My IQ has been increasing year by year.
Chapter 267 Intermediate Jacobi Cluster
Walking back along the path in front of the forest, the noise behind me gradually faded away.
The colorful welcome tents on the main campus, along with the freshmen running around with their suitcases, were gradually obscured from view by the tall trees. The temperature in the air seemed to drop as well.
Chen Zhuo did not walk fast.
He had his hands in his pockets, the undergraduate recruitment flyer he'd taken from the sophomore boy was casually folded twice and held in his hand. Woolley walked half a step behind him.
The administrative officer stood ramrod straight, his dark gray suit without a single extra wrinkle.
As they moved further away from the crowded area, Woolley's radar-like gaze gradually narrowed, and his tense jawline relaxed slightly. "Mr. Woolley."
Chen Zhuo suddenly spoke, breaking the silence between the two.
"Yes, Mr. Chen."
Woolley immediately slowed his pace and spoke calmly.
"How can I help you?"
"It's nothing."
Chen Zhuo looked at the ancient red brick buildings on both sides.
"I just feel that the trees here at the Institute for Advanced Study seem to be older than those on the main campus."
Woolley pushed up his thin glasses on the bridge of his nose.
"Your observation is very insightful. The greening plan for this area predates the partial expansion of the main campus. Dean Cyril has always opposed pruning the natural growth trajectory of these trees, believing that it would provide better physical sound insulation."
Chen Zhuo smiled.
"The physical soundproofing is really good. When I crossed that road just now, it felt like I was walking from one room into another." Chen Zhuo waved the flyer in his hand.
"Walking through a completely chaotic crowd actually cleared my head a bit, and I suddenly had a new idea about singularity redundancy variables." Woolley's gaze lingered on the flyer for a second.
He didn't ask what a singularity was, nor did he ask what a redundant variable was.
His administrative guidelines do not allow him to inquire about the specific research content of scholars.
"If it can inspire you, then your walk just now was worthwhile."
Woolley responded politely.
"yes."
Chen Zhuo quickened his pace.
"Let's go back quickly."
Pushing open the door of Fan Enlou, the only sound in the quiet corridor was their footsteps.
Woolley stopped at the door of his office and bowed slightly.
"Mr. Chen, I need to process a few daily reports for the logistics department. If you need anything, please feel free to call the internal phone on my desk." "Okay, thank you."
Chen Zhuo didn't linger and went straight to Pierre's office at the other end of the corridor.
Chen Zhuo pushed open the door and went in.
Pierre wasn't in the lounge; he came back here.
Several old journals were spread out on his desk, and he was holding a pencil, looking at something line by line.
Pierre didn't even look up when he heard the door open.
"Have you finished watching the excitement outside?"
"I've finished watching it."
Chen Zhuo walked to the water dispenser and poured himself a glass of water.
He took a couple of sips, walked to his desk, pulled out a chair opposite Pierre, and sat down.
Chen Zhuo placed the recruitment flyer in his hand on the table and flipped it over.
The flyer had the calculus problem that he had pointed out was printed on the front, while the back was a completely blank sheet of paper.
Chen Zhuo didn't look for special draft paper; instead, he picked up a black ballpoint pen from the pen holder on Pierre's desk and removed the cap.
"Did you find anything?"
Pierre put down his pencil and looked at the crumpled flyer.
"A little."
Chen Zhuo put the water glass aside.
Chen Zhuo did not write a long derivation process. He first drew a few scattered points, then connected these points with a few curves, and finally wrote two matrices in the center of the paper, connected by a symbol with a right-pointing arrow.
Above that arrow, he wrote a capital letter J.
Pierre's gaze followed the tip of the pen.
"Intermediate Jacobi cluster".
Pierre leaned back in his chair, looking at J.
"You've finally decided to get involved with this mess."
Chen Zhuo didn't rush to write; he tapped the table with his pen.
"Just now on the main campus, I saw thousands of new students moving between several buildings."
As Chen Zhuo spoke, he drew circles on the scattered dots with the tip of his pen.
"They were pulling suitcases, and their route was completely random, with no discernible pattern."
Pierre listened quietly without interrupting.
"If we consider these people as a continuous analytic manifold, when they are in an open area, this continuous deformation is very smooth; they can move around freely and go wherever they want." Chen Zhuo changed the subject and drew a solid black square in the middle of the paper.
"But once they encounter welcoming tents or roadblocks in the middle of the road, this continuity is broken, and the flow of people becomes congested, forced to stop, squeezed, and turned." He tapped the black square twice heavily.
"This is the singularity."
Pierre added a comment.
"Yes, the singularity."
Chen Zhuo raised his head and looked at the old man opposite him.
"Those people outside who study continuous manifolds are trying to track how these people's movements change when they encounter the tents. They want to write a perfect equation to calculate whether each person goes around to the left or squeezes to the right."
Pierre gave a cold laugh.
"That's a stupid idea."
Pierre offered his assessment without reservation.
"Once the dimensions increase, the number of variables becomes so large that it could burn out all existing computers; it's a tangled mess that's impossible to calculate."
"So I don't want to calculate it anymore."
Chen Zhuo lowered his head and drew four straight lines on the flyer with his ballpoint pen.
These four lines form a closed frame, firmly enclosing the solid black cube representing the singularity in the very center.
"I don't care how abortions are distorted."
Chen Zhuo's voice was very gentle, with little variation in tone.
"I plan to use a discrete grid to cut out the space around that tent directly."
He touched the edge of the square with the tip of his pen.
"Treat all the variables that come in and out continuously, and treat all the trajectories that attempt to transition smoothly, as redundant terms and forcibly truncate them."
The office fell silent.
Pierre stared at the square on the paper for a long time.
After a long while, Pierre slowly began to speak.
"Sever continuous mappings".
Pierre looked up from the paper and at Chen Zhuo.
"This means you've completely abandoned the smooth transitions in geometry. You know, if those gentlemen in Paris saw this frame you drew, they'd be furious. They'd probably say it's a betrayal of mathematical aesthetics."
Chen Zhuo twirled the ballpoint pen in his hand, a nonchalant smile on his face.
"They'll say you're a butcher with a pig-slaughtering knife."
Pierre stared at him, a slight smile creeping across his face, a glint of light in his eyes.
"They will tell you that the water flow cannot be forcibly cut off, as it is against the rules."
"Then I'll just become a butcher. It won't make a difference if I have to do it again."
Chen Zhuo stopped twirling his pen and met Pierre's gaze.
"If we don't break the continuous mapping, we will never find the zero of the normal function in high-dimensional space. As long as we can frame this singularity and lock its position with a discrete matrix, it can't escape. As for the rules, we can explain them to them slowly after we solve the problem."
Pierre suddenly laughed.
He leaned over, snatched the pen from Chen Zhuo's hand, and quickly wrote three supplementary algebraic constraints next to the box. "Use normal functions as detectors to directly capture that collapsing singularity."
Pierre spoke as he wrote.
"It's unreasonable and direct, it removes all the illusions of analysis and forces it to reveal its algebraic bones."
Chen Zhuo looked at the conditions Pierre had added and nodded.
"Yes, as long as we can prove that the points bound by this discrete matrix correspond to an algebraic cycle one hundred percent, then the path from analytic to algebraic will be clear." Pierre threw down his pen, leaned back, and crossed his hands on his stomach.
He sized up the boy before him, his eyes showing no condescension towards a student, only an equal scrutiny.
"You previously used a discrete mesh to fill the holes in the torsion section."
Pierre tapped his fingers on the table.
"That paper was published in full in the Annals of Mathematics, and my colleagues couldn't find any fault with it. You've cleared the minefield on the outside." Pierre gestured with his chin to the leaflets on the table.
"Now, you've finally hit the core of this problem, which is also the most illogical part."
Chen Zhuo leaned back in his chair and listened quietly.
"High-dimensional intermediate Jacobian clusters".
Pierre spoke slowly.
"Those guys outside who work on continuous manifolds are all stuck in the mud of analytical problems. They always think that as long as they write the differential equations beautifully enough, they can get their hands on water." Pierre pointed at the box.
"But since you didn't want to catch water, you built a cement pool, froze the water and mud together, then smashed it with a dart and only managed to pry out the stone inside," Chen Zhuo chuckled.
"This metaphor is very vivid."
"This is not only visually appealing, but also barbaric."
Pierre looked at him, his tone becoming serious.
"Use discrete matrices to frame the singularity, and as long as you can prove that this framed point corresponds to a polynomial equation... you'll bridge the gap between analysis and algebra." Pierre paused, seemingly giving this statement some weight.
"This is the most difficult hurdle to overcome in the entire Hodge conjecture."
Chen Zhuo's smile faded somewhat, and his expression became very calm.
He neither refuted it nor showed any excitement at being affirmed.
Finding the door and actually pushing it open are two completely different things.
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