Chapter 391: Epoch-making Equation

The Magic Science Laboratory was as lively as ever today.

The apprentices personally selected by Prince Kelin gathered here spontaneously as soon as class ended, and the air was filled with youthful and enthusiastic vitality.

Of course.

There was no lack of complaining whispers here.

After all, geniuses were the minority, and most people were just using mortal wisdom to do things within mortal reach.

"Saint Xisi above, this is too hard!" Jamie, the carpenter's son, was sighing at a draft paper filled with arcs and straight lines, "'Compass and straightedge construction of a regular seventeen-sided polygon'... it clearly looks so simple, why is it impossible to do?"

He wasn't the only one troubled by difficult problems.

Beside him, Ram, the clockmaker's daughter, was also holding her chin in distress, muttering to herself.

"... How can a walker walk through seven bridges once without repeating and without missing any, and finally return to the starting point."

Jamie, who was holding a ruler and measuring on the paper, was stunned and asked subconsciously.

"Is this some kind of brain teaser?"

"No, this is a thinking question assigned by Prince Kelin," Ram shook her head, "He asked me to study it in my spare time, saying I could try to associate it with geometric problems."

"Hiss... let me ponder it, it seems a bit interesting." Jamie scratched his head, muttering, and buried his head in the draft paper again.

Ram stretched and leaned back in her chair.

"Good luck... oh right, does your regular seventeen-sided polygon problem have requirements for the compass and straightedge? Only a straightedge is allowed, or both?"

Jamie shook his head.

"You can use a compass and a straightedge, but it must be a ruler without markings, and you cannot make marks on the ruler."

Ram: "A ruler without markings? What a strange problem..."

The two whispered to each other.

Although their respective problems still had no progress, they already had ideas for solving them.

And not far away, Oufiya was also thinking about her own problem, but her problem was more abstract—

【As the number increases, will the proportion of prime numbers in natural numbers become smaller and smaller? If so, please provide proof.】

Saint Xisi above, it was the first time she had heard such a strange problem!

And is studying this thing really useful?!

The Royal Academy of Fine Arts in the Shengcheng where she studied before did teach the concept of prime numbers, but that was only appreciated as a kind of "harmonious" and "sacred" numerical symbol. There were also some priests who believed that this contained the password left by Saint Xisi to the world.

But regardless, it would not affect an extraordinary person's spellcasting, nor would it make a weak mage suddenly become strong.

Just when she was troubled by this seemingly useless problem, a familiar figure suddenly broke into the corner of her eye.

That person was none other than Yilana!

I saw that girl who was usually as calm as water, clutching a notebook tightly with both hands, a trace of unusual flush on her cheeks.

She bit her lower lip gently with her pearly teeth, took several deep breaths, and finally took a step, walking toward Prince Kelin.

Wait—

What is the situation?!

Oufiya's alarm bells rang in her heart.

That appearance might be relatively strange to the bookworms of the Academy, but she, who came from the Shengcheng, knew that expression too well!

After all, she could encounter such presumptuous guys every few days...

Thinking of what Yilana was going to do next, Oufiya only felt her heart twitch slightly, and the mathematical symbols in her mind instantly dissipated like smoke, without a trace.

Could it be... she wants to do it here?! In front of everyone, ex, express... her feelings?!

This seemingly absurd thought was like a thunderbolt, exploding in Oufiya's mind, followed by a complex emotion mixed with panic, jealousy, and curiosity instantly seizing her heart, making her, who was originally calm and composed, lose her footing for a time.

She almost stood up subconsciously, holding that *Higher Mathematics* book like a heavenly book, pretending to pass by the aisle inadvertently, but actually quietly approached the desk and pricked up her burning red ears.

Not that she cared—

She believed Prince Kelin was not such a casual person and would definitely not easily agree to inexplicable requests.

She was just standing from the perspective of a lady from the Shengcheng, wanting to see what that girl from the Pierce Province intended to do to the Prince!

However, the first sentence Yilana spoke made Oufiya, whose alarm bells were ringing, freeze in place.

"Mentor..."

That slender voice carried a trace of imperceptible trembling, yet in those clear eyes burned an unprecedentedly hot determination.

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

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

Path optimization equation?

Oufiya, who was frozen in place, was at a loss, and the panic in her heart was extinguished by that complex and mysterious mathematical concept.

But soon, a touch of curiosity arose in her heart.

She naturally knew the path optimization equation; that seemed to be the unfinished topic of the former owner of this laboratory, Mr. James Wali.

It's just—

Can a mere black-iron-level apprentice solve this topic that even a formal mentor has broken his head over?

Not necessarily...

Oufiya swallowed a mouthful of saliva, hiding behind the *Higher Mathematics* textbook like an ostrich, staring straight at this side, her eyes full of curiosity.

Yilana didn't notice her existence; all her heart and soul were completely immersed in the great discovery she was about to present.

She carefully spread out the notebook in her hand in front of Prince Kelin, her voice, trembling with excitement, gradually becoming crisp and full of confidence.

"The variational method you taught me is like a key; it makes me understand that we can treat the 'total cost' of the entire 'path' as a function that can be solved. 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 extremum..."

"Just get to the point, Yilana." Luo Yan said concisely, "There is no need to repeat these trivial details."

"Okay, Prince."

Yilana nodded gently, her speaking speed changed suddenly, cutting directly into the main topic from the opening remarks.

Oufiya was confused.

Even though she had tried very hard to listen, those profound concepts were like obscure spells, making her unable to penetrate the mysteries within.

However, she could understand expressions.

With Yilana's narration, Prince Kelin's eyes, which always carried a trace of lazy smiles, lit up bit by bit.

That was a pure look.

Just like an artist looking with gratification at the artwork he had carved with his own hands.

Oufiya suddenly felt a bit jealous.

Clearly she could also... and clearly she was the one who came first.

"So, if my deduction is not wrong... this equation should look like this."

Yilana finally finished speaking.

She raised her head, looking at her most respected mentor with a nervous and expectant look, waiting for this Prince's evaluation.

The desk fell into a brief silence.

Luo Yan looked at the beautiful and complex differential equation on the draft paper, and while pleasantly surprised, he couldn't help but feel a thousand emotions.

Although he had influenced two worlds, this sense of achievement still couldn't compare to watching the small sapling he had cultivated with his own hands grow into a towering tree and bear fruitful results.

This feeling is really good.

After savoring this pleasant comfort for a moment, Luo Yan raised his head again, looked at Yilana standing in front of the desk, and said with a smile.

"A very great derivation process; to be honest, your application of the variational method is probably already above mine..."

Yilana lowered her head in panic.

"Mentor, you are being humble..."

"No, I am not being humble; I have always said what I have to say," Luo Yan smiled and said casually, "After all, I am not a professional scholar; there are some things I know that they are so, but I don't necessarily know why they are so... But I am very gratified that I met you; your talent fills the gaps in many places for me."

This is the truth.

He certainly knew the Euler-Lagrange equation, but if he were asked to write out the derivation process, he could only let the players search for it online for him.

Yilana standing in front of the desk and Oufiya eavesdropping both blushed, although for completely different reasons.

Luo Yan cleared his throat and continued with a smile.

"Back to the topic, do you know what an amazing thing you just accomplished?"

Yilana pondered for a moment and said honestly in a small voice.

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

"Not only that," Luo Yan shook his head gently and continued with a smile, "We can also use it to describe the motion of various systems, whether it is the motion of a mass point in a force field or the motion of magic elements in a magic field... as long as this system conforms to the 'principle of least action,' theoretically this formula is applicable."

"Relying on its characteristics, 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 definitely an epoch-making discovery!

Perhaps before long, a brand-new discipline called "Analytical Magic Mechanics" will be born in this world, and the research on extraordinary power will also move to a new level!

"Yilana," looking at the girl standing in front of the desk, his voice was gentle and solemn, each word seeming to carry the weight of recognition, "You have created a miracle."

Not expecting the mentor to think so highly of her research, Yilana couldn't help but feel her cheeks burning, and said in a small voice.

"I... am I that exaggerated?"

"Exaggerated? I think the word miracle is too conservative!" Luo Yan nodded with a smile, "I believe that any mage who has understood Mr. James Wali's research can see the value behind this research. I suggest you submit it to the *Sage's Report*; this research result deserves to be recorded in the history of the Academy!"

"The *Sage's Report*?! But I..." Yilana held her breath subconsciously; she had never thought that such a thing could be submitted, let alone dared to think that her paper could ascend to the top of this Great Sage's Tower.

"That is the tip of the Great Sage's Tower? I guess that must be what you are thinking, right?"

Looking at Yilana whose thoughts were spoken, Luo Yan smiled and continued in an encouraging tone.

"This has nothing to do with age; most mathematicians' most outstanding mathematical achievements were actually completed in their youth... hmm, most of the ones I know."

Yilana was shocked by this sudden reality and was at a loss, her small mouth slightly open, unable to speak for a while.

It wasn't just her who was shocked, but also Oufiya who witnessed all this on the side; that beautiful face was completely filled with the look of shock.

And beyond that shock...

She also gradually felt a trace of shame.

Especially when she saw the pure and sacred academic resonance between the two, a hot sense of shame climbed up her cheeks.

What on earth was she thinking just now... those filthy things?

She felt ashamed of her thoughts!

Oufiya retreated silently.

She lowered her head, holding the *Higher Mathematics* textbook in her arms, feeling for the first time the weight called "wisdom."

At the same time, a trace of unwillingness also surged in her heart.

Since Yilana could do it—

There was no reason why the young lady of the Kastelion family couldn't!

One day, she would also ascend to the top of this high tower!

By her own strength!

Watching Oufiya leave quietly from the corner of his eye, the corners of Luo Yan's mouth curled into an imperceptible smile, and he leaned back in his chair.

It seems that his previous "flattery" had touched the heart of this Duchess, and she would probably spend more time on mathematics in the future.

He cleared his throat and continued to Yilana who was stunned.

"A great discovery deserves a name of its own. Yilana Otavia, this is your glory."

He paused and made an announcement in a solemn and serious tone.

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

After all, this world didn't have Euler and Lagrange, and applying names from Earth here would only make people feel inexplicable.

Luo Yan originally thought Yilana would be very excited, but to his surprise, that cold face covered with red clouds suddenly buried itself.

After a long silence, she suddenly raised her head, looked at Kelin sitting behind the desk with sincere eyes, opened her mouth and said.

"Prince, I... have a request."

"Oh? What request?" Crossing his fingers on his knees, Luo Yan said amiably.

Yilana said in a small voice.

"Completing this equation was not my own strength; if it weren't for your guidance and the mathematical methods you taught me... I could never have found it so quickly."

It was true that she completed this equation independently, but she had always had a feeling in her heart that this approachable Prince actually knew of its existence from the beginning.

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

Although he might not have noticed it himself, she clearly saw the calmness hidden behind his kind gaze...

And it was precisely because she believed that this formula must exist that she was able to find it so quickly in the ocean of numbers.

If she swallowed all the glory, she couldn't accept it in terms of reason or emotion.

Looking at the stubborn Yilana, Luo Yan smiled.

"I beg to differ. I did give you some guidance, but that doesn't mean this isn't your credit. Yilana, you can be more confident; I am very gratified that you can apply the tools I gave you to such an extent. I have given many people similar topics, but you are the first, and the only one, who has truly mastered the knowledge I taught you."

"I know... but your proposal still makes me feel uneasy; please forgive my immaturity and presumption." After a pause, Yilana looked at him with hot and firm eyes and made her request in a small voice, "I just thought, can I... put your surname in front?"

"Let's call it the 'Kelin-Otavia Path Optimization Equation'!"

She said these words almost in a pleading tone. That firm appearance was as if he wouldn't write this paper if he didn't agree.

Looking at Yilana's serious eyes, Luo Yan was slightly stunned, then couldn't help but smile.

This bit of empty fame actually didn't matter to a god.

Anyway, when people study her life in the future, they will always be unable to bypass his name and the "scientific" school he leads.

The chosen one will not share the glory of the god; both sides are existences that share honor and disgrace. He was also confused a long time ago about why gods didn't enjoy all the power of belief exclusively, but as he walked along this path, he also gradually realized that the mystery of becoming a god actually lies in "sharing."

However, if he only needed to nod his head to make a smart and clever girl feel at ease, he certainly wouldn't reject satisfying her wish.

After all, this world is still in the feudal era, and the sparks of enlightenment have just been lit. If there is no sufficient backing, even real gold will be buried in the dust of reality.

Actually, the backing he originally prepared for her was Oufiya.

It's just a pity that the genius's speed was really too fast; Miss Kastelion had just learned the variational method, and Yilana had already run to the finish line.

Looking at Yilana who was serious, Luo Yan shrugged slightly and said in a teasing voice.

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

Yilana was slightly stunned, then understood Prince Kelin's words, and a smile of heartfelt joy instantly bloomed on that cold face.

He agreed!

But not long after, she probably thought of something, and suddenly felt embarrassed again, scratching her slightly flushed cheeks with her index finger.

Would two names seem too deliberate?

Should I add another one...

Of course, this thought only lasted for two seconds in her mind before it automatically dissipated, because this topic really couldn't find a third person who had participated.

She couldn't lie.

"Then... shall I go write the paper?" Yilana said in a small voice.

"Go ahead," Luo Yan nodded happily, "I look forward to your work."

"Hmm... that, this is my first time... writing this kind of paper. If there is anything I don't understand, can I ask you?"

"Of course, happy to serve you."

Watching Yilana's back leave, Luo Yan had an approving smile on his face, guiding the teapot on the table to pour himself a cup of black tea.

A great law sufficient to overturn the foundation of the Academy's existing magic theory was born in this small laboratory in a nearly calm way.

Of course—

Any great discovery, when it is first born, is almost certainly not going to be favored by conservative eyes.

Wanting to shake the high tower is not that easy.

Yilana will probably hit a wall; even with his name on it, it won't change the fact that the paper was written by an apprentice.

However... so what?

Real gold can shine anywhere; even if it's not in the Academy, it can shine on his territory.

He didn't intend to keep his precious apprentices on this snowfield forever.

Just like the diamond he placed in Mr. Andes's hands, this is just bait for him to cast a long line to catch a big fish.

At this time, a burst of hurried footsteps interrupted Luo Yan's thoughts.

Teaching Assistant Keji ran into the laboratory like a gust of wind as usual, running straight to his desk, panting out of breath.

"Prince!"

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

"It must be Heketuo who sent you."

Keji, who was about to speak, was stunned, then scratched his head embarrassedly.

"Yes, Mentor. He said the Council's latest resolution has something to do with you, please go to his office when you have time, he has something to discuss with you... or you can make an appointment for a place and he will go. I see his mood seems good, I think it should be a good thing."

Luo Yan raised his eyebrows unexpectedly.

"Got it, tell him to wait for me for a while, I will go over before evening." ===== CHAPTER 392 =====