The Demon King is unfathomable

Chapter 390 The Epoch-Making Equation
The Magic Science Laboratory is as lively as ever today.

The apprentices, personally selected by His Highness Colin, spontaneously gathered here as soon as get out of class ended, filling the air with youthful and enthusiastic energy.

of course.

There was no shortage of whispered complaints here.

After all, geniuses are few and far between; most people are just using their ordinary wisdom to do what ordinary people can do.

"By Saint Sith, this is too difficult!" Jamie, the carpenter's son, sighed as he looked at a sheet of paper filled with arcs and straight lines. "'Constructing a regular heptadecagon with a compass and straightedge'... It looks so simple, why can't I do it?"

He wasn't the only one troubled by this problem.

Beside him, the watchmaker's daughter, Ram, also looked distressed, resting her chin on her hand and muttering to herself.

"...How can a pedestrian cross all seven bridges in one go without repeating any or missing any, and finally return to the starting point?"

Jamie, who was measuring on the paper with a ruler, paused for a moment and asked instinctively.

Is this some kind of riddle?

“No, this is a thought-provoking question assigned by His Highness Colin,” Ram shook his head. “He told me to study it in my spare time and said I could try to connect it with geometry problems.”

"Hmm... Let me think about it, it seems to have some interest." Jamie scratched his head and muttered to himself as he buried himself back in his draft paper.

Ram stretched and leaned back in his chair.

"Keep it up... Oh right, does your problem about the regular heptadecagon have any requirements regarding rulers and compasses? Is it only allowed to use a ruler, or is either one fine?"

Jamie shook his head.

"You may use a compass and a ruler, but the ruler must be unmarked and you must not make any marks on it."

Ram: "A ruler without markings? That's a strange question..."

The two of them communicated in low voices.

Although their individual problems remain unresolved, they have already developed ideas for solutions.

Not far away, Ophelia was also pondering her own problem, only hers was more abstract—

As numbers increase in size, does the proportion of prime numbers in the natural number system decrease? If so, please provide a proof.

Saint Sis, this was the first time she had ever heard of such a strange question!

Is researching this stuff actually useful?!
The Royal Academy of Arts in St. John's, where she previously studied, did teach the concept of prime numbers, but only as a kind of "harmonious" and "sacred" numerical symbol. Some priests, however, believe that they contain a code left to the world by Saint Sis.

However, it will not affect the casting of spells by extraordinary individuals, nor will it suddenly make a weak magician stronger.

Just as she was fretting over this seemingly useless problem, a familiar figure suddenly caught her eye out of the corner of her eye.

That person was none other than Ilana!

The girl, who was usually calm and composed, was now nervously clutching a notebook in her hands, her cheeks flushed an unusual red.

She bit her lower lip lightly, took several deep breaths, and finally took a step towards Prince Colin.

etc--

What's happening here? !

Alarm bells rang in Ophia's mind.

That look might be unfamiliar to the bookworms of Xuebang, but she, coming from the Holy City, knew all too well what that expression meant!

After all, she encounters these presumptuous guys every now and then...

Thinking about what Ilana was about to do, Ophia felt a slight pang in her heart, and all the mathematical symbols in her mind vanished like smoke in an instant.

Could it be... that she's going to express... her feelings here?! In front of everyone?!

This seemingly absurd thought exploded in Ophia's mind like a thunderbolt. Immediately afterward, a complex mix of panic, jealousy, and curiosity seized her heart, throwing her, who had been calm and composed, into disarray.

She stood up almost instinctively, holding the incomprehensible book "Advanced Mathematics," and pretended to casually walk past in the aisle, but actually quietly approached the desk, her ears burning red.

It's not that I care—

She believed that Prince Colin was not such a casual person and would certainly not easily agree to inexplicable requests.

She was simply standing on the position of a lady from the Holy City, wanting to see what that girl from the province of Pierce planned to do to His Highness the Prince!
However, Ilana's first words stunned Ophia, whose internal alarm bells were ringing.

"tutor……"

The delicate voice trembled slightly, yet her clear eyes burned with an unprecedented, unwavering determination.

"Do you remember the 'path optimization equation' I mentioned to you before?"

"I might... have really found it!"

Path optimization equation?

Ophia stood there dumbfounded, her panic instantly extinguished by the complex and mysterious mathematical concepts.

However, soon, a sense of curiosity arose in her heart.

She certainly knew the path optimization equation, which seemed to be an unfinished project by the laboratory's former owner, Mr. James Walley.

only--

How could a mere Iron-level apprentice solve a problem that even a proper mentor would struggle with?
Not so much...

Ophia swallowed hard, hiding behind her "Advanced Mathematics" textbook in a self-deceptive manner, her eyes fixed on them, filled with curiosity.

Ilana was unaware of her presence; her entire being was completely absorbed in the great discovery she was about to make.

She carefully unfolded the notebook in her hand in front of Prince Colin, and her voice, which had been trembling with excitement, gradually became clear and confident.

"The variational method you taught me is like a key. It made me realize that we can treat the total cost of the entire 'path' as ​​a solvable function. And I discovered that as long as every point on a path satisfies a specific equilibrium condition, the total cost S of this path will reach an extreme value..."

"Let's get straight to the point, Ilana," Luo Yan said succinctly. "There's no need to repeat these minor details."

"Okay, Your Highness."

Ilana nodded slightly, her speaking speed suddenly changing as she went straight from the opening remarks to the main topic.

Ophia was completely confused.

Even though she tried her best to listen, those profound concepts were like obscure incantations, preventing her from deciphering their mysteries.

However, she could read expressions.

As Ilana recounted her story, Prince Colin's eyes, which always held a hint of a lazy smile, gradually brightened.

It was a pure gaze.

Like an artist, looking with satisfaction at the artwork he has created with his own hands.

Ophia suddenly felt a little jealous.

She could have done it herself... and she was the one who came first.

"So, if my deduction is correct... this equation should look like this."

Ilana finally finished speaking.

She raised her head, looking at her most respected mentor with a mixture of trepidation and anticipation, awaiting the prince's evaluation.

A brief silence fell over the desk.

Looking at the beautiful yet complex differential equation on the manuscript paper, Luo Yan was filled with surprise and also couldn't help but feel a surge of emotions.

Although he has influenced two worlds, the sense of accomplishment is still not as great as watching the sapling he planted grow into a towering tree and bear abundant fruit.

It feels so good.

After savoring the pleasant feeling for a moment, Luo Yan looked up again at Ilana standing in front of his desk and said with a smile.

"A truly excellent derivation. To be honest, your application of the calculus of variations is probably already beyond my reach..."

Ilana lowered her head in fear.

"Professor, you're too modest..."

“No, I’m not being modest. I always say what I think,” Luo Yan smiled and said casually. “After all, I’m not a professional scholar. There are some things I know how to do, but I may not know why I do them… But I’m very glad that I met you. Your talent has filled many gaps in my knowledge.”

This is the truth.

He certainly knew the Euler-Lagrange equations, but if he were to write out the derivation, the players would have to search for it online for him.

Ilana, standing in front of the desk, and Ophia, who was eavesdropping, both blushed, though for completely different reasons.

Luo Yan cleared his throat and continued with a smile.

"Getting back to the point, do you know how amazing you just did?"

Ilana thought for a moment, then spoke honestly in a low voice.

"We can use it to find the critical value function of a functional..."

“Not only that,” Luo Yan shook his head slightly, smiling as he continued, “we can also use it to describe the motion of various systems, whether it’s the motion of a point mass in a force field or the motion of magical elements in a magic field… As long as the system conforms to the principle of ‘least action,’ theoretically this formula is applicable.” “Relying on its properties, we can not only greatly simplify the design of magic arrays, but also reduce the loss of energy in magic crystals in unnecessary circulation links.”

This is absolutely a groundbreaking discovery!
Perhaps it won't be long before a brand new discipline called "Analytical Magic" is born in this world, and the study of supernatural powers will take a new step forward!
“Ilana,” he said, looking at the girl standing in front of his desk, his voice gentle yet solemn, each word carrying the weight of approval, “you have created a miracle.”

Ilana blushed and whispered, surprised that her supervisor thought so highly of her research.

"Am I... really that exaggerated?"

"Exaggeration? I think the word 'miracle' is too conservative!" Luo Yan nodded with a smile. "I believe any magician who has learned about Mr. James WALL-E's research can see the value behind it. I suggest you submit your work to the Sage's Gazette; this research deserves to be recorded in the annals of the academic world!"

“The Sage’s Journal?! But I…” Ilana subconsciously held her breath. She never thought that such a thing could be submitted, let alone that her paper could reach the top of the Great Sage’s Tower.

"Is that the very top of the Great Sage's Tower? I bet that's what you're thinking, right?"

Seeing that Ilana's thoughts had been exposed, Luo Yan smiled and continued in an encouraging tone.

"It has nothing to do with age. Most mathematicians actually achieve their most outstanding mathematical results in their youth... well, most of the ones I know."

Ilana was so shocked by this sudden reality that she was at a loss for words, her mouth slightly agape.

She wasn't the only one shocked; Ophia, who witnessed everything firsthand, was also stunned, her beautiful face completely filled with a look of shock.

And beyond that shock...

She gradually felt a sense of shame.

Especially when she saw the pure and sacred academic resonance between the two of them, a burning blush crept up her cheeks.

What filthy things were I thinking just now?

She felt utterly ashamed of her thoughts!
Ophia retreated silently.

With her head down and clutching her advanced mathematics textbook to her chest, she felt for the first time the weight of that thing called "wisdom".

At the same time, a sense of resentment welled up in her heart.

Since Ilana can do it—

There's no reason why the young lady of the Castellion family couldn't do it!
One day, she too will climb to the top of this tower!

She relied on her own strength!
……

Out of the corner of his eye, Luo Yan glanced at Ophia as she quietly left, a barely perceptible smile playing on his lips as he leaned back in his chair.

It seems that his previous "praise" had some effect on the duchess, and she will probably spend more time on mathematics in the future.

He cleared his throat and continued speaking, looking at the stunned Ilana.

“A great discovery deserves its own name. Ilana Octavia, this is your honor.”

He paused, then made the announcement in a solemn and serious tone.

"Let's call it... the 'Ottavia Equation'!"

After all, this world doesn't have Euler and Lagrange; simply transplanting Earth's names here will only leave people confused.

Luo Yan thought Ilana would be very excited, but to his surprise, her cool face, flushed with a blush, suddenly fell silent.

After a long silence, she suddenly raised her head, looked sincerely at Colin sitting behind the desk, and opened her mouth to speak.

"Your Highness, I...have a request."

"Oh? What request do you have?" Luo Yan asked with a gentle smile, his fingers interlaced on his knees.

Ilana said in a low voice.

"Completing this equation was not my own achievement. Without your guidance and the mathematical methods you taught me, I could never have found it so quickly."

It's true that she completed the equation independently, but she always had a feeling that this approachable prince actually knew about its existence from the beginning.

So much so that when he encouraged her to explore in this direction, he used the same tone as when "assigning homework".

Although he himself may not have realized it, she clearly saw the composure hidden behind his kind gaze...

It was precisely because she believed that this formula must exist that she was able to find it so quickly from the sea of ​​numbers.

She couldn't accept taking all the glory for herself, neither emotionally nor logically.

Looking at the stubborn Ilana, Luo Yan smiled.

“I disagree with that. I did give you some guidance, but that doesn’t mean it’s not your achievement. Ilana, you can be more confident. I’m pleased that you’ve used the tools I gave you to such an extent. I’ve assigned similar tasks to many people, but you are the first and only one who has truly mastered the knowledge I taught you.”

“I know… but your suggestion still makes me uneasy. Please forgive my immaturity and overstepping.” After a pause, Ilana looked at him with a burning and determined gaze, and softly made her request, “I just thought, could I… put your surname first?”

Let's call it the 'Colin-Ottavia Path Optimization Equation'!

She spoke these words almost pleadingly. Her resolute expression suggested that she wouldn't write the paper if he didn't agree.

Seeing Ilana's serious expression, Luo Yan was slightly taken aback, then couldn't help but smile.

This little bit of empty fame is actually nothing to the gods.

In any case, when people study her life in the future, they will inevitably have to mention her name and the "scientific" school of thought she led.

The chosen ones do not share in God's glory; they are beings who share both honor and disgrace. He had long been puzzled as to why the gods did not monopolize all the power of faith, but as he progressed along the way, he gradually came to understand that the secret to becoming a god actually lies in "sharing."

However, if simply nodding his head could reassure a clever and intelligent girl, he certainly wouldn't refuse to grant her wish.

After all, this world is still in a feudal era, and the sparks of enlightenment have only just been lit. Without sufficient support, even the finest gold will be buried in the dust of reality.

Actually, the support he initially prepared for her was Ophia.

Unfortunately, the genius was just too fast. Miss Castellion had only just learned the calculus of variations when Ilana had already reached the finish line.

Looking at Ilana's serious face, Luo Yan shrugged slightly and said in a teasing tone.

"It seems that future students will have to remember one more name."

Ilana was slightly taken aback, but then she understood what Prince Colin had said, and a genuine smile of joy instantly bloomed on her usually aloof face.

He agreed!

However, not long after, she probably thought of something and suddenly became embarrassed, scratching her slightly reddened cheek with her index finger.

Wouldn't having two names seem too deliberate?
How about adding another one...?

Of course, this thought only lasted for two seconds before it automatically disappeared from her mind, because there really wasn't a third person who had participated in this project.

She can't lie.

"Then... I'll go write my thesis?" Ilana said softly.

“Go ahead,” Luo Yan nodded happily. “I’m really looking forward to your work.”

"Um... this is my first time... writing this kind of paper. If there's anything I don't understand, may I ask you for help?"

"Of course, I'd be happy to help you."

Watching Ilana's figure disappear into the distance, Luo Yan smiled approvingly and guided the teapot on the table to pour himself a cup of black tea.

A great law, capable of overturning the foundations of the existing magical theories of the Academy, was born in this small laboratory in an almost peaceful manner.

certainly--

Almost every great discovery is initially viewed unfavorably by conservative eyes.

It's not so easy to shake a tall tower.

Ilana will likely run into trouble; even if she puts her name on it, it won't change the fact that the paper was written by an apprentice.

But... so what?

True gold shines wherever it is; even outside of Xuebang, it can shine on his turf.

He had no intention of leaving his precious apprentices on this snowy plain forever.

Just like the diamond he placed in Mr. Andes's hand, it was merely bait for him to catch a big fish with a long line.

Just then, a series of hurried footsteps approached from afar, interrupting Luo Yan's thoughts.

As usual, the teaching assistant, Corgi, rushed into the lab like a gust of wind, ran straight to his desk, and was panting heavily.

"Your Highness!"

Before he could speak, Luo Yan raised his head with a knowing smile on his face.

"Hector sent you, didn't he?"

The corgi, who was about to speak, paused for a moment, then scratched its head somewhat embarrassedly.

"Yes, mentor. He said the council's latest resolution is related to you, and asked you to come to his office when you have time, as he has something he wants to discuss with you... or you can arrange a place for him to come. He seems to be in a good mood, so it must be something good."

Luo Yan raised an eyebrow in surprise.

"Okay, tell him to wait for me a while. I'll be there before evening."

　It burned out yesterday, and today it's a bit shorter... ==
　　
　
(End of this chapter)