The Lord Demon King is Unfathomable!

Chapter 1329 - 389: The Epoch-Making Equation (Part 2)

She carefully spread out the notes in her hand in front of Prince Colin, her voice, trembling with excitement, gradually becoming clear and filled with confidence.

"The variational method you taught me is like a key that made me understand that we can view the 'total cost' of the whole 'path' as a solvable function. And I discovered that as long as every point on a path satisfies a particular equilibrium condition, the total cost S of this path will achieve an extremum..."

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

"Alright, Your Highness."

Ilana gently nodded, her speaking pace abruptly changed, transitioning directly from the preamble to the main topic.

Ophelia listened in a fog.

Even though she tried her best to listen, those profound concepts were like obscure spells, leaving her clueless about the mysteries within.

However, she could read expressions.

As Ilana explained, the eyes of Prince Colin, always carrying a hint of a lazy smile, were gradually lighting up.

It was a look of pure gaze.

Like an artist contentedly viewing the artwork they crafted by hand.

Ophelia suddenly felt a bit jealous.

Clearly, she could do it too... and clearly, she was the one who came first.

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

Ilana finally finished speaking.

She raised her head, gazing expectantly and anxiously at her most respected mentor, waiting for the prince's assessment.

A brief silence fell over the desk.

Luo Yan looked at the line of beautiful and complex differential equation on the draft paper, his heart filled with joy, and couldn't help but be emotional.

Though he had influenced two worlds, this sense of accomplishment still didn't compare to watching this sapling he cultivated grow into a towering tree, bearing fruitful achievements.

This feeling was truly wonderful.

Savoring this delightful comfort for a moment, Luo Yan raised his head again, looking at Ilana standing before the desk, and said with a smile.

"The derivation process is excellent, honestly, your application of the variational method is probably even above mine..."

Ilana bowed her head in apprehension.

"Master, you're being modest..."

"No, I'm not being modest at all, I always say things as they are," Luo Yan smiled casually, "After all, I'm not a professional scholar, there are things I know in theory, but don't necessarily understand their essence... I'm very glad, however, to have met you, your talents fill many of my gaps."

It's the truth.

He certainly knew the Euler-Lagrange equation, but if he had to write out the derivation process, he'd have to have players search for it online.

Ilana, standing in front of the desk, and Ophelia, who was eavesdropping, both blushed, albeit for entirely different reasons.

Luo Yan cleared his throat, smiling as he continued.

"Returning to the main topic, do you realize you've just accomplished something incredible?"

Ilana thought for a moment, then honestly whispered.

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

"Not just that," Luo Yan gently shook his head, smiling as he went on, "We can also use it to describe the motion of various systems, whether it's the movement of mass points in a force field or the motion of magic elements in a magic power field... as long as the system conforms to the 'principle of least action', theoretically, this formula can be applied."

"By relying on its properties, we can not only greatly simplify the design of magic arrays but also reduce energy loss in demon crystals during unnecessary circulation stages."

This is absolutely an epoch-making discovery!

It might not take long before a new science—"Analytical Magic Mechanics"—is born, and the research on extraordinary power will take a new step forward!

"Ilana," looking at the young girl standing in front of the desk, his voice warm yet solemn, with every word seemingly carrying the weight of recognition, "you've created a miracle."

Unexpectedly, her mentor held her research in such high regard, Ilana felt her cheeks heat up and quietly said.

"I... is it really that exaggerated?"

"Exaggerated? I actually think the word 'miracle' is overly conservative!" Luo Yan nodded with a smile, "I believe any mage familiar with Mr. James Walli's research would see the value behind this research. I suggest you submit your work to the 'Sage Report', this research outcome deserves to be recorded in the chronicles of the Academic State!"

"The 'Sage Report'?! But I..." Ilana instinctively held her breath, she never thought such a thing could be submitted, not to mention dreaming of her paper reaching the top of the Tower of Great Sage.

"Isn't that the pinnacle of the Tower of Great Sage? I bet that's what's on your mind, right?"

Seeing Ilana's thoughts accurately guessed, Luo Yan smiled, using an encouraging tone to continue.

"This isn't related to age; most mathematicians' most outstanding mathematical accomplishments are actually completed in their youth... uh, most that I know of."

The sudden reality left Ilana in a state of confusion, slightly opening her mouth, rendering her speechless for a moment.

It wasn't just her who was shocked; Ophelia, witnessing this all unfold beside her, her pretty face was entirely filled with an expression of awe.

And beyond the shock...

She gradually felt a tinge of guilt.

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