Alchemy Principles of Type-Moon World

"Is this the sanatorium my father arranged for me?" Kotomine Kirei pondered silently, a hint of doubt rising in his heart, but more than that, he was filled with joy that his body had almost recovered to its original state. He propped his arms on the edge of the bathtub, feeling the stark contrast between the cold tiles and the warmth of the water. He began to slowly move his body.

He slowly stood up and stretched his limbs slightly, feeling a long-lost strength returning to his body. Kotomine Kirei reached out and took the towel to dry himself. He pushed open the inner door of the bathroom and glanced at the side cabinet, where he found his clothes neatly folded.

The service level of Matou Housekeeping is getting higher and higher.

After leaving the bathroom, Kotomine Kirei stepped into the hallway, his feet creaking softly against the dark brown wooden floorboards. The walls on either side of the hallway were painted a light beige. A simple chandelier hung from the ceiling, emitting a warm and soft glow that illuminated the entire hallway. In the corners, a few potted plants, freshly trimmed and seemingly newly placed, were placed, lush and green.

Kotomine Kirei walked through the corridor and felt that the decoration style was familiar.

Before the Holy Grail War began, he and his father went to negotiate with the three great families as representatives of the Holy Church.

"It's the Matou family," he thought, then subconsciously touched his body. As a priest and agent of the Holy Church, someone who dedicated his body to the Lord, yet his body was healed by a magus. However, Kotomine Kirei didn't care about this; he just felt it was a bit absurd.

As he walked forward, Kotomine Kirei arrived at the living room. The scene before him didn't match his memory, leaving him momentarily dazed. The furnishings, once deliberately cast in shadows, had completely changed. The heavy, oppressive, old furniture had been removed, replaced with simple yet modern pieces. The sofa had been replaced with a comfortable fabric one, and a few small desks and wooden chairs were placed against the wall.

The person sitting at the desk, reading a stack of paper documents, was the one he had only met a few times before.

——The follower who claimed to be the Messiah.

"Awake?" The man put down the documents in his hand, turned his head and glanced at Kotomine Kirei, his tone cold and impatient, "If you have nothing to do, get out. Your father is waiting for you at your home."

Kotomine Kirei subconsciously glanced at the documents on the table. The edges of the pages were slightly curled, obviously having been read over and over again. Although he knew every word, he couldn't understand a single word when they were put together. He could only barely understand the title.

Abstracts of the conference “L-Functions and Arithmetic in the Field of Mathematics (IV)”.

"Excuse me, is it you..."

"My student saved you, Xing Qingfeng." Newton stared intently at the information in front of him, his fingers tapping lightly on the pages. He obviously had no time to pay attention to Kotomine Kirei. He took a piece of white paper from the side, picked up the pen and pondered for a while before writing the title on it:

Correction and Improvement of the Omissions in the Construction of Euler's System in the Proof of Fermat's Last Theorem

Seeing that the Messiah before him had no time for him, Kotomine Kirei raised his hand, made the sign of the cross, bowed slightly, and turned to leave. His footsteps echoed in the quiet room, each step seeming to betray his hesitation.

He placed his hand on the doorknob, the cold metal touch making him feel dazed for a moment. He paused, the question that had been bothering him for a long time coming to mind. This question was like a thorn, deeply embedded in his heart, making him unable to let go.

He didn't know how long the Messiah in front of him would continue to stay in the world, and he wanted to confess to the Messiah, but this was probably his only chance.

He turned back and quietly stood aside, trying not to make any noise, fearing to disturb the Messiah's train of thought. Newton was concentrating on writing on the white paper, the tip of his pen scratching against the paper. The setting sun shone through the window onto Newton, casting a golden glow on his focused face.

------------

"Kenneth!" Newton put down the pen in his hand, tidied up the manuscripts on the desk and shouted loudly. His voice was particularly loud in the quiet room.

He ignored Kotomine Kirei who was waiting quietly on the side, and left the living room and walked straight towards the garden of the Matou residence.

When he reached the garden, he saw a funny scene:

Kenneth and Matou Tsuruno were holding a lawn hose, spraying water at Xing Qingyu non-stop. Xing Qingyu stood in the middle of a lawn, his clothes soaked through, looking disheveled, but his expression was filled with helplessness and helplessness.

"..." Newton stood there, watching the scene in front of him in silence.

"What's going on?" he asked after a long silence.

"Xing Qingjiu came back covered in bird droppings," Kenneth said, continuing to manipulate the hose. The water splashed against Xing Qingjiu's body, making a popping sound. "And the bird droppings seem to be immune to magic. There's no way to clean them up with magic."

Matou Tsuruno nodded and agreed, "Yes, we tried several magic tricks, but none of them worked. So we had to use this method."

..." Newton thought for a moment and asked Xing Qingfeng, "Did you really go and shoot pigeons with a slingshot?"

"Yes, teacher, didn't you say He would like it?" Xing Qingqi said. His tone was a little innocent. "I just took a stone and threw it at the pigeons pecking at the popcorn at the gate."

Newton frowned and looked at Xing Qingqi, who was soaked by the water. After thinking for a moment, he said, "What happened next?"

"Then, inexplicably, a flock of seagulls flew over, and then, um... it started to rain," Xing Qingqi said helplessly. "It's ridiculous. How on earth did they manage to rain so precisely on me without splashing anything else?"

"Ha, it seems He might be in a bad mood lately." Newton smiled. "When I did that back then, I was just hit by a tree full of apples that never bore fruit."

"And then you had an epiphany about gravity?"

"I proved the law of universal gravitation a long time ago," Newton scoffed. "I still don't understand why you associate me with an apple tree. Would a normal person sit under a tree that knows it will drop its fruit and think about things?"

"Okay, Kenneth, please send this paper over urgently." Newton handed the paper to Kenneth.

Kenneth took a few steps closer, took the stack of freshly sorted manuscripts, glanced at the title on the first page, and raised his brows slightly.

"Fermat's Last Theorem?" he read the title. "Is that the famous problem where 'I have a wonderful proof, but the space here is too small to write it down'?"

"Well, I looked it up. At last year's conference, a mathematician named Wiles gave a proof," Newton said, his eyes gleaming with wisdom. "But there are some omissions in the proof. I looked up the relevant materials and wrote an opinion."

Kenneth nodded, his eyes resting on the manuscript for a moment, then looked up.

"Send it to Newton College in Cambridge," Newton added, his tone a bit nonchalant. "However, even without my corrections, they should be able to quickly identify the problem and complete the work independently."

In fact, the winter of 1994, during the Fourth Holy Grail War, was precisely the time when Wiles was preparing to summarize the reasons for his failure in proving Fermat's Last Theorem. Even without Newton's correction, he would have soon discovered the correct proof in his summary of the reasons for his failure.

Just as the Holy Grail calls the dead from history back to the world, a famous mathematical problem from over 300 years ago is about to be solved -

Known as the most fascinating mathematical puzzle in history, the proof of Fermat's Last Theorem stretches across the entire history of modern mathematics. In other words, it bears witness to the development of advanced mathematics.

----------------

Tomorrow, Xing Qingfeng and the others plan to leave Dongmu.

Kotomine Kirei found Newton alone and expressed his desire to seek confession from this man who claimed to be the Messiah.

Kotomine Kirei was one of the few people who didn't object when Newton called himself the Messiah, but simply accepted the fact. His intuition told him that there was nothing wrong with Newton calling himself the Messiah.

To some extent, this intuition might be proof that he was born with divine favor. It was also because of this intuition that Kotomine Kirei successfully won Newton's favor and made Newton agree to listen to his questions.

"Let me guess. You're trapped by your origins, your soul is flawed, and therefore you can never feel happy, right?" Newton took a closer look at Kotomine Kirei's soul and saw through his innate mental flaws. "Have you ever seen a psychiatrist?"

No one had ever seen through Kotomine Kirei's true nature at first glance in his life, which made him even more convinced that Newton was the Messiah.

As for Gilgamesh? The dead are not human.

"Uh……"

"The human body is composed of spirit, soul, and flesh. These three elements form a dynamic system that is interconnected and mutually disturbing." Newton said something that Kotomine Kirei did not understand. "Deficiencies in your spirit will also affect your body, and problems in your body will also affect your spirit."

"I have studied spirits and minds in particular," Kotomine Kirei said, "but I still can't find a way to correct my shortcomings."

"Although I don't know much about modern medicine..." Newton pondered for a moment, "I suggest you get a comprehensive physical examination."

Kotomine Kirei was silent for a moment, pondering Newton's words. This didn't sound like a confession at all, more like a mentally ill patient seeking help from a psychiatrist. However, perhaps for a priest, confession itself could be considered a form of psychotherapy.

"Check your endocrine system or something," Newton said. "It should be relieved. This should be the most effective treatment that can be done without involving your origins—"

"--Then it comes to the question of your origin." Newton sighed.

"..." After a long silence, Kotomine Kirei finally asked, "Do I still bear original sin?"

"There's no such thing as original sin. Anyone who believes Augustine's stuff is mentally ill." Newton chuckled contemptuously. "Although Yahweh's current side is difficult to describe, he truly loves the world."

"But..." Kotomine Kirei hesitated, then added, "I feel happiness when I witness suffering, and I feel pleasure when I witness evil."

"What you gain is only a temporary understanding of the feeling of being human," Newton said. "Due to your innate deficiency, you are unable to identify with the so-called 'self' and refuse to identify with the innate constraints—"

"—Isn't this proof that you were born a human being?"

"Reject the constraints of innate nature, reject the impulses in your blood. Acquire rationality through acquired education, and use rationality to resist your innate bestiality. This is what it means to be human."

"That's your essence, a patient with a congenital defect," Newton replied. "What kind of self do you want to identify with? Think about it yourself."

Newton recognized what Kotomine Kirei had been doing since childhood - pretending to be a normal person, or in other words, he had been trying to fight against his congenital defects.

"...Then can I be redeemed?" Kotomine Kirei asked after a long silence.

"Go see a doctor first, get your endocrine system checked, and then take some medicine. That might help." Newton yawned. "It's not that I can't fix your congenital deficiency, but if it causes extreme mental changes in a short period of time, and you've never really felt confident in yourself—"

"—It's hard to say whether you will still be yourself at that time." Newton concluded, "You need to affirm your self first."

------------

Xing Qingqiu quietly packed his belongings in his room at the Matou residence. His luggage wasn't large, just a few books. The covers were a bit worn, and the corners were slightly curled, showing signs of frequent use. However, the books remained neatly clean, revealing their owner's love for them.

Xing Qingjiu had already memorized the key points in these books, even reciting them fluently. He only brought them with him because he was reluctant to part with the notes he had left on the pages. His notes were densely packed on the margins, occasionally with some scribbled diagrams and marks.

He had almost repaid the favors he owed to Fuyuki. It was just a city he had lived in for less than a year, so there wasn't much to miss.

If there was anything he truly couldn't bear to part with, it would be these books filled with his notes. Kenneth had already booked a flight for tomorrow. They were going to Germany with Emiya Kiritsugu to visit the Einzbern family. Newton said he had something to give to the Einzbern family—

——But Xing Qingyu felt that he just wanted to see Mrs. Alice's daughter.

Xing Qingyu stood at the window of the Matou residence, gazing out at the courtyard through the glass. Night had fallen, and the outside was pitch black, save for a few streetlights emitting a faint glow in the distance. The quiet of the night brought a sense of peace, and he could almost hear the barking of dogs in the distance and the occasional roar of a passing car engine.

"We're leaving tomorrow," Xing Qingfeng sighed. "I've just gotten used to life here, and now I have to say goodbye again."

Xing Qingfu has no household registration, and it is difficult for the Matou family to send him to a high-standard university in a short period of time. After all, the Matou family's influence is only local, so it is quite difficult to send Xing Qingfu to the University of Tokyo.

Therefore, Xing Qingyu will follow Kenneth to study in the UK——

However, Xing Qingfeng's goal wasn't to study magic at the Clock Tower. While some modern magic systems were valuable to learn, his real goal was to pursue further studies at Newton College in Cambridge.

After all, he needed to complete the most basic scientific research training before he could truly embark on the path of exploring the world. From an academic perspective, Xing Qingfeng had only inherited a tiny bit of Newton's alchemy. After all, Newton was not a good teacher, and the teaching time was only a week.

——What he truly inherited was Newton’s ideas and way of thinking.

Suddenly, there was a knock on the door. Xing Qingyu was startled and looked up. There was a gentle knock on the door, the rhythm was a little rapid. He walked over and opened the door, and saw the youngest son of the Matou family, Matou Shinji, standing at the door.

Shinji Matou stood there somewhat stiffly, his eyes flickering, obviously having something to say but being too embarrassed to speak.

Xing Qingqi smiled, rubbed Shinji's head and welcomed him into the room.

"Shinji, it's so late, what's going on?"

"Um...I..." Matou Shinji hesitated for a moment, but finally mustered up the courage to say what he wanted to say: "I want to learn magic!"

"Ok?"

"My dad and Uncle Kariya locked the library and told me not to go in until the contents were sealed," Matou Shinji said with a pout. "When I mentioned I wanted to learn magic, they got really excited and told me to give up the idea."

"I know that magic makes my father and Uncle Kariya very sad. Uncle Kariya was quite high-spirited when he came back, but after getting involved in magic, he became very scary."

"But, aren't you the ones who changed all this also magicians?" Matou Shinji said seriously, "I don't want to learn magic that makes people scary. I want to learn your magic, the kind that can bring back Uncle Kariya."

Shinji Matou actually admires his uncle very much. Even in the original work, he was unaware of the tragic death of Matou Kariya. He admired Matou Kariya who had cut off ties with his family very much, and even revealed his desire to travel like Matou Kariya.

Matou Shinji, who admired Matou Kariya, witnessed his uncle's tragic condition and his uncle's resurrection.

——He longed for this kind of power, wanted to have the power to not be powerless when something like this happened.

"There's something wrong with the way Kariya-kun and the others raise their children..." Xing Qingfeng thought as he rubbed Shinji's head. "In this kind of situation, the more you deny a child, the more they want it."

He respected the Matou family's desire for their children to have ordinary happiness, but he would not arbitrarily deny the children's dreams.

"Do you want to learn?" Xing Qingfeng squatted in front of Matou Shinji, trying to make his eyes level with his. "But it will be very tiring."

"I'm not afraid!"

"Okay, then let's make a deal, okay?" Xing Qingqiu turned around and pulled out a book from his luggage. "Study hard from now on. When you can understand the contents of the book, have your father contact me."

"I'll teach you magic then, how about that?"

"Then we have a deal!" Xing Qingqi raised his pinky finger. "How about we pinky promise?"

"As expected, we can't deny a child's dream." Xing Qingfeng thought secretly, "Let mathematics deny the child's dream."

He handed a thick hardcover book to Matou Shinji——

——"An Epsilon of room: I: Real analysis", Chinese name "ε space I: real analysis", a textbook on functional analysis.

To describe this book simply, it is a textbook that only graduate students will use.

Xing Qingqi believes that if things proceed at a normal pace, Shinji Matou will have to at least reach adulthood to understand the contents of the book. By then, he will have his own set of values and will be able to take responsibility for his own choices.

If he still wanted to learn magic at that time, Xing Qingjiu would naturally teach him everything he knew.

The only problem was that, at that moment, Matou Shinji had no idea what terrifying demonic whispers lay within the mouth of his angelic, amiable, and easygoing brother Xing. In Matou Shinji's mind, Xing must have handed him a book like the introductory magic notes from a fantasy novel.

----------------

I've sped up the pace a bit, so this chapter is a bit fragmented, please forgive me!

Interested readers can explore the history of the successive proofs of Fermat's Last Theorem, which truly runs through the development of advanced mathematics. Wiles, the final prover, didn't actually prove it all at once. His initial proof was quickly criticized for flaws, which Wiles acknowledged and promised to address. But after eight months, nothing was accomplished. Wiles and his collaborators were about to give up. Taylor, his collaborator, decided to return to Cambridge a month later, and Wiles published his manuscript, announcing his failure to the world.

But before doing so, Wiles needed to write down the reasons why his proof failed. After all, knowing why something is wrong is equally valuable in science. While sorting through the reasons for his failed proof, he discovered the idea that would truly prove Fermat's Last Theorem. This happened in the winter of 1994, during the Fourth Holy Grail War. I think this synchronicity is quite romantic to a certain extent.

I stayed in the library for a long time today and got home too late, so the update is also late. I am really sorry.

The above is all. Please vote, comment and feedback. If there are any uncomfortable or wrong parts in the reading, I will change them. Thank you!

------------

I recommend this book, it's a fan fiction of Arknights, it seems to be similar to the road novel? If you are interested, you can take a look

Ark Journey

Volume 1: From the Fourth War onwards, the Refined No Doctor's Eightfold Path, the Rising of the Land of the Golden Apprentice: Chapter 64: The Diffusion of the Million Holy Grail War