Chapter 173 Take it slow

Chapter 173 Take it slow

At four o'clock in the afternoon, the only sound in Li Jianming's research room was the rapid tapping of chalk on the blackboard.

The voice was heavy, with a sense of gritted teeth.

"Click".

The piece of chalk broke off on the blackboard because of excessive force.

The broken piece fell to the ground and rolled into a thin layer of chalk dust.

Wu Tao stopped what he was doing.

He stared at the blackboard, his brows furrowed.

His hair, which was originally combed fairly neatly, is now a messy bird's nest, and his shirt is rolled up to his elbows, with his forearms covered in white chalk dust.

The blackboard was covered with formulas.

From left to right, from top to bottom.

Integrals in continuous fields, the derivation of the Gauss-Bonnet theorem, transformations of the Jacobian matrix... Some parts were vigorously erased with a blackboard eraser, and new formulas were then covered on the half-dry blackboard, leaving behind blurry white marks.

Wu Tao's chest heaved as he took two steps back, seemingly trying to get a better view of the blackboard from a more macroscopic perspective.

I watched it for a full minute.

He took a deep breath, and the broken piece of chalk slipped limply through his fingers and fell into the blackboard tray.

"It doesn't make sense."

Wu Tao's voice was very dry.

Behind his desk, Li Jianming sat in an old wicker chair.

He wasn't wearing his usual reading glasses for studying documents. There was a thick stack of calculation papers on the table, and the top page was covered in pencil scribbles, full of various calculus paths marked with crosses.

In the white porcelain teacup beside me, the tea leaves had long since sunk to the bottom, and the tea had completely cooled down.

Upon hearing Wu Tao's words, Li Jianming did not look up. He simply threw the pen in his hand on the table and rubbed his temples vigorously.

"It can't be contained, right?"

Li Jianming's voice was filled with deep weariness.

"Um."

Wu Tao turned around and leaned against the wall next to the blackboard, looking somewhat dejected.

"The local problem is completely solved. The imaginary time variable that Chen Zhuo introduced earlier did indeed smooth out the singularity of the Jacobian determinant distortion. The entry point for that discrete matrix was simply brilliant, but..."

'

Wu Tao paused, his tone full of resentment and confusion.

"However, it's like we've cut out a broken heart, repaired it outside the body, and now we're trying to put this discrete heart back into the body of the entire continuous network topology. When we're stitching it up, a big problem arises."

He turned his head and pointed to the long integral equation in the bottom right corner of the blackboard.

"The error terms on the boundary cannot converge at all."

Wu Tao walked quickly back to the blackboard and pointed to the end of the equation with his finger.

"As long as the number of network nodes N approaches infinity, this error term will start to oscillate infinitely. It's like a madman, sometimes large and sometimes small. The traditional Gauss-Bonnet theorem completely fails here. If the boundary cannot be closed, all the singularity cuts we did before are just castles in the air in mathematical logic. Without convergence, the proof is invalid."

A hush fell over the office.

This is the most despairing moment in pure mathematical proofs.

What's scary isn't having no idea from the start, but rather when you think you've climbed over the highest mountain, only to find that there's a cliff you can't cross at all.

The method was clearly correct, and their intuition told them that this path would work, but they were just missing the final step: a convergence proof.

I just can't get past this.

Chen Zhuo was nestled on the somewhat faded sofa in the corner.

On the old coffee table in front of him, there were also more than a dozen sheets of draft paper filled with formulas.

He sank into the sofa, holding a pencil in his hand, staring at the top draft paper.

On the paper was the boundary oscillation term that Wu Tao had just written on the blackboard.

Hearing Wu Tao's complaint, Chen Zhuo stopped the pen that was unconsciously spinning in his hand.

He sat up straight, picked up the draft paper, and looked at it in the light coming in from the window.

"Brother Wu is right."

Chen Zhuo began to speak, his pace slow and his tone calm, as if he were objectively stating the facts.

"I derived four different integration paths, and the results were all the same. As long as you try to put it back into the framework of continuous calculus, the high-frequency oscillations on the boundary cannot be erased."

He put the draft paper back on the coffee table, picked up the half-warm water next to him, and took a sip.

"It doesn't seem like we miscalculated anything."

Chen Zhuo looked at the blackboard, a hint of helplessness in his voice.

"It's more like... there's something wrong with the tool itself."

Wu Tao paused for a moment, then turned to look at Chen Zhuo.

"The tool is malfunctioning? What do you mean?"

Chen Zhuo put down his water glass and crossed his hands on his knees.

"Calculus deals with smooth, continuous manifolds, but what we're facing now is a network boundary that has been cut by discrete matrices, with nodes approaching infinity. Senior Wu, don't you think we're a bit like using an extremely sharp scalpel to cut a piece of clay that's constantly deforming?"

He looked at Wu Tao, a faint smile playing on his lips.

"No matter how finely it is cut, the edges of the clay will always be rough. If you force the limit of the continuous domain to fit it, it will of course oscillate."

Wu Tao opened his mouth, wanting to refute.

As a traditional pure mathematics doctoral student, when faced with divergent integrals, my first reaction is always how to smooth and scale them using more sophisticated analytical methods. This is an academic instinct ingrained in my bones.

"But if we don't wrap it back to the continuous domain..."

Wu Tao frowned.

"How do we use the Gauss-Bonnet theorem? Without this theorem, the curvature and genus of the entire topological network cannot be connected, and the problem becomes a dead end, right?"

Li Jianming leaned back in his rattan chair and let out a long sigh.

"Xiao Wu is right."

The old professor stood up, walked to the window, and looked at the students who occasionally walked by downstairs.

"Chen Zhuo, your approach using discrete matrices is indeed brilliant, but mathematics is mathematics. Mathematics doesn't believe in intuition; it only recognizes rigorous logic. If the boundary convergence fails, everything before is in vain. If we can't find a tool to replace the Gauss-Bonnet theorem..."

Li Jianming turned around, looking at the wall full of drafts and the blackboard, his voice a little muffled.

"This road is probably heading into a dead end again."

The office fell silent again.

The atmosphere was even heavier than before.

Chen Zhuo did not refute.

He knew that Li Jianming was telling the truth.

He can propose a discrete perspective and introduce imaginary time variables, but if he cannot provide a logically consistent closed loop in the final stage, this paper, which is capable of competing in top international journals, will only be a pile of meaningless waste paper.

He looked at the oscillating error term on his draft paper.

My mind was racing.

If calculus doesn't work, then what does?

In physics, how do physicists deal with unpredictable oscillations at the boundaries of a system?

No matter how much local fluctuations occur, some things remain constant.

Energy, momentum, charge...

What about in mathematics?

Chen Zhuo's brows furrowed slightly.

He felt as if a thin layer of paper was blocking his mind.

That feeling was extremely uncomfortable, like having a name on the tip of your tongue but being unable to say it.

He vaguely grasped a clue, a clue completely different from the analytical perspective, but the clue was too blurry, and before he could see it clearly, it slipped away again.

Chen Zhuo hadn't experienced this feeling of being stuck for a long time.

Even when he was deriving the imaginary time variable, he wrote it out naturally.

But today, on this issue of closing the boundary, he has hit a real wall.

Seeing Chen Zhuo's furrowed brows and silent expression, Wu Tao felt a little better for no reason.

Even this oddball was stumped.

It seems that it wasn't that Wu Tao was stupid, but rather that the question itself was a complete trap.

"How about we try constructing an auxiliary function from a different perspective?"

Wu Tao was still unwilling to give up. He walked to the blackboard, picked up the chalk, and tried to add something next to the oscillation term.

"If we introduce a weighted attenuation factor at the boundary, we can forcibly suppress the amplitude of the oscillations..."

, 3

"it's useless.

Chen Zhuo interrupted him.

Chen Zhuo stood up, stretched his stiff neck, walked over to Wu Tao, and looked at the formula O.

"Senior brother, it's like a balloon that's about to burst. Instead of finding a stronger net to cover it, you try to pinch the part that's about to burst with your hands. If you pinch the left side, the right side will bulge out. The error term can't be suppressed by the decay factor; it will continue to diverge in a higher dimension that you can't see."

Chen Zhuo's voice was calm. He turned his head and looked into Wu Tao's dark circles.

"Forget it, Senior Brother Wu, if you keep going, you'll erase holes in this blackboard."

Chen Zhuo patted Wu Tao on the shoulder.

"If you're heading in the wrong direction, the harder you try, the more desperate you'll feel."

Wu Tao's hand froze in mid-air, holding the chalk, unsure where to write.

Yes, the direction is wrong.

But what other roads are there besides this one?

Li Jianming walked back to his desk.

He glanced at the clock; it was already 5:30 in the afternoon.

The sunlight was no longer glaring, but rather dim and yellowish, casting long shadows in the office.

"Alright."

Li Jianming's voice rang out in the quiet room, carrying the decisiveness and helplessness of an older generation of scholars.

That's all for today.

He gathered the stack of calculation papers on the table together and casually stuffed them into the drawer next to him.

"Scientific research is not manual labor. When your brain can't work, stubbornly persisting is a waste of time."

Li Jianming looked at the two young men in front of him: one was his student on whom he had placed high hopes, and the other was a prodigy from the gifted youth program.

At this moment, both of them wore obvious signs of exhaustion.

"Go back, everyone. No one is allowed to touch this topic again for the next few days. Clear your minds completely, go to sleep when you're supposed to, eat when you're supposed to, and let this boundary oscillation go to hell."

The old professor waved his hand, as if shooing people away.

"But teacher, what about the progress before..."

'

Wu Tao was getting anxious.

"The progress is just sitting there, it's not going to grow legs and run away!"

Li Jianming glared at him and couldn't help but swear.

"Look at you right now, your eyes are so red they're practically bleeding. Even if an inspiration were right in front of you, your mush-like brain wouldn't be able to grasp it."

Wu Tao opened his mouth, but in the end he helplessly lowered his head.

"Understood, teacher."

He turned around and began slowly tidying up the books and documents on his desk, his movements mechanical and sluggish.

Chen Zhuo didn't have the same psychological burden as Wu Tao.

Anyway, he's still young. It's common for him to get stuck on problems of this level for weeks or months. Besides, if every problem could be solved in an afternoon, then the Seven Millennium Mysteries would have been solved long ago.

He walked to the sofa, neatly folded his dozen or so pages of draft paper, and then folded them in half.

This document records the dead ends they encountered, as well as the troublesome boundary oscillation term.

Chen Zhuo casually stuffed the stack of papers into his jacket pocket.

"Then we'll head out first."

Chen Zhuo looked at Li Jianming, smiled, and his tone returned to its usual easygoing and relaxed manner.

"Professor Li, you should go back and rest early too. Remember to take your blood pressure medication on time. Although you got stuck on this question, at least it didn't make your blood pressure rise. That's the biggest research achievement of the day."

Hearing this disrespectful teasing, Li Jianming's heavy mood eased a little.

He pointed at Chen Zhuo with an annoyance.

"You little brat, you never say a serious word. Get lost, and don't let me see you in the math department building for the next couple of days."

"Alright."

Chen Zhuo picked up the borrowed book and casually tapped it twice on Wu Tao's desk.

"Let's go, Senior Brother Wu. Stop looking at it, it's getting more and more confusing. The second canteen should have stewed pork ribs today. If we go too late, there won't even be any soup left."

Wu Tao smiled wryly as he slung his bag over his shoulder.

"I can't eat any more ribs. My head is filled with endless vibrations right now, and I feel nauseous no matter what I eat."

The two greeted Li Jianming and left the office one after the other.

The door closed behind him with a dull thud.

The hallway was somewhat dimly lit.

Not long after class ended, the teaching building was bustling with students coming and going. Some were chatting and laughing, while others were rushing to the cafeteria with their lunchboxes, creating a lively and vibrant atmosphere.

Wu Tao walked beside him, still looking somewhat dazed.

He looked at the carefree undergraduates and suddenly sighed.

"Chen Zhuo, do you think... we chose the wrong path from the very beginning? Forcibly stitching together discrete and continuous geometry, this kind of cross-disciplinary operation has very few successful examples in the history of mathematics. Perhaps Professor Li's initial idea was correct, and we should have honestly followed the foundation of algebraic geometry."

Wu Tao's voice was very low, as if he were asking Chen Zhuo, or perhaps asking himself.

Chen Zhuo slowed his pace.

He did not answer Wu Tao's question directly.

He reached into his jacket pocket and, through the thin fabric, could feel the stack of folded draft papers, the slightly rough texture of the paper gliding between his fingertips.

"Senior Brother Wu."

Chen Zhuo looked at the window at the corner of the stairs ahead.

A tree branch swayed in the wind outside the window.

"There is no right or wrong path. If a path is blocked, it's simply because the tools we have are not suitable."

Chen Zhuo's voice was calm, offering neither comfort nor discouragement.

"Just because continuous domain calculus can't cut through that knot doesn't mean other things can't. It's like repairing a circuit board. If a multimeter can't find the fault, you have to replace the oscilloscope. Tools are inanimate, but people are adaptable."

He patted Wu Tao on the shoulder.

"Don't even think about it. This sweet and sour pork ribs meal is on me today. Consider it a tribute to that boundary we just couldn't control."

Wu Tao was taken aback by his unconventional logic.

"Who uses pork ribs as a sacrifice for calculus...?"

'

Wu Tao shook his head, a slight smile finally appearing on his lips.

"Alright, you're treating. Then I'll have to get two extra portions of meat today. I've lost too many brain cells; I need to replenish them."

The two walked down the stairs.

They blended into the bustling crowd.

A gentle breeze, carrying the scent of magnolias, drifted in from the corridor windows at the end of spring.

Chen Zhuo walked in the crowd, seemingly no different from the ordinary boys around him who were discussing which internet cafe to go to for an all-nighter or complaining about the high failure rate of their advanced mathematics teacher.

But only he himself knows.

The ink on the stack of draft paper in my pocket still seemed to be hot.

That infinitely oscillating boundary error term, like a tangled mess, lingered deep within his mind.

Calculus is not good.

Analysis doesn't work.

The Gauss-Bonnet theorem fails.

So what exactly is it that can lock down the global attributes of a network topology amidst chaos and turmoil?

What exactly is unaffected by local deformation?

Chen Zhuo walked down the steps of the teaching building.

The afterglow of the setting sun shone on his face.

He narrowed his eyes slightly.

It's okay.

Chen Zhuo said to himself.

The most important lesson his rebirth taught him was patience.

In this vast labyrinth of logic and numbers, as long as you don't give up searching, you'll eventually find the thread hidden in the shadows.

As for now.

Chen Zhuo touched his somewhat shrunken belly.

Let's go eat ribs first.

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