My IQ has been increasing year by year.

Chapter 326 An Encounter

2:30 p.m.

Chen Zhuo strolled slowly along the sidewalk.

The heating in David's apartment was on full blast, but the air was a little stuffy.

David was at the dining table in the living room checking several long lists of documents, some of which were dozens of pages long, and reviewing some paper backups that would be needed for tomorrow's report.

Sam and Allen sat on the sofa, each holding a laptop, going through the slideshow over and over again.

Chen Zhuo did not prepare any slides.

When David asked him if he wanted to make an outline, he said no, just bring a piece of chalk tomorrow.

David glanced at him, nodded, and didn't press the matter, continuing to check the list with his head down.

Chen Zhuo sat in the apartment for a while, then, feeling a bit bored, pushed open the door to get some fresh air.

After walking along the street for about twenty minutes, Chen Zhuo crossed two blocks and arrived near Harvard Square.

There were more pedestrians here, mostly students or faculty members wearing coats and walking hurriedly.

A thin layer of condensation formed on the glass windows of the roadside cafe, allowing the warm yellow light inside to shine through.

Chen Zhuo stopped at a traffic light intersection and glanced across the street.

There was a small, independent bookstore with a slightly worn, dark green door frame. The window display had no fancy posters, just a few stacks of heavy hardcover books.

The red light turns green.

Chen Zhuo followed the flow of people across the zebra crossing, walked to the bookstore door, and pushed it open.

The warmth from the shop's heating enveloped me, dispelling the chill that clung to my body.

The air was filled with a very unique smell, the musty smell of old paper that had dried after being damp, mixed with the aroma of roasted coffee beans emanating from the coffee machine in the corner.

The bookstore is very long, with rows of dark solid wood bookshelves stretching all the way to the end.

Because it was a weekend afternoon, there were about ten customers in the store.

Everyone was very quiet. Some stood in front of the bookshelves, heads down, reading, while others sat on round stools in the middle of the aisle. Occasionally, there was the rustling of pages turning or the sound of light footsteps.

Chen Zhuo walked along the corridor.

At the far end of the bookstore, against the wall, is the mathematics and physics science section.

The natural light here is a bit weak, and a row of lights is installed on the top of the bookshelf, casting warm semi-circular halos of light downwards.

Chen Zhuo stopped and his gaze swept across the spine of the book.

This row of bookshelves is mostly filled with academic monographs published in the 1970s and 1980s or even earlier. Many of the books have damaged and yellowed covers, and some even have worn-out gold lettering on the spines that is no longer legible.

He reached out and pulled out an old book about the foundations of algebraic geometry from the middle shelf.

The book had no outer cover. Chen Zhuo leaned against the bookshelf and casually flipped through the pages.

The paper is slightly brittle and has a rough texture.

It was printed with formulas produced by an early typesetting machine, the font was a bit stiff, and the line spacing was narrower than that of modern publications.

Chen Zhuo looked at one of the pages about the derivation of manifold mapping, his gaze slowly moving over the old symbols.

The bookstore was very quiet.

About ten minutes later, Chen Zhuo prepared to turn the page.

At that moment, he heard a very soft sigh.

Chen Zhuo turned his head slightly, his gaze passing over the edge of the book in his hand.

About two people's distance to his right, in front of a bookshelf, stood an elderly white man who had appeared out of nowhere.

The elderly man was thin and wore a well-tailored dark gray tweed suit over a light blue Oxford shirt. He wasn't wearing a tie, and the top button of his shirt was casually undone. His white hair was neatly combed, and a pair of silver-rimmed half-rimmed reading glasses sat on his nose.

The old man wasn't holding any of the old books, but rather a brand-new magazine with the logo of a well-known top mathematics journal printed on its cover.

The magazine's plastic wrapping had just been torn off, and he crumpled the transparent plastic sheet into a ball and held it in his left hand.

He held a mechanical pencil in his right hand.

The old man was looking down, his eyes fixed on a particular page of the journal.

His brows furrowed slightly, and then he raised his right hand and used the pen to draw a circle on a line of formulas on the page.

Chen Zhuo has excellent eyesight.

That is a nested matrix derivation involving higher-order topological homology groups.

Chen Zhuo withdrew his gaze, looked at the old book in his hand, and spoke calmly.

"The LaTeX package compilation failed."

In the quiet corner, Chen Zhuo's voice was neither loud nor soft.

The old man standing next to him paused for a moment while holding the pen.

"The indices i and j in the nested matrix are reversed."

Chen Zhuo did not turn his head, but continued to speak calmly while looking at the pages of the book in his hand.

"The integral brackets on the right side exceeded the preset page boundary, causing half of the differential operator that followed to be missing from the print."

The old man slowly turned his head and looked at the young man leaning against the bookshelf through the lenses of his reading glasses.

The young man kept his head down, as if those few words were just a meaningless monologue.

The old man lowered his head and took another look at the formula he had circled.

As the young man said.

The subscripts are reversed, and the differential operator is missing half.

The old man closed the magazine in his hand, put the pencil into the breast pocket of his suit, and then put the wad of discarded plastic wrap into the wastepaper basket next to him.

"You are very observant."

The old man looked at Chen Zhuo, speaking slowly and with a calm and clear demeanor that came from years of lecturing on the podium.

Chen Zhuo closed the old book in his hand and turned his head away.

"Nowadays, journal editorial departments don't even do this basic typesetting and proofreading anymore."

The old man gently tapped the cover of the journal with his finger.

"They rely too much on the automatic generation of computer programs. Once they press the compile button, they no longer use their eyes to check the symmetry of the formula line by line."

"Computers only execute instructions; they don't care about the aesthetics of layout."

Chen Zhuo put the old edition of the monograph back into the gap on the bookshelf.

"When symmetry is disrupted, the logical coherence of time is greatly reduced. The presentation of mathematical formulas on paper should itself be a kind of visual logical proof."

The old man nodded, his gaze sweeping over the book Chen Zhuo had just put back.

"That was a book on the foundations of algebraic geometry published in 1976, and some of the concepts in it have been removed from current textbooks."

"Just flipping through it," Chen Zhuo said.

The old man glanced at Chen Zhuo, stepped aside, and pointed to the rest area by the window at the back of the bookstore.

"There are seats over there. If you're not in a hurry, you can sit with us."

The old man spoke in a very natural tone.

"The drip coffee at this shop is pretty good."

Chen Zhuo glanced in the direction the old man pointed.

Two dark green single leather sofas were placed by the window, separated by a small, dark round wooden table. Outside the window was a bustling street.

"it is good."

Chen Zhuo nodded.

The two walked to the rest area one after the other.

Chen Zhuo went to the bar and ordered two cups of coffee. He carried the two paper cups back and placed one of them on the round table in front of the old man.

"Thanks."

The old man sat down on the sofa, holding a warm paper cup in both hands.

Chen Zhuo sat down on the sofa opposite him.

"Richard, at the Harvard Institute for Topology."

The old man took a sip of coffee, looked at Chen Zhuo, and simply gave his name and workplace.

"Chen is at Princeton."

Chen Zhuo gave a similarly simple answer.

Richard raised an eyebrow slightly and put down the paper cup.

"Princeton is a great place to do pure mathematics."

Richard leaned back slightly against the sofa.

"How's Pierre Deligne's temper these days? I heard he kicked a teaching assistant out of class last semester because his handwriting on the blackboard wasn't neat enough."

He doesn't talk much, but he'll still swear when he needs to.

Chen Zhuo took a sip of coffee, and the bitterness of the coffee spread in his mouth.

Richard chuckled softly and shook his head.

"In our line of work, if you don't have an almost obsessive requirement for logic, you can't hold the line."

Outside the window, a yellow school bus slowly drove by, its red warning lights flashing at the rear. Pedestrians on the roadside turned up their coat collars to ward off the increasingly chilly autumn wind.

Richard looked away and his gaze fell on the mathematics journal on the table that he had just circled.

His fingers tapped lightly twice on the cover.

"Since you've come all the way from Princeton, you must be here for the MIT seminar tomorrow."

Richard looked up at Chen Zhuo across from him.

"Come and take a look."

Chen Zhuo held up a paper cup.

"Have you read that paper about the underlying architecture of concurrent scheduling, especially 'Algebraic Foundations'?" Richard asked.

"I've watched it several times."

Chen Zhuo placed the paper cup on the table.

Richard took a deep breath, his easygoing demeanor fading slightly, replaced by a seriousness befitting an academic discussion.

"Young man, since you study algebraic geometry, you should be aware of the problems in that paper."

Richard crossed his hands on his knees and leaned slightly forward.

"Those researchers from the engineering department used this truncation operator, known as constant C, to run a closed loop of a high-dimensional manifold on a supercomputer. This is indeed an achievement worth recording in applied physics and computer engineering."

Richard’s tone was calm, without any emotional fluctuation, as if he were simply stating an objective fact.

"However, this does not conform to the rigor of mathematics."

Richard looked at Chen Zhuo, his voice steady.

"The architecture of mathematics is built brick by brick; every theorem and every transition must be supported by rigorous logical proof."

"That paper made a serious leap at the extreme point of the transition from continuous physical space to discrete matrices."

Richard stretched out a finger and drew a line in the air, then suddenly stopped in the middle.

"He directly presented a constant C without any calculus derivation."

"It's like building a skyscraper. When you get to the fiftieth floor, the designer suddenly skips a crucial load-bearing wall and forcibly connects the two ends of the structure with a piece of wood that was temporarily found."

Richard withdrew his hand and grasped the warm paper cup again.

"Right now, the building doesn't appear to have collapsed, and the computer has processed the data, but this doesn't prove that the plank can withstand the weight of the entire building in the future when faced with more extreme variable shocks."

Richard's gaze was fixed on the center of the table.

"Therefore, at tomorrow's defense meeting, as fellow participants, we must ask him to complete the drawings of this load-bearing wall. He needs to derive the omitted part of the calculus bridge step by step on the podium."

The bookstore remained quiet.

At the next table, a short-haired girl was writing something in her notebook, the pen tip making a soft scratching sound as it glided across the paper. In the distance, the hissing sound of a coffee machine frothing milk came from the bar.

Chen Zhuo listened to Richard's words, his gaze falling on the table.

Richard's logic is extremely rigorous, perfectly conforming to the standard thinking pattern of a traditional mathematician.

Chen Zhuo picked up the paper cup and took a sip of coffee.

"Professor Richard, the analogy of a load-bearing wall is very apt."

Chen Zhuo put down his cup, casually rested his hands on the armrests of the sofa, and looked at the old man opposite him.

"But is it possible that when the author got to that point in the deduction, he discovered that load-bearing walls were not needed at all?"

Richard's brow furrowed slightly.

"The contraction of physical continuity will inevitably lead to collapse at the extreme point. Without a load-bearing structure, the mapping of the manifold cannot be completed."

Richard's tone conveyed academic affirmation.

"He didn't sever the mapping."

Chen Zhuo calmly accepted the question.

Richard looked at him without interrupting.

"If it's a traditional solution, it does require complex calculus to deal with those tens of thousands of redundant variables, to build a bridge, to construct a wall."

Chen Zhuo's tone was as if he were stating an extremely common sense fact.

"But the computing power of engineering has its limits."

Chen Zhuo extended his right index finger and lightly drew a short straight line on the texture of the round table.

"Instead of spending time proving how that load-bearing wall was built, it's better to directly change the interior layout. That physical extreme point, in the entire high-dimensional algebraic structure, may not be a load-bearing wall, but just a partition wall."

Chen Zhuo raised his eyelids and looked calmly at Richard.

"Since it's a partition wall, removing it won't affect the main structure. That constant C is just a soundproofing panel that was casually put up to fill the gap after the wall was removed."

Richard paused slightly in his hand holding the paper cup.

He did not immediately refute.

Richard looked at the wood grain on the table, his mind pausing for a few seconds on the assumption of the partition wall that Chen Zhuo had put forward.

If we step outside the local perspective of topology and consider those variables as non-load-bearing elements that can be independently separated...

Richard shook his head.

"This is an extremely risky form of pragmatism."

Richard picked up his coffee cup, took a sip, and looked at the young man in front of him.

"Skipping the proofs directly and relying on intuition to dismantle high-dimensional structures in order to solve immediate engineering problems, while ignoring the derivation process of classical mathematics."

Richard put the cup down.

"You young people always tend to be pragmatic. You think very fast and are willing to take shortcuts to get results, but you can't do that in pure mathematics."

Richard looked out the window; the streetlights on Massachusetts Avenue were beginning to come on one after another.

"And, to put it another way, even if it really was just a partition wall..."

Richard turned his head and looked back at Chen Zhuo.

"He also has to prove to everyone on the blackboard tomorrow, using rigorous formulas, that it is indeed a partition, not a load-bearing wall."

"Demolition without blueprints in front of hundreds of colleagues is not in accordance with building codes."

Chen Zhuo looked at the old man.

"I see."

Chen Zhuo nodded.

Richard glanced down at his watch.

"It's getting late, I need to go back to the hotel to sort out the details of the questions I need to ask tomorrow."

Richard stood up and put the mathematics journal into his briefcase.

Goodbye, young man.

Richard picked up his briefcase and looked at Chen Zhuo.

See you at the venue tomorrow.

"goodbye."