Study Monster Cultivation System

The serious Wind God.

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Was smiling.

In the awed and dumbstruck presence of Li Zheng and Lin Yujing, he occasionally flashed a knowing smile, then immersed himself in the next phase of thought.

He turned around a few times, wanting to share his joy, but seeing their expressions, he reluctantly kept it to himself and continued his calculations.

This process was very much like Li Zheng wanting to share the beauty of solving a problem with Liu Xin.

Li Zheng had witnessed many explosive displays of Academic Power and had dealt with some geniuses who thought very highly of themselves.

But at this moment, he was still intimidated.

He had galloped through the years, and his friends in the circle flattered him by calling him God Zheng.

If it was his Physics friends who called him that, he could accept it.

If his Chemistry friends did, he could also accept it.

He even brusquely accepted the accolades from Biology and Computer Science.

But as for Mathematics, as long as Gu Jianfeng was around, he feared he would never be able to live up to that name.

Right now, what Gu Jianfeng was facing was the "Solution of the Magic Angle."

It was a mathematical problem that Li Zheng had painstakingly converted from a Physics paper.

In the problem, he used a method almost akin to conversing with a computer, to translate the electrical properties of two-dimensional Graphene, its electrons, and the physical presentation of stacked layers into a series of complex functions and matrices, all to clearly lay them out before Gu Jianfeng, allowing him to focus entirely on the task at hand.

As for Li Zheng himself, if faced with the same problem, he might be able to derive the five solutions mentioned in the paper given enough time, but to expand them to eight? It wasn’t a matter of lacking a method, but rather not even having a clue about where to start thinking about a method.

After admiring him for about ten minutes, Gu Jianfeng actually pulled out a stack of blank papers and shook his head with a smile.

"No, no, it’s not imaginary numbers; they can only provide the conventional solutions…"

"My intuition... was wrong?" Li Zheng asked weakly.

"The intuition is correct, but the tools are wrong. Your matrices are already akin to imaginary numbers... we need to extend the theory even further…" Gu Jianfeng turned back, his face flush with excitement as he raised his hand, "Quaternions! You actually pushed me to this stage; I like this problem."

"!!" Li Zheng’s eyes widened in shock, and it took him a while to remember there was indeed such a thing, "Quaternions... I recall it’s an extension beyond the imaginary part?"

"Yes, a more complex yet purer mathematical form, with computation piling up as well. Let’s aim to solve it before nightfall," Gu Jianfeng turned around, twisting his neck while gasping for breath, "If that still doesn’t work, I’ll have to use octonions... Compiling over and over, even for me it would take a week’s time... Now that I think about it, it’s quite exciting..."

"Wait, you can take a break..."

By then, however, Gu Jianfeng could no longer hear Li Zheng speaking.

At that moment, he was in conversation only with Mathematics.

"Um..." It was only now that Lin Yujing dared to voice out, tugging at Li Zheng, "I understand imaginary numbers, basically like complex numbers, right? But what the heck are quaternions?"

"Well... they’re a rather early mathematical concept that has only found application in recent years," Li Zheng said with a smile, "Even you have such a day!"

"My brain only records knowledge I can use, unlike you who remembers every piece of trash knowledge."

"That’s what you don’t understand; knowledge is the fountain of inspiration," Li Zheng declared, clenching his fist, "As long as I have enough knowledge, who knows when I could combine two completely unrelated pieces of information."

And with that, Li Zheng proceeded to explain.

Imaginary numbers are a subset of complex numbers, so the concept of "complex numbers" is more often used when speaking about this part of mathematics.

Complex numbers, in fact, are just high school material, although most people promptly forget about them after they learn it and are unlikely to encounter the term for the rest of their lives.

However, for mathematicians, it is a tried and true tool. While normal people can’t understand mathematicians’ speech, they do say things that are somewhat comprehensible, such as—

[In the real number domain, the shortest path connecting two truths passes through the complex number domain.]

By "somewhat comprehensible," it means everyone understands "connecting," "shortest," and "path."

But once you mix in "real number domain" and "complex number domain," it becomes incomprehensible.

In such cases, the remedial lessons Li Zheng offered to Liu Xin became useful again. In fact, all it took to help Liu Xin understand was an apt analogy—

[The shortest route between any two points on the surface of a balloon is to go through the inside of the balloon.]

Alright, even with this explanation, Liu Xin might still not understand.

Fortunately, not many in the human group are like him.

```

If real numbers are like 1, 2, 3, which can be intuitively sensed and definitely exist, then complex numbers are beyond intuition, like the square root of -1 or the square root of -2—numbers that, objectively speaking, could never be found to have a square equal to -2.

In this case, the real domain is like the visible surface of a balloon; no matter how it curls or expands, it remains a two-dimensional plane. And the interior of the balloon—the part that lies outside of numerical intuition but theoretically could exist—is the complex domain.

One could say that imaginary numbers have added a new dimension to mathematics, also known as complex numbers.

So what about the quaternions that Gu Jianfeng mentioned?

It is another elevation of dimension over the complex numbers...

At this level, it’s very hard to find an example that Liu Xin can understand.

As for the octonions that lie beyond quaternions, humanity has not yet found a suitable application for them; perhaps they belong to knowledge that exists outside of this universe.

In the room, as Lin Yujing came to understand quaternions, she also expressed her amazement: "It’s already this deep... No wonder Grandpa no longer fusses about us skipping class... He’s always finding papers for Feng Feng to devour..."

"Hmph," Li Zheng said with disdain, "Fickle, the old man is just an old scum."

Lin Yujing laughed and scolded, "You really take every opportunity to take a dig at Grandpa, don’t you?"

"Doesn’t Grandpa take digs at me?"

"Mmm... It’s, it’s not too bad..."

"Damn, he must have badmouthed me quite a bit."

"Let’s not talk about Grandpa anymore, let’s focus on Feng Feng." Lin Yujing, looking at Gu Jianfeng’s occasionally chuckling silhouette, grew more reflective, "Even though quaternions came a bit suddenly, I have this intuition that we’re definitely heading in the right direction."

Li Zheng nodded repeatedly.

The expansion of mathematical dimensions by Gu Jianfeng reminded him of the "two-dimensional quantum tunneling" mentioned in the system notification.

That led to the idea of expanding the Magic Angle Model to three dimensions, thus unleashing the true theory of superconductivity.

Once these issues are involved, mere physical observations and experiments wouldn’t be able to yield theoretical results; on the contrary, all they could offer were enigmas, more and more enigmas.

Imagine, if manned spaceflight had been achieved before the Theory of Relativity.

Then the astronauts in the space station who discover the clocks running slow would be just as perplexed and astonished as the observer who, during the double-slit experiment, found that "waves turned into particles."

At that time, the discussions on the nature of time, space, and energy would probably be as chaotic and hallucinatory as the current state of Quantum Mechanics.

Of course, even in such chaos, conducting more experiments, even if they are blind, is beneficial.

The more mysteries, the more material for theoretical research.

But this is just a process of accumulation, and all accumulation leads to only one outcome—

To pierce through the physical balloon using the weapon of mathematics.

At this thought, Li Zheng’s eyes widened.

"Brilliant! I finally understand why high school physics competitions are turned into calculus competitions; the Physics Association has such a far-reaching vision."

"Since that’s the case, let’s brush up on quaternions a bit," Lin Yujing said as she massaged her face, "Although we can’t keep up with Feng Feng, at least I want to understand the work he’s doing. Since we’re free, Scum Chap, go find the lecture notes!"

"Free?" Li Zheng frowned, "Shouldn’t we use this rare leisure time to cultivate our feelings instead?"

"Here you go again..."

"Fine, studying is our couple’s sport..."

That day, Papa Feng came home three times.

The first was at noon when he thought they would have gone out for lunch...

But seeing the three of them in the room, silently working on problems...

He was quite panicked.

Was his son’s weekend social life now expressed through mathematics?

The second time was at two o’clock in the afternoon.

They were still working on problems, and the lunch money on the table remained untouched.

The third time was at six o’clock in the evening; Father Feng tiptoed to the door again to observe surreptitiously.

This time things were a bit better. Although Jian Feng and the boy were still working, the girl had finally collapsed into sleep.

```

```

It’s probably because I’m hungry...

Wait a second... Sleeping on your stomach is okay... but you just blatantly lie on that boy’s legs... and drool...

Never mind... Jian Feng... it’s time to grow up.

At that moment, Li Zheng had also become so hungry that he felt a bit delirious and noticed Father Feng returning.

"Ah, hello Uncle..." Li Zheng greeted, glancing out the window subconsciously.

Seeing that night had fallen, he could only sigh.

It’s always like this, studying the Theory of Relativity is a constant—

[Studying the Theory of Relativity]

[Once you start studying, the flow of time accelerates]

[Time spent studying = Real time * the square root of (1 - (current studying speed² / C²))]

Here, C is 300,000 times the studying speed of Liu Xin, a constant cosmic constant.

Such a profound theory, naturally Father Feng couldn’t deduce from Li Zheng’s eyes, only smiled wryly and mouthed, "What do you want to eat tonight? I’ll cook for you."

"Ah... this..." Li Zheng looked awkwardly at Gu Jianfeng, "How much longer do you need? If not, shall we postpone it?"

Gu Jianfeng still did not answer.

And that seems about right.

Perhaps his studying speed had already surpassed C.

If that were the case, even the study of the Theory of Relativity would delve into the realm of complex numbers, and his flow of time would become an imaginary number, independent of this universe, a concept that only exists in theory.

Thinking this,

"Ah..." Li Zheng rubbed his forehead.

No, I’ve thought too much about these things today, I’m probably on the verge of Entering Demonization.

For the first time, he wanted to stop studying for the day, to take a break.

While his head ached, Father Feng had already brought over two boxes of milk, handing one to him and placing the other next to the dozing Lin Yujing’s head, which was on Li Zheng’s legs.

"Mathematical calculations are very taxing on the brain, you’ll get a headache if your nutrition can’t keep up." Father Feng then stepped back maintaining a polite distance, and said with a smile, "Actually, we have met before."

"Oh? I’m sorry..." Li Zheng scrutinized him carefully but indeed had no recollection.

"During the mathematics competition." As Father Feng also took a box of milk, inserting a straw while he spoke with a smile, "Back then, Jian Feng suddenly called saying he could barely make it. I immediately dropped what I was doing and rushed over by high-speed rail, but by the time I entered your room..."

As Father Feng spoke, he smiled and raised his hand, "The scene was exactly like today."

"!!" Li Zheng then remembered, "I remember now, we had been studying the whole day, only seeing the note you left after you had gone, which was impolite."

"This is actually my third time coming back today."

"???"

"Haha, no worries, it’s quite good like this, and I want to thank you guys." Papa Feng said while sipping his milk, "Ever since the math competition, he hasn’t had any ’unbearable’ situations up until now, seems like he found a new method, or perhaps he’s gotten stronger. I thought he couldn’t survive the IMO, but he persisted. Thanks to you guys."

"I actually didn’t do much." Li Zheng rubbed Lin Yujing’s head, looking at Gu Jianfeng with a smile, "If I have to say, I’ve received much more from him than I’ve given."

"You are being modest; I’ve checked your background and achievements, and they are much stronger than Jian Feng’s." Father Feng then smiled and nodded towards the sleeping Lin Yujing, "The results speak for themselves."

"Ha, ha." Li Zheng laughed dryly, scratching his head, "I’m just greedy for more, in the most critical area of mathematics, I’m content to be Gu Jianfeng’s scratch paper."

"That’s modest of you to say, but I understand..." Father Feng shook his head and sighed, "You guys study too deeply, I can’t even see your backs... I know I’m being selfish, but if possible... What I really wish for... even if it means he turns out an ordinary person, healthy... even if a bit slower..."

As Father Feng said this, he turned to the side, covering his face, "Sorry... um, what would you like to eat? I’ll get ready."

A sourness inevitably arose in Li Zheng’s heart.

He had no doubt that, to academia, even humanity, Gu Jianfeng was certainly a treasure of immense value.

But to a father, to a family, this treasure is, in front of health, worth next to nothing.

"You’ve worked hard." After Li Zheng spoke, he lifted and threw Lin Yujing to the side, stood up and patted Gu Jianfeng, "Stop calculating, just this once, cook a meal for your dad."

"???" Gu Jianfeng faltered, and after a long pause, he cursed dazedly, "Taking advantage of me again! I’m not cooking for you!"

```

The situation was getting out of control.

Li Zheng hurriedly raised his hand to steady Father Feng, "Among familiar guys, calling each other ’dad’ is a perfectly reasonable joke."

Then he looked at Lin Yujing, who was rubbing her eyes and had just woken up to the surprising news of Li Zheng becoming a dad, "Keep sleeping."

Finally, he grabbed Gu Jianfeng, "You must be pleased with your calculations, but your dad didn’t want to bother us, so he hesitated to come back home and wandered outside all day. Stop chatting and take the opportunity to do something nice for your dad by cooking a meal while I, the little owner of Lake Ying, am here."

"Ah..." Gu Jianfeng was dazed for a long time, glanced at the sky outside, and then habitually looked at the small table to his right.

This habit had been there for a long time, whenever he was too hungry or too tired to study, the table would unexpectedly be covered with ready-made dishes, as though it were all natural, like a law of physics.

"It’s okay," Father Feng quickly wiped his eyes, "I’ll cook, you guys continue..."

Gu Jianfeng hadn’t replied when he was met with Li Zheng’s angry glare.

"Ah... shall we still..." Gu Jianfeng had no choice but to stand up while rubbing the back of his head, and said sideways, "Let’s cook today... Li Zheng is really good at cooking."

Father Feng was about to refuse again, but Li Zheng had already pushed him away, "Go watch TV outside, see if I don’t train our son... I mean, get our Feng Feng into shape today."

With Li Zheng’s insistence and demeanor no easy to refuse, Father Feng had no choice but to actually go and watch TV.

What followed was Li Zheng, with Feng Feng by his side, dragging the half-asleep Lin Yujing into the kitchen, confirming everyone’s favorite dishes, sending Lin Yujing to buy ingredients, listing cooking steps for Li Zheng, and Gu Jianfeng making overall plans and arrangements, all leading up to cooking together.

Li Zheng thought Gu Jianfeng would blame him for interfering, but he saw Gu Jianfeng taking the cooking even more seriously than himself, trying hard to recall his father’s preferred flavors and continually reminding Li Zheng to control the seasoning.

Before eight o’clock, steaming fish, meat, vegetables, and soup were served.

Father Feng started off with endless praise, but as he praised, his eyes reddened, and he fell silent.

Gu Jianfeng was the same.

In the end, it turned into Li Zheng and Lin Yujing forcing conversation.

"Leave some fish for others."

"Ugh, ugh, ugh... I was scared. I got a bone stuck."

"Serves you right."

"Really... ugh, ugh... it’s stuck in my throat."

"Oh? Then I’ll help you suck it out."

"It’s okay now, it’s okay."

"Why are you still picking at the fish? Leave some for others!"

In this cyclic fish-eating atmosphere, the mood finally lightened up again, and Gu Jianfeng actually snatched a piece of fish from Lin Yujing’s grasp and placed it in his father’s bowl, then tilted his head and whispered in a very low voice.

"Dad... thank you for your hard work."

"Hey, what’s with all that?" Father Feng chewed on the fish with rice, all smiles, "It’s really delicious, who knew you had this talent."

"Not me... it’s mainly Li Zheng... I’m far behind him..." Gu Jianfeng said with his head down.

"What are you talking about?" Li Zheng glared, pointing with his chopsticks to a clump of ginger on the fish that was cut into a strange shape, "This ginger strip was cut by Jian Feng, quite imaginative."

Father Feng was also pleased, grabbing the ginger strips and chewing them, nodding continuously, "Good, good, all good, this ginger strip is the tastiest, it warms the body."

Now that was a bit of a stretch.

To ease the awkwardness, Li Zheng quickly gave Lin Yujing a clump too, "Here, have some ginger, it warms the body."

"I don’t... mmm..."

Watching Lin Yujing being force-fed ginger, both father and son laughed together, non-stop.

In the end, while the father and son were watching the evening sports news together, Li Zheng left a note saying "Discuss further tomorrow" and quietly left with Lin Yujing.

The bad news was, there were no results for the day.

The good news was, the day was blissful.

But Lin Yujing wasn’t feeling it.

She kept thinking, she had been sleeping so comfortably...

How did she end up on the floor?!