My IQ has been increasing year by year.

Chapter 194 New Problems

As Chen Zhuo walked out of the Physics Department building, the wind blowing in his face made him instinctively pull down the zipper of his jacket.

He walked slowly, his hands in his pockets.

Through a layer of fabric, I could clearly feel the bank card in the inside pocket of my right hand.

Two million.

The number now rests quietly against his chest.

Chen Zhuo didn't look back at the physics building, which had an industrial feel, nor did he take out his card to take another look.

The biggest weight in my life has been lifted.

Being able to move to a better house for my family and make my parents' lives a little better is wonderful, it couldn't be better.

Only after a person has solved their most basic needs for survival and security will their mind become exceptionally clear.

Chen Zhuo turned a corner and walked along the path on campus toward the red brick building of the School of Mathematics.

The building of the School of Mathematics is quite old. Ivy has spread along the cracks in the red bricks all the way to the windowsill on the third floor, and its leaves have begun to turn red this season.

Chen Zhuo climbed the steps to the second floor.

At the end of the corridor was Li Jianming's office; the door wasn't closed properly, leaving a crack.

Chen Zhuo reached out and pushed open the door.

The office was a bit messy, but messy in a way that fit the image of an old mathematician. The bookshelves on both walls were crammed full, and some large journals were even piled on the floor.

"Paper jam! Paper jam again!"

Opposite the desk, Wu Tao was squatting on the floor by the coffee table, looking rather disheveled. He was holding a stapler and staring at the old-fashioned printer next to him, looking worried.

The printer's indicator light flashed red, and it emitted a screeching sound that made your teeth ache.

Li Jianming sat behind his large desk, a pair of reading glasses perched on his nose. He ignored the student squatting on the ground, leaned forward slightly, held the mouse in his right hand, and stared intently at the bulky monitor in front of him.

I clicked the mouse.

Li Jianming didn't move, stared at the screen for a while, then released the mouse with some irritation, picked up the purple clay teapot beside him and took a sip.

"Not here yet?"

As Wu Tao reached into the printer to pull out the A4 paper stuck in the printer, he turned around and asked a question.

"What's the rush? There's a time difference in the US."

Li Jianming replied, his voice revealing a barely concealed anxiety.

Chen Zhuo stood at the door, watching this scene, and the corners of his mouth curved into a smile.

He went inside and closed the door behind him.

"Teacher, senior brother."

Upon hearing the sound, Wu Tao stood up, clutching the torn piece of printing paper, and dusted the toner off his hands.

"Chen Zhuo is here. Find yourself a seat. I'm having a really tough time with this broken machine. The thesis defense in November is being typed on this specific size of paper. It's such a hassle."

Wu Tao pointed to the pile of messy scraps of paper on the coffee table, his tone full of exhaustion.

Chen Zhuo walked to the water dispenser, took a disposable paper cup from the box next to it, and poured himself a glass of warm water.

"Have you finished preparing the presentation slides for your defense?"

Chen Zhuo carried a water glass and sat down on the sofa.

"It was finished a long time ago, now we're just polishing the format."

Wu Tao sighed and glanced at Li Jianming with a guilty look.

"As long as the high-voltage line on my supervisor's side doesn't leak electricity, I'm pretty much safe."

Chen Zhuo smiled but didn't reply, turning to look at Li Jianming behind the desk.

The old professor was looking away from the screen, taking off his reading glasses and tossing them on the table, then pinching his brow.

"An acceptance letter from the Journal of Mathematics?" Chen Zhuo asked.

Li Jianming nodded and let out a long breath through his nose.

"When you came last time, their editorial department replied that the reviewers' comments had been compiled, there were no major issues, and no major revisions were needed, but they still haven't sent them over."

Li Jianming pointed to the computer screen.

"These past few days, whenever I have a spare moment, I've been keeping my email open. Those foreigners are really slow."

Chen Zhuo looked at Li Jianming.

This is a highly respected professor in the Chinese mathematics community who has mentored countless outstanding individuals.

But at this moment, when faced with the world's top pure mathematics journal, the Annals of Mathematics, he still behaved like an undergraduate student waiting for his final exam results.

"No rush," Chen Zhuo said. "The logical chain is complete, and the lower bound problem in graph theory has been solved. They can't find any fault with it."

Looking at Chen Zhuo's nonchalant demeanor, Li Jianming couldn't help but shake his head.

"You're not in a hurry. You're the first author. As soon as this email is published, the domestic mathematics community will be in an uproar. You'll be inundated with seminars and conferences."

"Then I'll trouble you to handle this for me."

Chen Zhuo placed the paper cup on the coffee table, thus averting the trouble with a single sentence.

Li Jianming laughed in exasperation and pointed at him with his finger.

"Alright, stop joking around with me. You wouldn't come here without a reason. Weren't you conscripted by the alchemist these past few days to get wind tunnel data for that high-speed train locomotive at the physics department? What brings you here to sit idly?"

Wu Tao pulled up a chair and sat down next to Chen Zhuo, looking at him with some curiosity.

Chen Zhuo did not answer immediately.

He reached into his coat pocket and pulled out several folded A4 sheets of paper.

The paper was a little wrinkled, and it was covered with dense black ink writing.

Chen Zhuo flattened the papers, placed them on the coffee table, and then pushed them to the edge of Li Jianming's desk.

"The trouble with physics is resolved."

Chen Zhuo's voice was calm, without seeking credit or showing off.

"I took your advice and discarded the entire geometric mesh of the front of the car. I wrote a polynomial using algebraic isomorphism, and the matrix ran successfully on the supercomputer with beautiful convergence."

Li Jianming raised an eyebrow upon hearing this.

He reached out and took the few pages of paper.

"It ran successfully? Forty million grid cells, and you reduced the size using algebraic mapping?"

Li Jianming's tone carried a hint of relief; a purely mathematical approach he had casually suggested had actually resolved a deadlock in the engineering project in the hands of this student.

He put his reading glasses back on and looked down at the paper in his hand.

Chen Zhuo sat upright on the sofa, his hands folded on his knees.

"Due to the confidentiality agreement, I cannot leave a single word of the specific engineering parameters, so there are no physical units on these few sheets of paper."

Chen Zhuo looked at Li Jianming.

"I stripped away its physical shell, and now it's just a pure polynomial algebraic equation approximating the boundary of a manifold."

Ji Jianming nodded without saying a word, his gaze already sweeping over the formulas.

At first, the old professor's facial expression was very relaxed.

Chen Zhuo's handwriting is very clear, and his logical reasoning is as clean and concise as ever.

From defining a topological space to establishing a vector field and then introducing a polynomial ring, every step was taken very solidly.

Wu Tao sat next to him, craning his neck to take a look, but he only saw a long string of non-singular algebra cluster symbols and wisely looked away.

The only sound in the office was the rustling of Li Jianming turning over papers.

When he turned to the third page, Li Jianming stopped flipping through the paper.

His gaze was fixed on a derivation formula in the middle of the page.

Time seemed to stand still for five or six seconds here.

Li Jianming's brows slowly furrowed, his eyebrows almost twisting into a knot between them.

He leaned closer, seemingly unable to believe what he was seeing, and looked at those few lines of formulas over and over again three times.

The facial muscles, which were originally relaxed, gradually tightened.

Li Jianming suddenly raised his head and stared intently at Chen Zhuo sitting on the sofa through the lenses of his reading glasses.

If gazes had warmth, Chen Zhuo would have been ignited by now.

"What is this?"

Li Jianming reached out and poked the paper twice, making it crack loudly.

Chen Zhuo looked at Li Jianming's slightly flushed face, but still maintained his gentle and peaceful demeanor.

"First-order truncation".

Chen Zhuo answered softly.

"I'm asking you what this thing is!"

Li Jianming's voice suddenly rose eight octaves, even carrying a trembling tone of exasperation.

Wu Tao was startled and almost slipped off his chair. He had been with his mentor for so many years and rarely saw Li Jianming lose his temper like this, especially when looking at mathematical derivations.

Ji Jianming grabbed the paper and shook it, making a rustling sound.

"I told you to look for the beauty of algebraic symmetry! I told you to look at physics through a purely mathematical lens! Is this how you see it?!"

Li Jianming stood up abruptly from behind his desk, pointing at the formula on the paper, his fingers trembling.

"The derivation was going so well, it was about to reach the core of the manifold boundary, and then you stabbed me in the back?"

Li Jianming's chest heaved with anger.

"You've calculated an infinite-dimensional expansion, and when you get to this point you realize it can't converge. You don't even bother to say goodbye, you just grab an axe and chop off all the higher-order terms? Do you think this is like butchering pork at the market, where you just throw away the excess?!"

Chen Zhuo sat there, neither dodging nor shrinking back, letting the old professor's spittle fly through the air.

Wu Tao swallowed hard and whispered a word of advice.

"Teacher, please calm down..."

"7

"Calm down my ass!"

Li Jianming turned and glared at Wu Tao, then turned and stared at Chen Zhuo.

"In physics and engineering, you call this patching, you call it pragmatism! As long as the machine can run, you dare to add any heinous cuts!"

Li Jianming slammed the paper on the table with a loud thud.

"But in mathematics, that's just being a scoundrel! That's being shameless! That's building castles in the air! Without underlying homology mappings to prove why your truncation is valid, no matter how beautifully you write the preceding parts, it's all just garbage!"

Li Jianming's roar echoed in the office.

In their view, mathematics is sacred and requires rigorous logic to prove, step by step.

Chen Zhuo's approach of forcibly cutting off infinite dimensions for the sake of a result is simply an insult to the discipline of mathematics.

Chen Zhuo patiently waited for Li Jianming to finish venting.

He looked at the old professor's neck, which was slightly red from anger, stood up, walked to the water dispenser, took another paper cup, filled it halfway with warm water, walked to the desk, and gently placed it next to Li Jianming.

"Please have some water first."

Chen Zhuo's voice remained calm and unhurried, without any hint of resentment or bitterness after being reprimanded.

Li Jianming, panting heavily, glanced at the glass of water but didn't touch it.

Chen Zhuo withdrew his hand, placed both hands on the edge of the desk, leaned down slightly, and looked into Li Jianming's eyes.

"Teacher, you're absolutely right."

Chen Zhuo looked directly at the old professor, his tone very sincere.

"This forced patching method is really unsightly; from a purely mathematical point of view, it's simply unacceptable."

Li Jianming snorted coldly.

"At least you have some self-awareness."

"but."

Chen Zhuo then changed the subject.

He extended a finger and gently touched the A4 paper that had been slapped on the table, right next to the first-order truncation formula.

"The machine is working."

Chen Zhuo looked at Li Jianming, his eyes becoming deep and calm.

"The supercomputer did not crash. After this rogue truncation without any logical support was added, the matrix converged perfectly under the pressure of 40 million virtual nodes, and the final data it provided matched the physical reality perfectly."

Li Jianming's eyes flickered.

Chen Zhuo straightened up, his tone carrying a pure sense of inquiry.

"The real world doesn't lie, and nature won't evolve according to a wrong formula."

77

Chen Zhuo pointed to the piece of paper.

"Since it converges in reality, it means that beneath this ugly cut, on the other side, lies a very beautiful, very symmetrical, and so rigorously precise algebraic geometric structure that it has no flaws."

Chen Zhuo smiled slightly.

"It must have legitimate proof of synchronization, but my current foundation is too weak. I can't see what it looks like, let alone dig out its roots."

Chen Zhuo took a step back and stood in front of the desk.

"The physics department has already given me the money, and I could easily take it and leave, but I can't get over that mental hurdle."

Chen Zhuo looked at Li Jianming.

"So I've come back. I'd like to ask you to take a look and see what's buried down there."

The office fell silent instantly.

All that can be heard is the faint boiling sound of the water dispenser heating up.

Ji Jianming stood behind his desk, the rise and fall of his chest gradually subsiding.

He stopped swearing.

He lowered his head, staring intently through his reading glasses at the first-order cutoff formula on the table, which he had called a hooligan.

The mathematician's fastidiousness made him deeply abhor this crude approach.

But the mathematician's curiosity and competitive spirit were completely ignited at that moment by Chen Zhuo's words.

A seemingly illogical cutoff perfectly aligns with the convergence of reality.

It's like a grotesque, foul-smelling, yet perfectly fitting, building block forcibly embedded into this exquisite edifice of theory.

How was it embedded?

How can it fit in?

Li Jianming's eyes gradually brightened, and the anxiety and fatigue caused by waiting for the email were swept away by a pure sense of excitement.

He slowly reached out and picked up the paper.

He read very slowly, no longer in the superficial way he had just done before, but following Chen Zhuo's interruption, trying to trace back in his mind.

One minute.

Two minutes.

Li Jianming's brows furrowed deeper and deeper, but his eyes grew brighter and brighter.

He found that he couldn't immediately disprove the truncation in his mind.

There is an extremely hidden and complex mapping channel here, which has been forcibly concealed by this truncation.

"Smack."

Li Jianming suddenly put the paper back on the table.

He ripped off his reading glasses and tossed them casually next to the keyboard.

Then, he reached out and unbuttoned the collar of his shirt, took off the gray knitted vest he was wearing, and casually tossed it onto the back of the boss's chair.

The old professor's movements were swift and decisive, as if he were about to go into battle.

He walked around the desk and strode to the huge blackboard against the wall.

The blackboard was still covered with several homology group formulas that Wu Tao had used to derive his graduation thesis a couple of days earlier.

Li Jianming didn't even glance at it before picking up the blackboard eraser from the lectern.

With a few vigorous wipes, accompanied by swirling chalk dust, Li Jianming ruthlessly wiped away all the conventional formulas that Wu Tao had spent two sleepless nights developing.

"teacher!"

Wu Tao panicked and suddenly stood up.

That was me...

'

"Shut up!"

Li Jianming didn't turn his head, his voice carrying an irresistible authority.

"Your crappy synchronization groups are already written on your hard drive, why are you still hanging them on the blackboard? They're just taking up space!"

Wu Tao was speechless, and could only sit back down in his chair, feeling wronged.

Li Jianming threw the blackboard eraser onto the lectern with a dull thud.

He took a brand new white piece of chalk from the chalk box.

He forcefully wrote down the initial conditions of Chen Zhuo's equation at the top left of the blackboard.

After writing the first line, Li Jianming stopped writing and turned to look at Chen Zhuo standing by the table.

The old professor's eyes no longer held reprimand, but only a fervent enthusiasm for seeing something new.

"Close the door and lock it."

Li Jianming pointed to the office door with the finger holding the chalk.

Chen Zhuo's lips curled into a gentle smile.

He turned around, walked to the door, grasped the doorknob, gently closed the door, and then pressed the latch.

"Click".

The sound of the door lock clicking shut was particularly clear in the office.

"come over."

Li Jianming greeted him.

Chen Zhuo walked to the blackboard and stood side by side with Li Jianming.

"Since you know there's something down there, don't just stand there watching."

Li Jianming broke off half of the chalk in his hand and threw a small piece to Chen Zhuo.

"I'll build the geometric framework, and you're in charge of calculating the discrete matrix for me. Even if I'm working until midnight tonight, I'll still use orthodox algebraic geometry to fix this piece of trash of a dog."

Chen Zhuo reached out and caught the half of the chalk.

"it is good."

Chen Zhuo nodded.

Li Jianming turned around and faced the blackboard.

"Start with the definition of a complex manifold. Put your first-order truncation into a vector bundle and see how it converges at the edges."

As Li Jianming spoke, the chalk in his hand moved rapidly across the blackboard.

One by one, difficult algebraic and geometric symbols appeared on the blackboard.

Chen Zhuo stood to the side, his eyes following Li Jianming's chalk.

His brain was like a newly started supercomputer, quickly transforming the geometric concepts written down by Li Jianming into discrete algebraic matrices.

"Teacher, if we substitute it into the vector bundle, the boundary here will diverge in the third order."

Chen Zhuo raised the chalk in his hand and quickly wrote down the derivation of the matrix multiplication in three rows below Li Jianming's formula, and finally drew an arrow pointing to an infinity symbol.

Li Jianming stopped writing and looked at the result written by Chen Zhuo.

"It's diverging?"

Li Jianming frowned and stared at the infinity for a while.

"That means the mapping channel is incorrect. Erase it and start over. Let's try the algebraic closed chain approach."

Li Jianming picked up the blackboard eraser and wiped away what he had just written without hesitation.

Wu Tao sat on the sofa.

His gaze passed over the coffee table in front of him and landed on the backs of the old man and the young man in front of the blackboard.

The chalk in Li Jianming's hand moved quickly across the blackboard.

Gone was the impetuousness he had displayed when reprimanding Chen Zhuo; his movements now exuded pure focus.

Algebraic cluster symbols, representing complex manifolds and vector bundles, gradually took shape in the white chalk dust.

Wu Tao leaned forward habitually, pulled a blank sheet from the pile of discarded typesetting papers on the coffee table, and picked up the black ballpoint pen he had been biting.

He lowered his head and, following the initial conditions that Li Jianming had written on the blackboard, began to derive the convergence of that boundary on paper.

The first step is to introduce vector bundles.

The second step is to calculate the homology class of the edges.

Wu Tao's pen moved quickly across the paper. His thinking was clear, and this was a standard and rigorous algebraic proof.

If he just keeps going down the path, he can figure out exactly where the problem will occur in five minutes at most.

He had just finished writing the third line of the formula and was about to substitute the next variable.

"Teacher, if we substitute it into the vector bundle, the boundary here will diverge in the third order."

Chen Zhuo's voice rang out in the office.

His voice was soft, and his tone was so calm it was as if he were saying that the food in the cafeteria was a little salty at lunchtime.

Wu Tao's pen suddenly stopped.

He looked up at Chen Zhuo, who was standing in front of the blackboard.

Chen Zhuo did indeed have the half-piece of chalk in his hand, but he did not write any calculations on the blackboard at all.

He just stood there, looking at the initial conditions that Li Jianming had just written, and directly reported the result.

Wu Tao fell silent for a moment. How could one possibly calculate the divergence order of such a mapping involving multi-dimensional matrices and high-order polynomials directly in one's mind?

He didn't speak, lowered his head, gritted his teeth, and continued pushing the paper down.

One minute.

Two minutes.

A fine layer of sweat appeared on Wu Tao's forehead as he substituted the derived homology class into the matrix and performed matrix multiplication.

I've figured it out.

The result does indeed diverge at the third order, eventually pointing to infinity.

Wu Tao let out a long breath, looking at the results on the draft paper. An indescribable feeling rose in his heart. How come his junior brother is getting more and more powerful? He feels like he's on a completely different level than when he first arrived.

He tapped the paper with the tip of his pen, looked up, and prepared to join the discussion.

"teacher."

Wu Tao spoke, his voice carrying a hint of excitement after deriving the result.

"Since the third order diverges, could we try introducing a Laplace operator here to decompose this divergence term..."

Before he could finish speaking, his words caught in his throat.

Because Li Jianming had already picked up the blackboard eraser in front of the blackboard.

"It's diverging?"

Li Jianming stared at the blackboard for a second, then frowned.

"That means this mapping channel is completely blocked."

With a whoosh.

Without hesitation, Ji Jianming erased all the complicated formulas he had just written down.

"This path is useless. Let's start over. We'll try to take the algebraic closed chain approach to bypass this vector bundle."

As Li Jianming spoke, he picked up the chalk again and wrote a new equation on the blackboard.

Chen Zhuo nodded, and Zi Guang followed Li Jianming's new formula closely. He made two random strokes with the chalk in his hand, and his brain started working at high speed again.

Wu Tao sat on the sofa, mouth agape, watching the two who had completely moved on to the next stage.

His suggestion to introduce the Laplace operator was like a leaf falling into a rapid current; it didn't even make a splash before being left far behind.

The only sound left in the office was the "tap-tap" of chalk hitting the blackboard.

Wu Tao looked at the draft paper in his hand, which was filled with the derivation process.

He suddenly understood.

It wasn't that he couldn't understand what the two people were saying, nor was it that his math skills were particularly poor.

It's rhythm.

It's the kind of rhythm difference that arises from superhuman intuition and extreme computing power.

He was like a well-equipped and well-trained mountaineer, making sure to drive in rock pitons and secure safety ropes before taking the next step.

That's not wrong; that's how conventional scholars make a living.

But the two people in front of the blackboard were not.

With the insight accumulated over decades in the deep sea of ​​pure mathematics, Ji Jianming directly pointed out the foothold on the cliff.

Chen Zhuo, on the other hand, was like a human computer, not even bothering with a safety rope, and simply jumped over the landing point.

By the time Wu Tao had painstakingly hammered in his rock bolts and climbed up, ready to discuss the scenery, the other two had already jumped to the next hilltop.

It's practically species segregation in academia.

Wu Tao took a deep breath.

He gently placed the ballpoint pen back on the coffee table.

Then he stood up.

Wu Tao walked to the water dispenser, took two clean paper cups, and filled them with warm water.

He walked to the blackboard, without making a sound to disturb them, and simply placed the two glasses of water gently on the edge of the lectern.

Li Jianming didn't look at him. He wrote with the chalk in his hand at lightning speed, and the wrinkles on his forehead were squeezed together, as if he was fighting against that invisible geometric structure.

Chen Zhuo noticed Wu Tao.

He turned his head, smiled gently at Wu Tao, and said in a very low voice.

"Thank you, senior brother."

Then, Chen Zhuo immediately turned his head and quickly filled in a row of matrix dimensionality reduction transition formulas in the blank space of the blackboard with the half piece of chalk in his hand, steadily catching the geometric framework thrown over by Li Jianming.

Wu Tao looked at Chen Zhuo's focused expression and smiled as well.

He didn't go back to the sofa.

He walked to his desk, opened a drawer, and took out a notebook that had never been used before.

Wu Tao turned to the first page, moved a chair, and sat down not too far from the blackboard.

Remove the pen cap.

Wu Tao stopped trying to interrupt and stopped trying to use his own draft paper to calculate.

He looked up, his gaze fixed intently on the algebraic symbols on the blackboard that were constantly being created, overthrown, and reconstructed.

He prepared to write these things down; he suddenly had a premonition that he should record them.

The sound of chalk on the blackboard grew more and more frequent, like a sudden downpour hitting glass.

Li Jianming's coat was draped forlornly on the back of the chair.

A thin layer of chalk dust had already settled on Chen Zhuo's cuffs.

The sky outside the window gradually darkened.

The wind seemed to have stopped.

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