Chapter 390: A Groundbreaking Equation
The Magic Science Laboratory is as bustling as ever today.
The apprentices personally selected by His Highness Colin gathered here spontaneously after class, and the air was filled with youthful and enthusiastic vitality.
certainly.
There was no shortage of murmurs of complaint here either.
After all, geniuses are only a minority, and most people are just using mortal wisdom to do things that are within the reach of mortals.
"God bless you, this is too hard!" Jamie, the carpenter's son, sighed over a sheet of paper covered in circles and straight lines. "'Construction of a regular heptagon with ruler and compass'...it looks so simple, why can't I do it?"
He wasn't the only one troubled by the problem.
Beside him, the watchmaker's daughter Ram was also holding her chin with a distressed look on her face, muttering to herself.
“…how can a walker walk across all seven bridges in one go without repeating or missing any, and finally return to the starting point?”
Jamie, who was measuring on paper with a ruler, was stunned for a moment and asked subconsciously.
"Is this some kind of brain teaser?"
"No, this is a problem His Highness Colin assigned me," Ram shook his head. "He told me to study it in my spare time and try to connect it with geometry problems."
"Hiss... I think about it, it seems interesting." Jamie scratched his head, muttered, and buried his head in the draft paper again.
Ram stretched and leaned back in his chair.
"Come on... Oh, by the way, does your regular 17-gon problem require a ruler and compass? Only a ruler, or both?"
Jamie shook his head.
"You may use a compass and ruler, but they must be unmarked and you cannot make marks on them."
Ram: "A ruler without a scale? What a strange question..."
The two of them communicated in low voices.
Although there has been no progress in solving their respective problems, they already have ideas for solving them.
Not far away, Ophelia was also thinking about her own problem, but her question was more abstract -
[As the number increases, does the proportion of prime numbers in natural numbers decrease? If so, please provide a proof.]
Saint Sis, this was the first time she had heard such a strange question!
But is it really useful to study this stuff? !
The Royal Academy of Arts in the Holy City where she had studied had taught her about prime numbers, but it was only appreciated as a symbol of "harmony" and "sacredness." Some priests, however, believed that they contained a code left by Saint Francis of Assisi.
But no matter what, it will not affect the spellcasting of the extraordinary person, nor will it make a weak magician suddenly become strong.
Just as she was worrying about this seemingly useless question, a familiar figure suddenly appeared in the corner of her eye.
That person was none other than Ilana!
The girl, who was usually as calm as water, was now nervously clutching a notebook in her hands, with an unusual blush on her cheeks.
She bit her lower lip lightly with her pearly teeth, took several deep breaths, and finally took a step forward and walked towards His Highness Colin.
etc--
What is going on? !
Ophelia's heart was filled with alarm.
That look might be unfamiliar to the nerds in Xuebang, but she, who came from the Holy City, knew what that expression meant very well!
After all, she would encounter such presumptuous guys every now and then...
Thinking of what Ilana was going to do next, Ophelia felt her heart tighten slightly, and the mathematical symbols in her mind instantly dissipated like smoke, leaving no trace.
Could it be... that she was going to express...her feelings here?! In front of everyone?!
This seemingly absurd idea exploded in Ophelia's mind like a thunderclap, and then a complex emotion mixed with panic, jealousy and curiosity instantly gripped her heart, making her, who had been calm and composed, lose her composure for a moment.
She stood up almost subconsciously, holding the "Advanced Mathematics" that was like a heavenly book, pretending to pass by the aisle casually, but in fact she quietly approached the desk and pricked up her red ears.
Not caring——
She believed that His Highness Colin was not such a casual person and would definitely not easily agree to an inexplicable request.
I am just standing on the position of a lady from the Holy City, wanting to see what the girl from Pierce Province intends to do to His Royal Highness!
However, the first words Ilana said made Ophelia, whose heart was filled with alarm, freeze in place.
"tutor……"
There was a barely perceptible tremor in the delicate voice, but an unprecedented determination burned in those clear eyes.
"Remember the 'path optimization equation' I mentioned to you earlier?"
"I might... have actually found it!"
Path optimization equation?
Ophelia stood there in a daze, her panic instantly extinguished by the complex and mysterious mathematical concepts.
But soon, a hint of curiosity arose in her heart.
Of course she knew about the path optimization equation, which seemed to be the unfinished project of the former owner of this laboratory, Mr. James Wally.
only--
How could a mere Iron-level apprentice solve a problem that even the genuine instructors had a hard time solving?
Not really...
Ophelia swallowed her saliva and hid behind the "Advanced Mathematics" textbook, staring at this side with curiosity in her eyes.
Ilana didn't notice her presence; all her mind was completely immersed in the great discovery she was about to make.
She carefully spread out the notes in her hand in front of His Highness Colin, and her voice, which had been trembling with excitement, gradually became clear and full of confidence.
"The calculus of variations you taught me was like a key. It made me understand that we can regard 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 extreme value..."
"Let's get straight to the point, Ilana," Luo Yan said concisely. "There's no need to go into all the details."
"Yes, Your Highness."
Ilana nodded slightly, and her speaking speed suddenly changed, going straight to the point from the opening remarks.
Ophelia was confused.
Even though she tried very hard to listen, those abstruse concepts were like obscure spells, preventing her from comprehending the mysteries.
However, she understood the expression.
As Ilana spoke, His Highness Colin's eyes, which always had a lazy smile, gradually brightened up.
It was a pure look.
Just like an artist, looking at the work of art he has carved with his own hands with satisfaction.
Ophelia suddenly felt a little jealous.
Obviously I can do it too... and obviously she was here first.
"So, if my inference is correct... this is what the equation should look like."
Ilana finally finished.
She raised her head and looked at her most respected mentor with nervous and expectant eyes, waiting for the prince's evaluation.
There was a brief silence at the desk.
Luo Yan looked at the beautiful and complex differential equation on the manuscript paper, and he was surprised and filled with emotion.
Although he has influenced two worlds, the sense of accomplishment is still not as great as watching the saplings he planted with his own hands grow into towering trees and bear abundant fruits.
This feels so good.
After savoring the pleasant comfort for a moment, Luo Yan looked up again, looked at Ilana standing in front of the desk, and said with a smile.
"Excellent derivation. Honestly, your application of the calculus of variations is probably even better than mine..."
Ilana lowered her head in fear.
"Teacher, you are too modest..."
"No, I'm not being modest. I always say what I think," Luo Yan said casually with a smile. "After all, I'm not a professional scholar. I know the facts of some things, but I may not know the reasons behind them... But I'm very relieved to have met you. Your talents have filled the gaps in many areas that I lack."
This is the truth.
Of course he knows the Euler-Lagrange equation, but if he wants to write out the derivation process, he can only ask the players to search the Internet for him.
Ilana, who was standing at the desk, and Ophelia, who was 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?"
Ilana thought for a moment and whispered honestly.
"We can use it to find the critical value function of the functional..."
"Not only that," Luo Yan shook his head slightly, then continued with a smile, "we can also use it to describe the motion of various systems, whether it's the motion of particles 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."
"Depending on its characteristics, we can not only greatly simplify the design of the magic circle, but also reduce the loss of energy in the magic crystal during unnecessary circulation."
This is definitely a groundbreaking discovery!
Perhaps it won’t be long before a new discipline called “Analytical Magic” will be born in this world, and the research on extraordinary powers will also reach a new level!
"Ilana," he said, looking at the girl standing in front of the desk. His voice was gentle and serious, and every word seemed to carry the weight of recognition. "You have created a miracle."
Ilana said softly, her cheeks flushed as she didn't expect her mentor to be so optimistic about her research.
"Am I... that exaggerated?"
"Exaggeration? I think the word miracle is too conservative!" Luo Yan smiled and nodded. "I believe that any magician who has learned about Mr. James Wall-E's research can see the value behind this research. I suggest you submit your article to the Sage's Journal. This research result deserves to be recorded in the history of the school!"
"The Sage's Journal?! But I..." Ilana subconsciously held her breath. She had never thought that she could submit such a thing, and she never dared to think that her paper could reach the top of this great Sage's Tower.
"That's the spire of the Great Sage's Tower? I guess that's what you're thinking, right?"
Looking at Ilana, whose thoughts were hit upon by what he said, Luo Yan smiled and continued in an encouraging tone.
"It has nothing to do with age. Most mathematicians 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 was slightly open, and she was speechless for a while.
Not only was she shocked, but also Ophelia, who witnessed it all with her own eyes. Her beautiful face was completely filled with shock.
Besides the shock...
She also gradually felt a little ashamed.
Especially when she saw the pure and sacred academic resonance between the two, a burning shame crept up her cheeks.
What kind of filthy things were I thinking about just now?
She felt ashamed of her own thoughts!
Ophelia retreated silently.
She lowered her head, holding the advanced mathematics textbook to her chest, and for the first time felt the weight of "wisdom".
At the same time, a sense of unwillingness welled up in her heart.
Since Ilana can do it——
There's no reason why the Castellón lady couldn't do it!
One day, she will also reach the top of this tower!
By her own strength!
…
Watching Ophelia quietly leave from the corner of his eye, Luo Yan raised the corner of his mouth with a barely perceptible smile and leaned back in his chair.
It seems that my previous "flattery" did touch the heart of this duchess, and she will probably spend more time on mathematics in the future.
He cleared his throat, looked at the stunned Ilana and continued.
"A great discovery deserves a name of its own. Ilana Octavia, this is your honor."
He paused and made the announcement in a solemn and serious tone.
"Let's call it... 'Ottavia's Equation'!"
After all, there is no Euler or Lagrange in this world, and forcing names from Earth here will only make people confused.
Luo Yan thought Ilana would be very excited, but to his surprise, that cold face covered with blush suddenly fell.
After a long silence, she suddenly raised her head, looked at Colin who was sitting behind the desk with sincere eyes, and opened her mouth to speak.
"Your Highness, I... have a request."
"Oh? What request?" Luo Yan said with a pleasant expression, crossing his fingers on his knees.
Ilana whispered.
"Completing this equation wasn't my own effort. Without your guidance and the mathematical methods you taught me... I would never have been able to find it so quickly."
It was true that she had completed this equation independently, but she always had a feeling 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 himself may not have noticed it, she clearly saw the calmness hidden behind the kind eyes...
It was precisely because she believed that this formula must exist that she was able to find it so quickly from the ocean of numbers.
If he took all the glory for himself, she would not be able to accept it either morally or logically.
Looking at the stubborn Ilana, Luo Yan smiled.
"I beg to differ. I did give you some guidance, but that doesn't mean you didn't do the work. Ilana, you could be more confident. I'm pleased that you've been able to apply the tools I gave you to such a high level. I've given similar lessons to many people, but you're the first and only one who has truly integrated what I've taught you."
"I know... but your proposal still makes me uneasy. Please forgive my immaturity and presumptuousness." After a pause, Ilana looked at him with a fiery and determined gaze and whispered her request, "I just wonder if I can... put your last name first?"
"Let's call it the 'Colin-Ottavia Path Optimization Equation'!"
She said this almost in a pleading tone, with a resolute look as if she would not write the paper if he did not agree.
Looking at Ilana's serious eyes, Luo Yan was slightly stunned, and then couldn't help but smile.
This little bit of false reputation actually means nothing to the gods.
In any case, when people study her life in the future, they will always be unable to avoid her name and the "scientific" school she led.
The Chosen Ones do not share the glory of God; both sides share honor and disgrace. Long ago, he too was puzzled as to why the gods did not keep all the power of faith to themselves, but as he journeyed, he gradually realized that the secret to becoming a god lies in "sharing."
However, if just a nod of his head could make a smart girl feel at ease, he would certainly not refuse to fulfill her wish.
After all, this world is still in the feudal era, and the spark of enlightenment has just been lit. Without sufficient support, even real gold will be buried in the dust of reality.
In fact, the person he originally prepared to rely on for her was Ophelia.
It's just a pity that the genius is too fast. Miss Castellón had just learned the calculus of variations when Ilana had already reached the finish line.
Looking at Ilana with a serious expression, Luo Yan shrugged lightly and said in a joking voice.
"It seems future students will have to remember one more name."
Ilana was slightly stunned, then she understood what His Highness Colin said, and a smile of genuine joy instantly bloomed on her cold face.
He agreed!
But not long after, she probably thought of something and suddenly felt embarrassed, scratching her slightly red cheek with her index finger.
Wouldn't two names seem too deliberate?
How about adding another...
Of course, this thought only lasted two seconds in her mind before it automatically dissipated, because there really was no third person who had participated in this project.
She couldn't lie.
"Then... I'm going to write my paper?" Ilana whispered.
"Go ahead," Luo Yan nodded happily, "I'm looking forward to your work."
"Um... well, this is my first time... writing a paper like this. If there's anything I don't understand, could you please help me?"
"Of course, I'm happy to help you."
Watching Ilana's back as she left, Luo Yan had an approving smile on his face and guided the teapot on the table to pour himself a cup of black tea.
A great law that could overturn the foundation of the school's existing magical theory was born in this small laboratory in an almost peaceful manner.
certainly--
Any great discovery, when it is first made, will almost certainly not be favored by conservative eyes.
It's not easy to shake the tower.
Ilana would probably run into a wall, because even if she put her own name on it, it wouldn't change the fact that the paper was written by an apprentice.
But...so what?
Real gold can shine anywhere, even if it is not in Xuebang, it can be found in his territory.
He had no intention of leaving his beloved apprentices on this snowy plain forever.
Just like the diamond he placed in Mr. Andes's hand, it was just the bait for his long-term plan to catch a big fish.
At this time, a burst of hurried footsteps came from afar, interrupting Luo Yan's thoughts.
As usual, Assistant Professor Corgi ran into the laboratory like a gust of wind and trotted straight to his desk, panting.
"Your Highness!"
Before he could speak, Luo Yan raised his head with a knowing smile on his face.
"Hector sent you here, didn't he?"
The Corgi was about to speak when he froze for a moment, then scratched his head embarrassedly.
"Yes, mentor. He said the council's latest resolution concerns you. He asked you to stop by his office when you're free. He has something he'd like to discuss... or you could arrange for him to go somewhere else. He seems to be in a good mood, so it's probably a good thing."
Luo Yan raised his eyebrows in surprise.
"Got it. Ask him to wait for me for a while. I'll be there before evening."
(End of this chapter)
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