

Chen Lin picked up a black pen, tested the tip, and looked up to ask, "May I explain the new method?"

"..."

The entire conference room fell into an eerie silence.

Everyone was stunned.

How much time has passed since I finished explaining the question? A minute? Or two minutes?

So you've come up with a solution already?

The young engineers' faces were filled with astonishment and doubt, and they couldn't help but whisper among themselves.

"So fast? Is this a scam?"

"Never even heard of him. Where did President Peng find such a remarkable person?"

"This is outrageous! Our team has been working on this plan for several nights in a row..."

On the contrary, Engineer Pan and General Manager Peng, who had already heard Sun Yu's detailed report on Chen Lin's first consultation, remained the most composed.

"We can start anytime." General Peng said with an encouraging smile.

Chen Lin nodded and said no more. He lowered his head, his pen tip landing on the white paper, writing smoothly as he explained in a calm and even tone.

"The alternative I proposed can be called the 'analytical-numerical hybrid method'."

"The core idea is to bypass the computational bottleneck of large-scale boundary element discretization and solving large dense linear systems that you are currently using. By leveraging the regularity of the caisson geometry, that is, the rectangle, and the symmetry of the problem, we can seek semi-analytical solutions or perform dimensionality reduction analytical processing."

His pen danced across the paper, producing lines of mathematical formulas and symbols that appeared clearly on the screen before everyone's eyes.

"First, the heave-pitch decoupling approximation. For the aspect ratio and draft of your caisson, at the target wave frequency, although the heave and pitch motions are coupled, we can use the two-dimensional slice theory of the bottom of the caisson to make a preliminary decoupling estimate."

He fluently wrote an analytical expression based on a two-dimensional source-sink distribution.

"This formula can be used to quickly estimate the main components of heave-added mass and pitch-added mass, namely the diagonal terms, with sufficient accuracy to serve as a benchmark."

"Secondly, the handling of key coupling terms, which is also the core issue." Chen Lin's voice was unhurried, as if he were stating a very simple common sense. "The key to the problem lies in the heave-swell-roll coupling added mass and coupled radiation damping. Here, I propose an analytical transformation."

"We map the fluid velocity potential perturbation induced by the pitching motion of the three-dimensional caisson surface to an equivalent two-dimensional water tank problem of varying depth."

"Then, by using complex functions and conformal transformation techniques, specifically a variant of the Zhukovsky transform, this complex boundary problem is transformed into an integral equation on the standard half-plane."

"This integral equation has a highly structured kernel function. Its form can be precisely expressed using a combination of first and second type complete elliptic integrals."

"Third, the closed-form solution of the coupling coefficient."

At this point, Chen Lin changed the subject and wrote down a long string of seemingly extremely complex formulas on the paper.

"Through the above transformation and identification, we can directly give analytical closed-form expressions for the heave-roll coupling added mass, namely (A_{35}), and the coupled radiation damping (B_{35})! This expression depends only on the caisson geometry, fluid density, gravitational acceleration, and wave frequency. The calculation is extremely fast and stable, completely avoiding the errors caused by large-scale numerical discretization and solution."

"Fourth, correction of wave excitation force..."

"Fifth, solving the equations of motion. We combine the exact analytical solutions of the key coupling coefficients we obtained with the other coefficients calculated by your software and substitute them into the rigid body motion equations. Since the core uncertainty is replaced by the exact analytical solution, the solution of the entire system of equations becomes very stable and reliable."

During Chen Lin's explanation, the atmosphere in the conference room underwent a wonderful change.

At first, all the engineers listened attentively, and the experienced senior engineers even nodded approvingly.

But gradually, when Chen Lin uttered terms like "Zhukovsky transform" and "complete elliptic integral," the young engineers' eyes began to look blank, their brows furrowed, and their expressions were as if they were listening to gibberish.

In the end, when Chen Lin finished writing that complex closed-form solution, it seemed that only Engineer Pan and the old engineer who had spoken could still barely keep up with his train of thought in the entire conference room.

After finishing the last step, Chen Lin put down his pen and summarized: "The analytical solution is essentially precise, eliminating the errors and instabilities caused by numerical discretization, integration, and linear solutions. The analytical formula I provided can be easily implemented in programming and independently verified."

"I was learning Python recently, and I remember one of the libraries has a ready-made elliptic integral toolkit that you can call directly. You can look it up later."

Engineer Pan took a deep breath, turned around, looked at his subordinates behind him, and asked in a deep voice, "Did everyone understand?"

The young employees were jolted awake, as if from a dream.

In the conference room, everyone looked at each other, their faces showing hesitation and embarrassment, and finally they all silently lowered their heads.

General Manager Peng was not surprised at all. He smiled, stood up, and clapped his hands: "Alright, that's enough for today. Engineer Pan, take this document written by Chen back and organize a team to study it thoroughly. Then, find the programmers in the department to do the programming verification."

"call--"

Chen Lin stretched lazily. He glanced at his phone and asked President Peng, "Is that all for today? I bought my return ticket; I'll be leaving in about two hours."

"No rush," Mr. Peng said with a smile, waving his hand. "Come to my office for a chat, have some tea and rest. If Engineer Pan and the others encounter any minor problems during their research, they can take the time to ask you. Then, I'll personally drive you to the high-speed rail station."

Chen Lin thought about it and agreed, so he nodded and followed President Peng out of the conference room.

Behind him, Engineer Pan was leading a group of engineers, who were carefully gathered around the few sheets of draft paper covered with formulas, looking at them and having a heated discussion.

As soon as Chen Lin stepped into President Peng's office, he felt an atmosphere of luxury.

The office is spacious, with a sophisticated and elegant design. One entire wall is a huge floor-to-ceiling window, offering a panoramic view of the bustling city.

The furniture was made of heavy solid wood, and two modern paintings that I couldn't understand but felt were very impressive hung on the wall. There was also a faint, comforting scent of incense in the air.

Chen Lin thought of the luxury sports car that General Manager Peng had picked him up in and wondered to himself, "This design institute looks like it's only of average size, so how come the boss seems so rich?"

"Please make yourself at home." General Manager Peng gestured to the leather sofa in the reception area, then walked to the exquisite tea cabinet, took out some tea leaves from an antique tea caddy, and began to boil water to prepare tea. "Try my Da Hong Pao."

Chen Lin sat down on the sofa, took out his phone, and first sent a WeChat message to his mother, Lin Xiaoqi: "I won't be home for dinner tonight."

He calculated the time; if he went back from Shanghai now and took the bus home, it would be past seven o'clock at the earliest. He planned to just buy something at the FamilyMart near his home to tide him over.

After a while, Chen Lin was browsing the Enki Love Forum when a post caught his attention: "If your best friend suddenly won 500 million, would you be happy for him or jealous?"

He clicked in with great interest and received a variety of replies.

Some sages said, "Of course I'm happy, I might even get a free meal," while others frankly admitted, "I'm happy on the surface, but I'm secretly incredibly jealous." Still others, including conspiracy theorists, analyzed, "This money will probably ruin our friendship."

Chen Lin pursed his lips, his fingers flying across the screen as he left a reply below.

"I can only marvel, 'Can this thing really work?'"

As soon as I clicked send, a rich and mellow aroma of tea wafted over and entered my nostrils.

Mr. Peng carried over an exquisite set of purple clay teaware and placed a small aroma-smelling cup steadily on the tea table in front of Chen Lin. The tea soup was orange-red in color, clear and bright, clearly not an ordinary product.

"Thank you, Mr. Peng." Chen Lin immediately locked his phone screen and sat up straight.

President Peng sat down on the sofa opposite him, poured himself a cup, then picked up the teacup, looked at Chen Lin, and his face showed a lingering sense of amazement.

"Chen, to be honest," he said with emotion, "when Xiao Sun told me about your high level of skill, I was actually a little skeptical. But seeing it with my own eyes today, I understand what it means to say that seeing is believing. Honestly, it's breathtaking."

General Peng's eyes were full of admiration, without a trace of feigned politeness: "From my layman's perspective, the way you solved those problems can't be simply described as impressive. You're a true genius."

Chen Lin simply smiled, picked up his teacup, and slowly replied with a joke.

"Mr. Peng, you flatter me," he shrugged, his tone relaxed. "No matter how talented I am, I'm still working for you to make money."

"Ha ha!"

Upon hearing this, General Peng was taken aback at first, then burst into hearty laughter, his eyes filled with even more admiration.

He enjoys dealing with intelligent people, especially young people who are intelligent, capable, humble, and relaxed.

General Peng smiled and shook his head, then continued, "Speaking of which, I'm reminded of the suggestion I gave you last time."

His smile faded slightly, his expression turned serious, and he leaned forward slightly, looking into Chen Lin's eyes as he asked:

"Have you thought it through? About switching to the math department?"