"... How did you know?"
So she really was a princess. If she wasn't, this would have been a little embarrassing. I knelt on one knee as Gwendolyn had taught me and spoke.
"I almost committed the discourtesy of failing to recognize Your Highness. Please forgive me."
A moment later, she opened her mouth to speak.
"Raise your head and rise."
I followed the princess's command. When I lifted my head, I saw no sign of shock or anger on her face. I knew that look.
It was the expression of a scholar who couldn't contain their curiosity.
She spoke.
"How did you know? I was using a royal disguise device."
I answered the princess.
"The outlines were faintly blurred. A collection of separate points can never create a truly perfect curve."
The princess's eyes shone sharply.
"If it were you, how would you improve this technology?"
"You would have to define the changes using a continuous graph connecting each point, using vectors. To calculate the rate of change..."
"Calculus would be essential."
She reached the conclusion before I could even finish my sentence. Her comprehension was above average. I had a feeling she could be a good business partner.
The princess gave a faint smile.
"To be honest, I don't know much about vectors and the like. But I have already read 'Principles of Calculus', a work of both your and Valerius's efforts, dozens of times."
"I already know everything. I heard your story from the Dean of the Magic Tower. Including who the true master of Calculus is."
She lightly patted my shoulder.
"I have just returned from the Imperial Palace, where I recommended you for a First-Class Medal of Honor. So stop hiding in the shadows and come out into the world."
"It wasn't that I wanted to hide..."
I muttered under my breath. The water was already spilt. Struggling any more would only get me on the bad side of the Imperial Court.
I nodded calmly.
"If it has already been decided, I will accept it."
Perhaps surprised by my obedient attitude, a curious light flickered in the princess's eyes for a moment. She smiled, seemingly satisfied.
"First, I have made a donation to your school in my name. It is an honor to sponsor a genius like you."
I bowed my head. I lowered my head gratefully.
"Thank you, Your Highness."
I was already getting 100,000 gold a week, but the more research funds, the better. I must not forget my days as a broke graduate student in my past life. Remember the days of starvation.
"However, there is just one thing I would like to say."
"Speak."
"I will gratefully accept the donation, but I am no genius. If I have been able to see something new, it is because I am a dwarf standing on the shoulders of giants."
Princess Isolde tilted her head.
"A dwarf, you?"
"Yes."
It was a rather famous saying on Earth, but it seemed not to be the case here. Well, of course. The Isaac Newton who would have made this phrase known doesn't exist here...
I added an explanation.
"The ancients must have had to start all their research from scratch. But I can learn of all their trials, errors, and fruits of their labor through just a few papers."
Calculus wasn't just whipped up out of my head. If it was, then I really would be a genius. Newton himself, one of the two masters of calculus, said so.
He said he too could see further because he stood on the shoulders of the scientists who came before him. That was true even in this world. Valerius had already devised a form of classical calculus represented by his 'Method of Continuity'.
It seems he set it aside because he couldn't overcome 'Achilles and the Tortoise' with the 'Method of Continuity'... but he was only a single step away. If he had researched just a little more, Calculus would have have been born from him or his successor.
"Therefore, I am neither a genius nor a giant."
In my past life and in my current one, I am just a graduate student standing on the shoulders of a giant. The princess stared at me for a moment. Her brilliant golden eyes seemed to peer right through me.
Soon, she smiled softly.
"I see. I understand what kind of person you are, Master Upperhills. In that case, help me with something, at least to earn the donation I made."
The princess gave me an unexpected request.
"I plan to give a speech at the upcoming medal awarding ceremony. I would like for that speech to be heard clearly by everyone gathered in the plaza. Can you do it?"
"If it's something like that, of course. Anytime."
I nodded readily.
On the day of the medal awarding ceremony, the plaza in the Imperial Capital was so packed with people there was no room to stand. As I sat drained of energy in the recipient's seat, the princess approached me.
"Are you ready?"
"Yes, Your Highness. It's perfect."
I had already cast my spells over the entire plaza. Since this was my sponsor's first request, I planned to deliver the best possible result.
"I'm looking forward to it."
The princess left a short remark and returned to her seat. Before long, the ceremony began. Clap, clap, clap, clap!
A thunderous round of applause erupted at the declaration of opening. After that followed the pomp and circumstance that glorified the majesty of the Imperial Court. I let that go in one ear and out the other.
But I did join in the moment of silence for the fallen heroes. The son of the bell tower keeper, Barnabas, would be among them. Time passed, and at last, it was our turn.
"Great Mage Valerius!"
"Senior Researcher Giuseppe Guarneri!"
"New Researcher Isaac Upperhills!"
Just as the princess had promised, all three of us were awarded the 'First-Class Sacred Golden Lion Medal', the Empire's highest honor. Senior Giuseppe was overcome with emotion and wiped away his tears, while Valerius just smiled silently. And as for me...
"I expect great things from you in the future."
"Thank you."
I was able to go through the etiquette without a hitch, just as Gwendolyn had taught me. What a relief. I didn't make any mistakes.
After all the medals were awarded, Princess Isolde finally stepped to the center of the stage for her speech. Now's the time. I activated the spells I had set up in advance.
Sound control was easy since I'd already done it during the Bell Tower incident. The princess's speech would now be heard clearly by the citizens in the back, and not be uncomfortably loud for the nobles at the very front. The princess would probably be moderately satisfied with just this.
But a truly 'well-heard speech' isn't made of sound alone. Visual effects are just as important. I activated the second spell.
E = 1/ r² First, I create a dazzling sphere behind the princess's back. Now, everyone in the plaza will think a divine halo is shining behind the princess. But I have no intention of stopping here. nisin01=n2sin02 Now it's time to refract the light.
To create a rainbow. I gathered water vapor from the atmosphere in the vast space between the light source and the crowd, arranging it at the optimal density. After going to all this trouble, it would be a shame if the result was just a regular rainbow.
My goal is to show them a circular rainbow, visible only from the most perfect angle. Pi ∝ e^(-εi / KT) And with that, I finished the probabilistic optimization of the water vapor distribution according to the crowd's distribution. Spell construction complete.
Manifest. Flash!
The crowd murmured at the sudden light. By now, they would be witnessing the sight of a circular rainbow floating between themselves and the princess. They would feel as if the princess was communicating with each and every one of them.
Listening in this state, even a recipe for kimchi stew would sound moving. Valerius, who was also on the stage, looked at me and muttered softly.
"Hah... He creates a new spell that's never been seen before every single week."
"Be quiet. The princess is speaking."
"Ahem."
The citizens were mesmerized by the wondrous sight. Now, everyone's attention was focused on one place. The princess, Isolde Arcanus.
I looked at her. 'Are you pleased, client?' Princess Isolde turned toward me and smiled subtly.
Good.
Mission 'satisfy the sponsor' is a success. I certainly hope you'll continue to support our school in the future.
Isolde watched Isaac's magic in awe.
"I only asked him to amplify the sound, but he's gone and created an entire stage."
She didn't know exactly what kind of magic it was, but the gazes of the citizens had changed. She looked at the black-haired young man standing awkwardly in a corner of the stage. The corners of her mouth turned up on their own, though she hadn't intended them to.
'Where did such a genius fall from?' He was a great blessing to the Empire. Isolde's gaze turned toward the citizens of the Empire.
"A short while ago, I had a curious conversation with a certain researcher."
Her voice, carried by Isaac's magic, resonated clearly in the hearts of everyone present. From the seats of the nobles in the very front to the commoners on the outskirts of the plaza. The voice of 'Isolde', the princess most beloved by the citizens, reached them all.
"I praised his research achievements and asked him, 'How can you produce such outstanding results?'"
Isolde recounted the 'giant and dwarf' analogy that Isaac had told her. Cutting out what was unnecessary, and embellishing the parts that would touch their hearts.
"He compared himself to a dwarf and gave all the credit to the mages who came before him."
The princess subtly added the contributions of fallen soldiers to this.
"The same must be true for the fallen heroes who made the present Empire possible. There may have been no single hero among them who turned the tide of war. But it is thanks to the sum of their sacrifices that the Empire exists today."
Many families of national patriots reside in the Imperial capital. They are even very active in participating in events. This time was no different.
A gentle wave of emotion rippled through those who had lost family and friends. Isolde continued with her next words at the very moment the audience's emotion peaked.
"That's right! All of us may be dwarfs standing on the shoulders of the giant that is our ancestors!"
She paused for a moment, then shouted with a charisma that overwhelmed the entire plaza.
"However!"
The gazes of the teary-eyed citizens, who had been looking at the ground, turned back to her.
"Is it not a great feat in itself to devote one's entire life to climbing and climbing the giant's shoulder, to finally show us a new horizon that no one has ever seen before?"
In response to her words, the citizens shouted.
That's right! Indeed!
Their shouts were followed by more shouts, like a wave. Isolde was a little taken aback by the response. 'Usually, the response isn't this good...?'
But today, the atmosphere was somehow different. The sunlight, the wind, the temperature, the humidity—everything seemed to have been fine-tuned for this very speech.
'Isaac Upperhills...
Is it because of him?' There was no other way to explain the current situation. 'He's a talent that would do well even in the Imperial Bureau of Propaganda.'
Isaac was a very useful man. The princess pointed to the sky and said.
"With that dwarf's discovery, we may one day be able to predict the orbital periods of all the planets, including the cycles of the sun and moon!"
Waaaaaah!!
"Calculus will be the vanguard of a brilliant future!"
"And it blossomed in the hands of a son of the Empire, 'Isaac Upperhills', after passing through the hands of the Great Mage Valerius!"
Isaac!! Isaac!!!
The tip of Isolde's finger pointed at Isaac. Isaac's eyes were shaking as if in an earthquake. The citizens were ecstatic.
At the fact that Isaac's background was not so different from their own. And that despite that, he had become great.
"Is the title of 'dwarf' even fitting for such a person?"
No!
It is not! The crowd shouted. At the top of their lungs.
To them, the words of the princess, wreathed in a shining halo and a rainbow, were like the words of a god.
"Then what should we call him?"
A hero!
Someone started the chant, and others began to join in.
Hero! Hero!
"That's right. He is a hero! The researcher 'Isaac Upperhills', who called himself a dwarf, is a hero who stood upon the shoulders of Sir Valerius!"
Soon, the plaza was filled with an explosive cheer so loud it seemed to shake the ground.
Waaaaaah! Hero! Hero!
Giuseppe shed hot tears as he patted Isaac's back repeatedly, while Valerius watched the scene with a pleased smile. And Isaac, standing at the center of all that glory... ...muttered blankly amidst the pouring cheers.
"What have I done...?"