Alchemy Principles of Type-Moon World

His mind was so caught up in calculations that he ignored his body's protests and the throbbing in his chest. He only needed to calculate a little more, push forward a little further, break through a level...

If you complete this question, Order Xing will definitely be very happy.

This was the last bit of willpower that kept him going, but unfortunately, his body no longer allowed him to continue calculating.

Grothendieck stretched out his hand and gently touched the magic mark that Flatt had implanted in his body through his skin with his fingertips.

The fingertips were slightly cool, in stark contrast to Flatt's hot skin.

Before he completely lost consciousness, he seemed to hear a voice——

——A familiar yet rare panicked voice.

"Flat!"

The wooden study door was flung open, its heavy thud causing the air to tremble slightly. Xing Qingfeng practically rushed into the room with anxious steps.

"Flat, what's wrong with you? I was just outside..."

The hurried words stopped abruptly the moment he saw Flat.

——He was stunned.

The scattered draft papers in the study were densely covered with formulas. The dim sunlight fell on Flatt through the curtains. He was slumped in the chair, his whole body soaked in sweat, his golden hair stuck to his forehead, and his chest heaving violently.

But... apart from this disheveled look, he didn't seem to be in any serious trouble.

"Hello, Order Xing is here," Flatt said, his voice a little unsteady, the corners of his mouth slightly raised, as if trying to hide his fatigue, "Sorry, I think I failed the challenge."

Xing Qingfeng didn't respond immediately, but instead frowned, silently observing his condition. He reached out and placed a hand on Flat's forehead, sensing a slightly higher-than-usual temperature. His gaze then fell on the table, scanning the unfinished formulas and calculations. The handwriting left deep indentations on the paper, clearly from excessive force. Faint magical fluctuations still lingered in the air, the chaotic, high-frequency presence of which made him purse his lips.

"What's wrong...?" Pierre's voice came from behind him. He stepped quickly into the study, his eyes swept between Flat and Xing Qingjiu, and keenly noticed the unusual atmosphere in the air. "I think Xing..." He was about to continue asking when he was interrupted by another cold voice.

“Ah, nothing,” Grothendieck lazily leaned aside, his tone as calm as if he were discussing the weather. “Wait outside for a moment.”

"But..." Pierre frowned slightly, obviously a little worried, but was interrupted by Grothendieck's unquestionable attitude.

"Okay, go ahead," he yawned lazily, his tone still casual, "and help me make dinner."

Pierre looked inside the room hesitantly, and finally sighed. Without saying anything more, he turned and walked out of the study, closing the door behind him.

The room returned to silence. Xing Qingyu took a deep breath and fixed his eyes on Grothendieck. "What... happened to him just now?" he asked in a low voice, his tone revealing his unconcealable anxiety.

“If you can’t figure it out, then you can’t figure it out. You actually force it.” Grothendieck sighed softly, his eyes glancing at Flatt, who was still slumped in his chair. “This kid can’t intuitively find the corresponding method, but he can intuitively see the direction and outline—”

"—So the child just tried his best to calculate, trying one thing at a time and making mistakes, that's it."

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OK, what's left is to wrap up this part of the story, and then it's time to continue with a chapter of daily life before starting the next part. I want to speed up but I always feel that there are too many things to say and I can't go fast. I'll try to compress the amount of information as much as possible, but if I compress it too much, the plot will be too dry and like an outline. I have to sort out the details.

The above is a new book by a new author. Please vote and give me feedback. Thank you!

Volume 60: Xing Qingfeng's Perfect Arithmetic Classroom: . Go buy a game console

The room was filled with a faint scent of ink. The setting sun outside the window gradually slanted, and the light shone through the glass onto the scattered papers.

Flatt leaned back in his chair, his back nearly drenched in sweat, the warmth of his skin faintly visible against the fabric of his shirt. He raised the corners of his mouth slightly, barely maintaining a familiar smile, but without the usual levity. His gaze fell on the drafts filled with formulas, his fingertips unconsciously caressing the tabletop.

"Haha, because it seems like this is the only way I can solve it..." His voice still sounded cheerful, but if you listened carefully, you could detect the fatigue hidden beneath the light tone. His voice was slightly hoarse, and his breathing seemed to have not yet recovered from the intense calculations. "But in the end, I still couldn't..."

Xing Qingqiu's gaze fell on the papers where he had calculated the numbers. He narrowed his eyes and continued to ask, "What about the magic fluctuation just now...?"

"I turned it off," Grothendieck said, leaning aside. His tone was calm, almost indifferent, as if he were stating something insignificant. His gaze swept over Flatt, a look of casual scrutiny between his brows. "The thing engraved inside is also a dead end. Can't even shut it down automatically..."

"Maybe it's because I don't want to stop." Flat blinked, as if thinking seriously, and slowly said, "He's a very kind person, so he will try his best to meet my requirements..."

Xing Qingqi frowned slightly, his fingertips slowly tightening. Who was the "he" Flatt was referring to? What exactly had Grothendieck done? These questions swirled in his mind, but he had no intention of delving into them. The more important thing right now was to confirm Flatt's physical condition.

He lowered his head, looking at Flat's wrists. He could still see the knuckles, slightly white from excessive exertion. His fingertips trembled slightly, perhaps from holding the pen too long while calculating, or perhaps from the effects of the magic seal. His magic circuits hadn't fully recovered, and even though his rationality had returned somewhat, his body was still in a state of lingering excitement.

The light outside the window grew dimmer, the orange-red afterglow gradually swallowed by the night. The shadows in the study stretched longer, making Flatt's face look a little pale. His forehead was still slightly damp, and a few strands of hair, wet with sweat, stuck to the side of his face, but his eyes were still bright, revealing an almost stubborn light.

There was still a faint scent of ink in the air, blending with the faint moisture evaporating from sweat, giving people an indescribable feeling of dullness.

Grothendieck's eyes fell on Flatt again, his expression less casual than usual, and his tone suddenly became serious:

"Flat, I'm going to ask you one last time. Are you sure you really like math?"

"Sure!" Flatt had almost no hesitation, his voice revealing his usual straightforwardness and confidence, as if this answer had never wavered in his heart.

Grothendieck narrowed his eyes slightly, as if waiting for him to continue.

Sure enough, Flatt paused, thought for a moment, and slowly raised a finger, "Two reasons. One is that Order Xing once told me that mathematics is knowledge that can leap across the earth." His tone was serious and solemn, and his blue eyes reflected the dim light in the study, as if he could really see some kind of vision beyond reality.

He then raised a second finger, the corner of his mouth slightly raised, as if he had mentioned the real reason for his excitement. "The second reason is—" He paused, the curve of his lips deepening a little, "—I have learned math well, and Order Xing will be happy."

"Is that all?" Grothendieck raised his eyebrows and asked in a noncommittal tone.

"That's right." Flatt thought about it and nodded firmly, his tone carrying a hint of self-righteousness and lightness. "Although the former sounds more important, I think the latter is more important to me."

As he spoke, he revealed a familiar smile. Although his body was still exhausted and the sweat on his forehead had not yet completely evaporated, and a few strands of golden hair were wet and stuck to his forehead, his smile was still bright, like the golden sunlight shining through the window lattice, even though there was a hint of fatigue, it was still dazzling.

"But it seems that Order Xing couldn't be happy this time. The challenge to the hidden Boss failed miserably..." Flat's voice suddenly lowered, and he muttered in disappointment. His eyes fell on the unfinished calculations on the table, and his fingers unconsciously stroked the edge of the paper.

Xing Qingfeng was stunned for a moment, his fingertips tightening slightly, the warmth still lingering in his palms. His gaze fell on Flatt, watching the usually lively young man, who always showed off in exaggerated ways, now seeming to quietly lament his failure, his eyes filled with a hint of undisguised frustration.

Xing Qingqiu's emotions grew more complicated. He knew what he should say, that he should respond to Flatt's feelings in a rational way, that he should offer guidance like a mentor, but he couldn't find the right words.

He didn't know whether he should be relieved, annoyed, or... regretful at this moment?

He wasn't even sure what he regretted.

Did he regret a casual remark he'd made that led Flatt to view mathematics as a challenge he had to overcome? Or did he regret not realizing earlier what Flatt was pursuing?

He lowered his head, his gaze falling on Flatt's golden hair. The familiar color was still dazzling. But at this moment, he suddenly found it difficult to look directly at it.

"Ah, I lost." Flatt finally sighed, his shoulders slumping slightly, as if he had completely accepted the situation. He shrugged and looked up at Xing Qingjiu, a cynical smile still on his lips. "Sorry, Order Xing, as punishment for losing, I'll be staying in class for the next week."

Xing Qingwu's guilt disappeared instantly.

"You still know you're dishonest..." Xing Qingfeng glanced at him, sighed, and placed his hand on Flat's sweaty head, feeling a damp warmth on his fingertips. His blond hair was slightly matted to his forehead due to the sweat, and looked a little messy. He wanted to pinch it hard as usual -

——But in the end, he just casually rubbed the fluffy golden hair and rubbed it twice, as if he was dealing with a wet dog... No, he should treat it like a human being.

Grothendieck rested his chin on his hand, his eyes languidly fixed on Flatt, a flicker of interest in his eyes. His tone was as casual as if he were commenting on something insignificant. "Let me be frank. He's a genius, but I can't teach him. He's not suited to the Bourbaki school."

He raised his hand and pointed at the papers covered with calculations on the desk, the corner of his mouth curled up slightly, "You want me to teach someone who writes purely based on intuition? That's too difficult for me."

After he finished speaking, he tilted his head slightly, as if thinking about something, and then continued bluntly: "What on earth is that kid Pierre thinking... Never mind, it's normal that mediocre people can't understand what genius is."

Perhaps only Grothendieck could call Pierre a mediocre person in front of outsiders so confidently.

"This kid doesn't care about the process. Because of his talent, he has trouble directly understanding overly abstract concepts." He continued, tapping his fingers on the table. "But as long as he can 'understand' it, his intuition will help him reach the answer to the problem."

"His obsession with precise numerical judgments causes him to suppress his own nature, making it difficult for him to achieve success in fields requiring strict numerical requirements." His gaze fell on Flatt. "Even studying these things itself is a form of torture for him—"

He paused, the corners of his mouth slightly raised, as if he had thought of a suitable path.

"—Go learn applied knowledge. Fuzzy math, probability, operations research, etc. You don't need to achieve the exact optimal solution, just an approximate one."

"Is that so..." Xing Qingfeng nodded thoughtfully, reflecting on Grothendieck's words. His eyes swept over Flatt, who was still sitting there, seemingly unperturbed by his future. Instead, he seemed to have received some kind of relaxing answer, unconsciously twirling a strand of his damp hair with his fingers.

"Thank you very much for your guidance. Then..." Xing Qingyu was about to confirm something when he was interrupted by Grothendieck.

"Don't you understand what I mean?" Grothendieck frowned, a hint of impatience in his tone. "It means I won't accept him, and don't send him to the Bourbaki school to waste his talent. I can take him home and teach him myself. He doesn't rely much on any education system. Just teach him a few things and give him a few topics to let him accumulate experience on his own."

He stretched himself and said in a tone that sounded like he was trying to get rid of someone, "Now, take that bastard Pierre out of my house!"

Xing Qingfu was still standing there, his brows slightly furrowed, his eyes moving back and forth between Flatt and Grothendieck, as if sorting out everything that had just happened.

He didn't delay. After a moment's hesitation, he asked directly, "Wait, I have another question." His voice was more urgent than before, with a hint of doubt. "What on earth happened to Flatt just now?"

When Grothendieck heard this, he looked away from the calculation paper on the table, as if thinking about how to express himself.

He picked up the teacup on the table, took a sip of the now-cold tea, and said casually, "You don't even understand your students' situation?" He paused, as if searching for a more modern, more appropriate metaphor. After a moment, he raised his eyes and said slowly, "Let's use a modern computer as an example. Your students have more than one operating system in their bodies."

Xing Qingqiu's brows furrowed slightly as he quickly digested this information. "......?" he pressed, "Second personality?"

"No, no!" Flatt waved his hands quickly, a helpless smile in his voice, "Tia is not me."

Grothendieck glanced at him, ignoring his interruption, and continued to explain, "Simply put, there are no people or machines in the current era that can carry the contents of his magical imprint." He touched his chin, thought, and added, "That's not right. If his imprint were transplanted into me, perhaps it would unlock even more capabilities."

Xing Qingqiu's frown deepened.

“—I’ve strayed off topic.” Grothendieck waved his hand, discarding the thought that had just come out of his mouth and returning to the main topic. “Originally, since there are almost no humans in this era who can run this system,” his tone remained flat, as if he were talking about a very ordinary matter, “but this child’s talent is indeed strong enough that he can barely run it.”

The study was briefly quiet for a moment, with only the breeze blowing through the window, causing a few thin sheets of calculation paper on the table to flutter slightly, making a slight rustling sound.

“Originally,” Grothendieck resumed, speaking at a steady pace, as if stating some perfectly natural principle, “there should only be one system in a person.” He paused, tapping the table with his index finger, making a slight sound. “When another system appears, the original system will cease to function, right?”

"—But Flatt was able to get another system up and running temporarily." He concluded casually, as if it was a matter of course. "This kid is a genius."

"Oh!" Flat's eyes lit up and he moved closer excitedly. "Grandpa, do you know anyone in our family?" He asked in amazement, his lips curled up. "It feels like you know Tia better than I do!"

Grothendieck glanced at him, as if too lazy to respond to such a meaningless question. He picked up his teacup and shook it gently, saying lightly, "I don't know him." He looked up at Flatt and added calmly, "Isn't it obvious at a glance?"

On the streets of Paris in the afternoon, sunlight shines through the gaps between the towering buildings. The air is filled with the faint aroma of butter wafting from the bakery. Some people are leisurely flipping through newspapers on the open-air seats of the corner cafe, and passers-by walk leisurely, as if the whole city is immersed in this lazy atmosphere.

Flatt and Xing Qingjiu walked side by side on the street, their steps casual, as if they were wandering aimlessly. Flatt's hands were in his pockets, and he occasionally kicked up pebbles on the road. He looked in a good mood, but his eyes were still a little wandering, as if he was thinking about something.

Finally, he raised his head, looked at Xing Qingjiu, and asked hesitantly, "Order Xing, did I disappoint you?"

Xing Qingqiu paused slightly, his gaze fixed on Flatt. His expression didn't change much, but his eyes darkened. "Why do you think that?" he asked calmly.

Flatt curled his lips, as if weighing his words. After a moment, he spoke, "Because the more questions I get right, the happier Order Xing will be..." As he spoke, he tilted his head slightly, watching the clouds drifting slowly across the sky. His tone became unusually serious. "Besides, the people we met a few days ago were all very impressive, right? Order Xing will definitely be even happier after passing the test."

Xing Qingyu looked at him, was silent for a moment, and then suddenly asked, "Are you happy?"

Flatt blinked, seemingly not expecting Xing Qingwu to ask that, but he quickly smiled and nodded without hesitation: "Of course I'm happy!"

He turned around, took a few steps forward, then suddenly turned back. The smile on his face was as bright as the sunlight streaming into the afternoon street, and his eyes were filled with undisguised excitement. "Because Order Xing can see the world as I see it! He can even see more and farther than I can!"

Xing Qingyu opened his eyes slightly, and his fingertips subconsciously tightened for a moment. He looked down at Flatt, and for a long while he said nothing, but an indescribable emotion emerged in his heart. So that's how it was. Xing Qingyu finally understood -

Did Flatt feel like he had found someone of his own kind? Or did he realize he wasn't an outlier?

He lowered his eyelashes, and the corners of his mouth moved slightly, as if he was sighing silently. Finally, he raised his head and suddenly said, "Flat!"

"Hmm?" Flatt tilted his head.

"Let's go pick out the rewards!" Xing Qingfeng's eyes turned, and his tone was a little deliberately light, "Let's buy a game console—"

"—go buy a GameCube!"

"Great!" Flat's eyes lit up instantly, as if he had just put aside all his thoughts, and responded excitedly.

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I originally wanted to give the senior brother and Pierre a small part, but after looking at the main plot structure, I decided to forget it and leave it as a side story.

This part of the plot can be said to be the Flatt chapter, and it ends here. I don’t know how it is written. I think on the one hand, it shapes and consolidates the relationship between the two masters and apprentices, and also plays a big role in the transformation of Xing’s educational philosophy.

The above is a new book by a new author. Please vote and give me feedback. Thank you!

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It suddenly occurred to me that some people might not have a clear idea of the genius of Grothendieck, the greatest mathematician of the last century, so I'll briefly mention it here:

Grothendieck did not receive much systematic mathematics education in his early years, and when he went to university, the mathematics education at his university was notoriously poor at the time.

He couldn't concentrate on math class at all and simply skipped it. Then he turned his attention to the high school textbooks he was using at the time. He felt that the high school textbooks were also poorly written and had too many loopholes.

——So he spent his three years of college life filling the gaps in high school textbooks, trying to provide the proper definitions of length, area, and volume, that is, independently reconstructing the entire concept of measure theory and Lebesgue integral.

Well, in just three years, with no math education, he taught himself and used the few tools at hand to reconstruct theories that had taken others decades to develop.

This is the God of algebraic geometry. It is no exaggeration to say that he is a genius who has opened up a new world for algebraic geometry.

Volume 61: Xing Qingfeng's Perfect Arithmetic Classroom: . My Lord, Times Have Changed

On an autumn afternoon, the classroom in the clock tower echoed with the rustling of pages, occasionally punctuated by the scraping of pens across paper. A gentle breeze rustled outside, bringing fallen leaves gently tapping against the window frame. Golden sunlight streamed in through the carved glass, casting a crisscross of light and shadow on the blackboard, desks, and chairs.

Xing Qingyu stood at the podium, holding a piece of chalk in his right hand, and quickly wrote a few complex symbols on the blackboard while continuing his explanation:

"Constructing a spiritual field is not just about gathering spiritual energy, but also about setting a stable boundary. Otherwise—"

Before he finished speaking, his eyes swept across the classroom and suddenly paused, his tone instantly rising several degrees:

"—Flat! What are you doing!?"

Flatt, sitting in the front row of the classroom, shuddered violently, raising his head almost reflexively, a guilty smile playing on his lips. His hand hovered in mid-air, a faint magical glow emanating from his fingertips. Near him, a faintly fluctuating spiritual energy field quietly took shape.

The problem is that he is not just building the astral field.

Xing Qingyu's pupils shrank slightly, and he instantly realized what Flat wanted to do - not only to construct a spirit field, but also to summon spirits directly on it.

This place is not an ordinary classroom.