Chapter 376 - 200: Unreconciled (Part 2)

Chapter 376: Chapter 200: Unreconciled (Part 2)

He attempted to use the blow-up method to reinflate the collapsed dimension, restoring it to a smooth complex manifold.

The fountain pen moved swiftly across the paper.

The first sheet of scratch paper was filled.

He casually tossed it aside and pulled over a second sheet.

Time slowly slipped by to the sound of the pen scratching against the paper. Outside, the sun rose higher in the sky, its rays piercing the glass to land on the floor.

The occasional sound of school bells and students walking in the hallway was blocked out by the heavy door.

As noon approached, Li Jianming stopped writing.

He looked at the half-derived formula on the page, his brow slowly furrowing.

’Something’s not right.’

Using the blow-up method to resolve the Singularity worked locally—the dimension was reinflated, and the space became smooth.

But when he tried to place this smoothed local section back into the grand algebraic cycle Chen Zhuo had constructed, a contradiction emerged.

The smoothing process had destroyed the original correspondence of homology classes.

The once perfectly matched boundaries were now completely misaligned, all because of this seemingly standard repair.

Li Jianming picked up his enamel mug and took a sip of tea.

The tea was long since cold, and a bitter taste spread through his mouth.

He pulled out the scratch paper covered in the blow-up process, stared at it for a moment, then drew a large X across it.

’This approach is a dead end.’

He crumpled the paper into a ball and threw it into the wastebasket by his feet.

Li Jianming opened a thick, foreign-language reference book beside him and began searching for another classical intersection theory.

He didn’t want to give up.

He was a proud man.

Years ago, he had studied abroad and returned upon completing his education. He had occupied this office for decades, mentoring one class of students after another.

He had always firmly believed that even if the soil for mathematics in his country wasn’t the most fertile, as long as one was willing to put in the grueling work, a towering tree could eventually grow.

Now, he saw that the seed had already sprouted.

He would never admit that his own patch of soil could not sustain this tree.

The afternoon sun began to slant westward.

The only sounds in the office were still the rustle of the fountain pen and the occasional turning of a page.

Li Jianming hadn’t even eaten lunch.

There had been a knock at the door, likely a department administrator delivering documents, but he didn’t make a sound. After knocking twice, the person outside left.

The stack of scratch paper on his desk grew higher and higher.

Li Jianming’s movements had lost their morning’s composure.

His writing speed fluctuated, sometimes fast, sometimes slow.

At times he would jot down a long string of equations; at other times, he would hover his pen in mid-air, staring blankly at the page for ten minutes or more.

"I can’t get past this part..." he muttered under his breath.

He was trying to use the linear equivalence of algebraic closed chains to replace Chen Zhuo’s discrete truncation.

This was the most conservative method in classical algebraic geometry.

He had filled four entire pages proving this equivalence.

But when he calculated the value of the limit in the final step, Li Jianming’s hand froze.

It diverged.

In the continuous domain, the infinity term that Chen Zhuo had so decisively cut off had, through Li Jianming’s attempt to maintain the continuity of the space, inevitably reappeared, completely collapsing the entire equation.

Li Jianming’s hand was trembling.

He gripped the pages, his fingers shaking.

RIP.

He tore the four pages in half, crumpled them into a ball, and forcefully threw it at the wastebasket.

The ball of paper hit the rim of the wastebasket, bounced off, and rolled into a corner by the bookshelf.

Li Jianming leaned back in his chair and closed his eyes.

He felt a wave of exhaustion wash over him, one that came from within. It wasn’t physical fatigue, but a profound sense of powerlessness.

But he refused to accept defeat.

He pushed aside the books on his desk and pulled over a fresh sheet of blank paper.

’There has to be a way.’

’There must be a path, a way to use the knowledge he possessed to fill that gap.’

The sun set completely.

The office was plunged into twilight.

Li Jianming didn’t turn on the overhead light, continuing to write by the glow of the desk lamp that cast a white luminescence.

The fountain pen ran out of ink.

He unscrewed the barrel, took out a bottle of ink from the drawer, refilled the pen, and continued to write.

Night deepened.

The Keda campus grew quiet. Occasionally, the wind would stir the branches outside, causing them to scrape against the windowpane.

Li Jianming’s breathing grew heavy.

The gray vest he wore was damp with sweat, clinging to his back with a chilling sensation.

He stared at the last line of the equation on the paper.

This was the last tool he could think of from the system of classical algebraic geometry for dealing with a Singularity.

He had substituted all the conditions into it.

The nib of the pen came to a halt on the paper.

He didn’t need to calculate any further. With his decades of experience, he could see the outcome of this line of reasoning at a single glance.

A dead end.

No matter how he maneuvered, no matter what exquisite classical techniques he employed, as long as he tried to maintain mathematical rigor and continuity, he would inevitably destroy the internal balance of Chen Zhuo’s fledgling framework.

Chen Zhuo’s thinking was simply not within the framework of classical algebra.

His "brutal" method of truncation was an instinctive call for the tools of higher-dimensional modern mathematics.

And those were tools Li Jianming did not possess.

They weren’t on his bookshelves, and they weren’t in his head.

CLACK.

The fountain pen slipped from his hand, fell onto the desk, rolled a few times, and came to a stop beside a book by Zariski.

Li Jianming slowly leaned his head against the back of the chair.

He turned his head and looked down by his feet.

The once-empty wastebasket was now overflowing with crumpled balls of scratch paper, with several more scattered on the floor.

This was the result of his entire day and night of relentless struggle.

A complete and utter failure.

Li Jianming stared at the balls of paper, and his eyes slowly began to burn.

He wasn’t heartbroken over his wasted effort, nor was he discouraged.

He simply felt anguish.

It was the anguish of an old teacher who had discovered a piece of peerless, uncut jade, only to find that all the carving tools in his hand were dull.

He wanted to keep Chen Zhuo by his side, to guide him personally, to watch this tree grow tall in his own courtyard.

But that was just wishful thinking on his part.

He had to admit a harsh truth.

His system of knowledge was too old.

The classical, orthodox methods he clung to were powerless when faced with a problem that touched the very ceiling of human intellect.

If he stubbornly insisted on forcing Chen Zhuo into his own system, on paving the way for him according to his own rules...

...that wouldn’t be helping him; it would be cutting the feet to fit the shoes.

It would be like locking a bird that could have flown so much higher with a rusty iron lock.

Li Jianming reached out and closed the thick reference book lying open on his desk.

It closed with a dull thud.

He sat under the dim desk lamp, looking at the twenty-two-page manuscript belonging to Chen Zhuo.

"My pond is too shallow."

Li Jianming’s voice, raspy with a sense of resignation, echoed in the quiet office.

"I can’t teach him."

He slowly rose to his feet and walked to the window.

Outside, the Keda campus lay serene in the night, the lights of distant dormitory buildings glittering like stars.

He stood there for a long time.

The night wind seeped in through the crack in the window, blowing against his face and gradually cooling his fevered mind.

’Protecting one’s own can’t turn into killing the goose that lays the golden eggs.’

’Since I can’t teach him, and since my old foundations can’t support him...’

’...the only choice is to look elsewhere.’

’Find someone who can handle this brutal axe.’

Li Jianming turned and walked back to his desk.

He swept all the scattered scratch paper from his desk into the wastebasket, then moved the heavy tomes back to the bookshelf one by one, placing them in their original positions.

Finally, he picked up Chen Zhuo’s manuscript.

He pulled out the first few pages containing the derivations, as well as the final page that reached the concluding closure.

He left only the two pages in the middle—the core of the work, concerning the discrete truncation.

He folded these two pages in half and placed them in his briefcase.

He flipped the switch on the desk lamp, and the office was plunged into darkness.

The lock clicked.

Carrying his briefcase, Li Jianming walked out of the office. The motion-activated lights in the hallway flickered on, illuminating his slightly stooped yet still resolute figure from behind.