Chapter 450: Functional Analysis!

"I didn't expect to meet you here, Miss Castellion," Luo Yan said with a soft sigh, meeting those bright, snow-clear eyes—he knew he couldn't avoid her anymore. "How is your father lately?"

Ophelia smiled gently, speaking with perfect courtesy.

"He is as healthy as when you left. He also asked me to convey his greetings upon seeing you, saying he misses our conversations deeply… by the way, I feel the same. Every day since you were gone, I've missed your voice, your face, your laughter."

Uh.

Is that how you use "voice, face, laughter"?

Luo Yan had no idea where she'd learned that phrase—beside him, Professor Hector was barely holding back a fit of suppressed laughter.

"I'm truly unworthy—I don't recall ever leaving such a deep impression on Miss Castellion—"

"Can you call me Ophelia?"

"... It's not impossible, but—"

"Thank you."

A satisfied smile spread across Ophelia's face; her long lashes curved like a gentle crescent moon, and her usually dignified poise revealed a rare, playful spark.

Luo Yan didn't know how to respond, so he simply shrugged slightly and took a sip of tea to mask his embarrassment.

At that moment, Professor Hector, who had been watching the scene from behind his desk, finally let out a smug little chuckle.

"Ha… youth is wonderful."

Seizing the moment, he lifted his teacup and gestured with his chin toward the unopened letter on the desk, teasingly prodding.

"Your Highness, the Duke of Castellion's personal letter still sits on your desk. Won't you open it? Don't slight his goodwill."

Luo Yan glanced at him.

This old man was always so serious on the surface, but inwardly he was a sneaky little joker.

He said nothing more, reaching out to pick up the letter sealed with a bronze sea-horse crest. On the journey from Shengcheng to the northern wastelands, Ophelia had kept it close to her body—the envelope still seemed to carry a faint warmth of a young girl's touch.

Luo Yan broke the seal and unfolded the paper.

The handwriting was strong and vigorous—clearly from the Duke of Castellion himself, the man who ruled Shengcheng with a wave of his hand.

【Dear Prince Roxe Prince Prince Kelin,

It has been a long time since we last met. I hope you are well.

Since your departure over a month ago, the people of Shengcheng have all cherished your generosity and benevolence, longing for your swift return to this land bathed in holy light.

I often hear servants from the estate speak of how, during your time in Shengcheng, every day brought something new, making one eagerly anticipate tomorrow.

Allow me, on behalf of His Imperial Majesty, to offer you my most sincere respect for your contributions to Shengcheng and the entire Empire!

The Sacred Knights' project is progressing steadily. We have established over a dozen ports along the coast of Jiana Continent, and the expansion into the New World is in full swing. The only minor concern is that Hell seems to have set its sights on that fertile land—a demon king named Ig has risen along the northern coast. But I believe, before the Empire's iron hooves, such a threat is negligible… not worth your concern.

Additionally, the Bai Lu District project, spearheaded by your distant relative Sir Tang Tai, has now gained solid momentum.

That knight has used debt as his main tool, leveraging powerful landowners to eliminate bankrupt tenants and small landholders. Once the large landowners are buried in debt, he then uses public opinion, law, and debt traps to strip them of their feudal protections—and along the way, he also taught greedy merchants a lesson. This land consolidation strategy flows like water, flawless—truly opened my eyes!

The sugar syrup processing facility under the Tang Tai Group has begun construction, and a new industrial park centered on high-quality rum is rising on the outskirts of Shengcheng. The local residents, blessed by your grace, will soon enjoy prosperity once sugar syrup flows steadily from the New World to Shengcheng.

Another matter that delights me personally: the Bai Lu District project has, as you promised, visibly boosted trade volume at Castellion Port! This strategy of using a core industry to drive surrounding development and intensive production is nothing short of genius! On behalf of the people of Castellion Port, I again express my heartfelt admiration for your foresight!

I also heard you've recently been invited to become a tutor at the Scholar's Domain, embarking on the exploration of magic and truth. When I heard this, I could hardly believe my ears—I never imagined you possessed such profound mastery in magic.

Saint Sis above, is there anything you cannot do? Please share some of this blessing with the Castellion family!

Ha! That last remark was a joke—please don't take it to heart. The Castellion family has already received much from the Holy Light. I sincerely wish you will restore the glory of the Prince Prince Kelin family, and I believe, as you said, you will not keep that glory to yourself!

By the way, my daughter Ophelia has long yearned for the mysteries of magic. It would be ideal if she could receive your personal guidance! I might not trust others, but with you, I have absolute confidence!

I entrust my daughter to you!

Your most loyal friend,

Duke Andre Castellion】

Luo Yan slowly folded the letter, his mind now crystal clear.

This letter, Biaomianshang a note of thanks and request, was in truth a carefully woven "open strategy" by Duke Castellion—impossible to refuse.

It first praised the great success of the Bai Lu District project, affirming his own contributions in Shengcheng and Sir Tang Tai's achievements, while subtly hinting at the Castellion family's crucial behind-the-scenes role.

Finally, it cut straight to the point in the fewest words, using personal favor as leverage to place Ophelia directly before him.

Honestly, Luo Yan wasn't troubled by Duke Castellion's harmless "calculation"—it was Ophelia herself that brought the trouble.

Her sudden appearance would introduce uncontrollable variables into his meticulously crafted "Prince Prince Prince Kelin" story.

The cardinal rule of juggling multiple identities is never letting all those identities appear in the same port—it may seem convenient, but the consequences are endless.

This is difficult…

Watching Prince Prince Prince Kelin's expression of helpless "headache," Professor Hector felt an unprecedented sense of delight.

So this is what you get!

Clearly not letting Prince Prince Prince Kelin off the hook so easily, he cleared his throat and interjected just at the right moment, giving Duke Castellion's daughter a helpful nudge.

"Your Highness, letters of recommendation are an imperial tradition. You are a prince of the Empire, and Duke Castellion is a pillar of the Shengcheng Senate. Since the Duke holds you in such high regard, I suggest you honor his wish!"

Using the Empire's princess to balance the Empire's prince was like using the Empire's spear to pierce its shield—Hector stroked his beard, convinced his idea was brilliant.

Since this prince entered the Mage Tower, he'd either been plucking Hector's wool or leading him by the nose, crushing him utterly in every exchange of power.

This was finally his chance to get even!

Sensing the fleeting flicker of distress on Prince Prince Prince Kelin's face, Ophelia, who had been quietly observing him, spoke gently.

"Your Highness, please don't misunderstand—I've come to the Scholar's Domain solely to study magic, with no intention of troubling you. If I may merely sit in on your lessons, I will be perfectly content… if you truly cannot bear to see me, I can pretend I'm not here."

She was, after all, a Castellion daughter—she had sensed that Prince Prince Prince Kelin and Professor Hector's relationship was far from the surface harmony.

Though she was glad Hector spoke for her, she had no desire to become his spear.

Rather, she wished to become the prince's shield—to compensate for his shortcomings… just as her mother had silently supported the Duke.

Fine, fine, playing the retreat-to-advance card, is it?

Luo Yan recognized this tactic well—he'd used it himself countless times, and it always worked. He just never expected Ophelia, this girl, had learned it too—and now used it on him.

He wondered who had taught her.

Seeing Professor Hector's lips twitching with barely contained amusement, Luo Yan sighed and spoke.

"How could I? Cast… Ophelia, even if I could ignore Professor Hector, I could never ignore someone as beautiful and captivating as you."

Ophelia was utterly unprepared for such a remark—her face flushed crimson, like a steaming teapot, as if steam were rising from her cheeks.

Ignoring Hector's indignant scowling, Luo Yan glanced at the clock on the wall and rose from the sofa.

"Come with me. I'll take you to the laboratory."

Since Miss Castellion had clearly prepared for "relentless persistence," and possibly even had her father's backing, continuing to cold-shoulder her as he had in Shengcheng would only walk into her comfort zone.

As a demon king who never played by the rules, if Miss Ophelia had played the retreat-to-advance card, then he'd just have to take it a step further.

No matter what Duke Castellion was plotting, on a demon king's territory, everything followed the demon king's rhythm!

In any case—

He needed a foolproof plan: either settle Ophelia within the Scholar's Domain, or find a way to make her give up.

Above all, he could not let her stay by his side, much less accompany him to the future "Duchy of Campbell"—otherwise, he had no idea how he'd keep spinning the tale of the "lost prince returned from overseas."

At this moment, Ophelia had no idea how Prince Prince Prince Kelin truly viewed her—she believed he'd been moved by her sincerity and determination.

Happiness had come so suddenly, she was momentarily flustered, instinctively murmuring "Mm," and rose hastily from the sofa.

The "unexpected reunion" had ended so abruptly—Hector, who had hoped for a good show, was deeply disappointed.

He'd expected Prince Prince Prince Kelin to endure a torturous game of chase, then finally turn to him with a pleading look.

Then, after much reluctant hesitation, he'd say, "Fine, I give up," and begrudgingly accept Ophelia as his gifted apprentice—thus gaining favor with both the Empire's prince and the duke.

But in the end, it had nothing to do with him.

Are you kidding me?!

Luo Yan nodded to Professor Hector and tossed off a brief "Goodbye," then walked toward the office door.

Ophelia bowed slightly to Professor Hector, then hurried after him into the corridor.

Standing in the corridor, Luo Yan paused for two seconds, then suddenly remembered something and turned to Ophelia.

"By the way, from now on, you are my apprentice. While you're in the Mage Tower, I'd like you to address me as Master, like the other students… is that acceptable?"

"Mm."

Ophelia nodded quickly, cheeks still flushed, entirely unaware this was her second "mm" in one minute.

…

After leaving Professor Hector's office, Luo Yan took Ophelia straight to the elevator and returned toward the laboratory.

Beside him, Ophelia had shed all her earlier stiffness in the professor's office—she was now as lively as a lark freed from its cage, chattering nonstop, asking questions about everything, utterly fascinated by the Scholar's Domain.

"Master, I heard from Professor Hector that you're researching 'arithmetic'?"

"Sort of," Luo Yan replied absently, pulling himself from his tangled thoughts. "I don't just study arithmetic—I occasionally teach students other things too."

"That's wonderful!" Ophelia beamed, her eyes sparkling with excitement. "I was the best in arithmetic at the Imperial Royal Academy of Arts! I can definitely help you!"

Huh?

Was that true?

Luo Yan was slightly surprised.

He'd always assumed Ophelia studied art—and had even wondered how this duke's daughter, who could embroider a sea-horse into an Arakdo, had even gotten into the Imperial Royal Academy of Arts.

Apparently, the Imperial Royal Academy of Arts taught more than just art.

As they talked, Ophelia slowed her steps, suddenly looking shy as she whispered, "Um… Master, you haven't thrown away the talisman I gave you, have you?"

"Of course not," Luo Yan smiled, answering with gentlemanly grace. "How could I ever forget something given to me by Miss Ophelia?"

He reached into the pocket of his robe—unseen, he withdrew the talisman Ophelia had sewn by hand from his storage ring.

Seeing her talisman carried by Prince Prince Prince Kelin, Ophelia's face lit up with a radiant smile, her cheeks blooming with a soft blush.

"That's wonderful… the Guardian Dragon I stitched for you is still here. It seems it has been protecting you well."

A dragon?

Luo Yan blinked in surprise, lowering his head to look again at the talisman in his hand.

He had always assumed the crooked, abstract embroidery on the talisman depicted the Castellion family crest—a bronze seahorse.

So all this time it was Taf?

Thank goodness Taf isn't here—otherwise that brat would've started spouting off again.

"... Master?" Observing Prince Prince Kelin's peculiar expression, Ophelia tilted her head in confusion, unsure what had suddenly come over him.

"Nothing."

Luo Yan slipped the talisman back into his pocket, then turned his gaze to the "Arcane Science" laboratory before changing the subject.

"We've arrived."

…

As the laboratory door opened, the lively discussion paused briefly. Dozens of eyes turned toward the entrance, especially settling on the girl beside Prince Prince Prince Kelin.

"Another one?" Jamie stared at the girl behind their Master, glancing sideways at Ram. "And a stranger… have you seen her in class before?"

Ram shook his head slightly, eyeing the girl with suspicion.

"No…"

She couldn't shake the feeling that this woman didn't seem like a magic apprentice at all—her aura clashed with the snowy wasteland, instead resembling Ilana's.

Could it be…?

Is she also from the Empire?

Luo Yan clapped his hands, drawing the attention of the busy apprentices, and smiled as he introduced her.

"Everyone, this is Miss Ophelia Castellion from Shengcheng. Starting today, she will join our laboratory as a probationary student… please welcome her."

A scattered round of applause broke out instinctively, but soon slowed, then faded entirely.

Castellion!

That name—famous throughout the Empire—struck like thunder, leaving every common-born apprentice stunned.

They gazed at the legendary duke's daughter in awe, utterly at a loss, unsure where to even place their hands.

To them, Duke Blackwood of Longshi City was already a towering figure—but this woman's father towered even higher.

The duke of Shengcheng sat on equal footing with the kings of vassal states—and in reality, his status was even greater.

Luo Yan observed their reactions, a faint, almost imperceptible smile tugging at his lips.

Though he had no desire for the other apprentices to ostracize Ophelia, if the duke's daughter herself grew unable to endure the atmosphere of these "overachievers" and chose to return to Shengcheng, it would suit him perfectly.

Yet Ophelia's next actions completely surprised him.

She showed not a trace of noble arrogance. First, she bowed with flawless grace, then spoke in a gentle, composed voice to introduce herself.

"Hello everyone, I'm Ophelia Castellion. Starting today, I'll be your classmate—and future colleague."

"To be honest, this is my first time traveling so far, my first time seeing such heavy snow, such towering towers… I'm utterly awestruck. I never imagined the world beyond Shengcheng was so vast, nor that I'd meet such gifted individuals on this unfamiliar land."

"I hope we're not just fellow apprentices studying together, but true friends… I look forward to your guidance in the days ahead."

Applause erupted again in the laboratory—this time louder, more heartfelt, than before.

For a duke's daughter to be so down-to-earth was a shocking revelation to the Rodians present.

Forget the duke.

In their hometowns, even barons wouldn't spare them a glance.

Having finished, Ophelia stole a glance at Prince Prince Prince Kelin beside her. When she saw his stunned expression, her lips curled slightly.

Keep going—

Ophelia!

Baron Corsia swallowed lizard dung just to survive—how could winning over classmates possibly be hard for you?

She was completely unaware of Prince Prince Kelin's ulterior motives, interpreting this as his first test for her.

Clearly, he wanted to see whether she had the merit to stand beside him as his assistant.

So right now, her task was clear: build rapport with her future "colleagues"—at least no longer behave as she had at the Royal Academy of Arts.

Luo Yan would never guess what had spurred this noblewoman.

But honestly, he was genuinely surprised. Clearly, the past three months had transformed this duke's daughter beyond recognition.

That was a good thing.

He'd prepared two strategies: if Ophelia didn't voluntarily retreat, he'd find a way to keep her here.

As long as she didn't follow him to the Campbell Duchy.

Luo Yan gave Ophelia an approving glance. After she finished greeting her classmates, he briefly explained the laboratory's workings.

"You don't need to report here daily—your priority remains your classes."

"Also, you're three months behind the other apprentices. I don't know your foundation—if you know nothing about magic, you've got a lot of catching up to do."

"You'll help me, won't you?" Ophelia blinked her clear eyes, gazing at him hopefully.

Luo Yan nodded politely.

"Of course. Anytime you have questions, come find me."

The laboratory buzzed again, returning to its relaxed, lively atmosphere.

Almost everyone was excitedly discussing the duke's daughter who had come from afar, speculating wildly about why she was here.

Ophelia's story became the lab's hottest topic—and unlike typical nobles, she welcomed the gossip with open arms.

Of course, it might also be because she saw it as some kind of "test."

Finally, emboldened by the noblewoman's approachability, a daring apprentice summoned the courage to ask.

"Miss Castellion… may I ask, why did you come to Xuebang?"

"Well…"

Ophelia subtly glanced toward Prince Prince Prince Kelin, watching his focused profile as he studied a magical tome, then smiled and winked gently.

"Secret."

That radiant smile turned the shy boy's face bright red. He bowed hastily in thanks, then fled back into the chattering crowd.

Amid this rapidly warming atmosphere, only Ilana seemed distracted.

She had no interest in the lab's gossip; she'd tried several times to approach the Master with questions from her notes, but never found the right moment.

Now, Master Prince Prince Kelin was fully absorbed in his magical texts. She wasn't sure whether she should interrupt him.

Her gaze kept drifting toward Prince Prince Kelin, hoping to catch his eye. And just as luck would have it, that intense stare was spotted by Ophelia, who was basking in her own satisfaction.

To Ilana herself, it was merely a normal, yearning look for knowledge—but to someone lacking understanding, it carried an entirely different meaning.

Especially with that cool, beautiful face—it stirred a flicker of instinctive suspicion in Ophelia's mind.

Could this girl also…?

No way.

He's my Master.

Ophelia had forgotten, of course, that she herself had just become Prince Prince Kelin's apprentice.

Behind his desk, Luo Yan finally noticed Ilana's hesitant, unspoken gaze.

He'd noticed it long ago—but preferred not to interfere in his apprentices' independent study, so he pretended not to see.

Yet two pairs of eyes kept scanning him like radar. He couldn't sit still any longer, so he closed his magical tome and walked over to her workstation.

"You seem troubled by an unsolved problem. Tell me what it is."

Hearing her Master's voice, Ilana snapped her head up. A flicker of flustered surprise crossed her face—but mostly, it was the joy of finally having the chance.

She shyly handed him her notebook, pointing to a page covered in dense, alien-looking calculations, and whispered:

"I… I've encountered a problem I can't figure out… Master. If there's a way to find the extremum of a function, is there a simpler method to find the extremum of a 'function of a function'?"

Worried he might dismiss her as overly convoluted, she added softly:

"Perhaps you'll think my idea strange, but my intuition tells me… solving this might help with James Wally's unfinished work."

It wasn't just intuition—her rational judgment agreed.

James Wally had tried to build a system using precise numbers to analyze mana—but lacked the mathematical language to describe the process.

Luo Yan took the notebook, his eyes falling on the calculations. A flicker of genuine surprise crossed his gaze.

He hadn't expected Ilana to learn so quickly.

He'd only just introduced the basic concepts of calculus in class—and she'd not only mastered them, but had already extended her thinking into a field far more advanced and complex than calculus—something he hadn't even taught yet!

This girl… might actually be a genius.

I've struck gold!

"Superfluous? Ilana, there's no such thing as 'superfluous' in this world—only fools who fail to see the value hidden beneath ordinary things."

A faint, almost imperceptible joy sparkled in Luo Yan's eyes. He placed the notebook back on the table and looked at Ilana, who wore a puzzled expression, praising her:

"Your question is excellent. Finding the extremum of a function of a function belongs to another vital branch of higher mathematics."

"I call it—'functional'!"

(End of Chapter)