My IQ has been increasing year by year.

Chapter 195 Hodge's Conjecture

The sky outside the window was completely dark.

The motion-sensor lights in the corridor stayed on for a while, then quietly went out as the last few students' footsteps faded into the distance.

The overhead lights were not on in the office.

Li Jianming casually turned on the old-fashioned desk lamp on his desk. The white light was somewhat diffused, barely illuminating half of the blackboard.

The remaining half of the blackboard was hidden in the dim shadows.

"This road is impassable."

Li Jianming stopped writing with the chalk.

He turned his head and looked at the long string of discrete matrix transformation formulas that he had just written down next to him.

"Isolating the singularity is the right idea, but when it is wrapped in an algebraic loop, the dimension of the complex manifold collapses."

The old professor wiped the sweat from his forehead with the back of his hand, which was covered in chalk dust.

"Once the dimension collapses, your first-order truncation is no longer a simple cutting off of higher-order terms; it will tear the entire topological space apart. It may converge, but in mathematical logic, it becomes a stillborn child."

Chen Zhuo stood at the boundary between shadow and light.

He tilted his head slightly, looking at the densely packed symbols on the blackboard.

His cuffs were so stained with chalk dust that their original color was no longer visible. He held the broken piece of chalk in his hand, his thumb and forefinger unconsciously twirling it back and forth.

"If it's dimensional collapse..."

"Chen Zhuo spoke, his voice still gentle, but his speech was slower than usual. The intense mental calculations had made his voice sound tired.

"Teacher, can we not consider it as a complete topological space?"

Li Jianming was stunned for a moment.

"What do you mean?"

Chen Zhuo took a step forward and stepped into the halo of the lamp.

He raised his hand and drew a small cross on the blackboard, where the chalk touched the symbol representing dimensional collapse.

"Since it's torn, we'll follow the tear."

As Chen Zhuo spoke, he started a new line next to the cross.

"We perform a homomorphism with reduced dimensionality, not requiring it to maintain the properties of a complex manifold globally, but only requiring it to align with the truncated boundary on the local rational algebraic closed chain."

Li Jianming stared at the half-line formula that Chen Zhuo had written.

His eyes narrowed slightly.

"Dimensional reduction homomorphism..."

Li Jianming muttered to himself, his mind racing as he considered the possibility.

"If the alignment is only local... then the singularity is no longer a problem; it becomes a trivial term in a low-dimensional space."

Li Jianming's breathing became heavier.

He suddenly turned to look at Chen Zhuo, a spark rekindling in his eyes.

"But how do you close the integral on the outer perimeter? The dimensions are mismatched; what do you use to fill the gap in the middle?"

Chen Zhuo thought for a moment.

"Fill in the gaps using the number of intersections of the algebraic variety."

Chen Zhuo handed the chalk in his hand to Li Jianming.

"You set the framework, and I'll calculate the matrix of intersection points. As long as the intersection points can be aligned in the rational number field, this gap can be filled by algebraic loops."

Li Jianming did not take the chalk.

He looked at Chen Zhuo as if he were looking at an unreasonable monster.

The number of intersections of algebraic varieties is used to fill the dimension gaps in the topological space.

This idea is utterly barbaric.

But logically, it seems to be flawless.

Li Jianming turned around and took another piece of chalk from the chalk box.

"I'll count the left, you count the right, and we'll meet in the middle, at the position of the homology class."

Li Jianming's voice carried an undeniable decisiveness.

"it is good."

Chen Zhuo took back the half of the chalk and walked to the right side of the blackboard.

Wu Tao sat in the chair behind the sofa.

The black ballpoint pen in his hand had run out of ink, so he casually tossed the broken pen onto the coffee table, pulled a new one out of the drawer, bit off the cap, and continued writing in his notebook.

His wrists were sore and numb.

The notebook has been turned over dozens of times, and each page is filled with derivation processes that make people dizzy just by looking at them.

He looked up and glanced at the blackboard.

Li Jianming and Chen Zhuo were incredibly fast.

They hardly communicated anymore.

One person finishes writing the previous step, the other glances at it, and they can immediately continue to the next step. That kind of tacit understanding has transcended language and become a kind of pure mental synchronization.

The blank spaces on the blackboard are getting fewer and fewer.

The glow of the table lamps seemed to dim somewhat during this intense simulation.

Ji Jianming wrote down the boundary conditions for the last complex manifold.

He stopped writing.

His chest heaved violently; he had reached his physical limit.

The old professor held the wooden trough under the blackboard with his left hand, pinched the chalk in his right hand, and turned to look to his right.

Chen Zhuo is still writing.

The chalk left white marks on the blackboard.

Those originally scattered and divergent discrete matrices, under Chen Zhuo's hands, began to converge towards the center little by little, as if they were living things.

Ultimately, it is reduced to a concise algebraic loop expression.

"Click."

The piece of chalk in Chen Zhuo's hand broke.

A small piece broke off and fell to the ground with a soft thud, rolling to the corner of the wall.

Chen Zhuo ignored it.

With the last bit of chalk, he drew an equal sign at the end of that algebraic loop.

Then, he connected the other end of the equals sign to the boundary condition written by Li Jianming.

On the left is a deep and complex algebraic geometry.

On the right is a cold, precise discrete matrix.

At both ends of the equal sign, they are perfectly aligned.

The first-order truncation that Li Jianming had originally called a hooligan has now completely closed under the influence of this massive algebraic cycle.

There is no infinity.

It did not diverge.

In the logic of pure mathematics, it is legal.

The office was deathly silent.

Only the pen in Wu Tao's hand made a slight scratching sound as it stopped on the paper after writing the last character.

Li Jianming slowly straightened up.

He neither cheered nor spoke.

He looked at the equal sign in the center of the blackboard, which represented perfection, and took a step back.

His heel hit the edge of the lectern with a dull thud.

Li Jianming seemed not to feel any pain, his gaze never leaving the blackboard.

The more he looked, the heavier his breathing became.

As a professor who has spent his entire life immersed in the field of pure mathematics, his insight is incredibly sharp.

What's written on this blackboard isn't boundary derivation of fluid equations at all.

That's just appearances.

In their efforts to repair the truncation and align the left and right sides, they unknowingly constructed an extremely large and complex non-singular complex projective algebraic variety.

Furthermore, they forcibly expressed it using a linear combination of rational algebraic closed chains.

Li Jianming's fingers began to tremble slightly.

The piece of chalk slipped from his fingers, fell to the floor, and broke into three pieces.

"teacher?"

Wu Tao sensed something was wrong. He closed his notebook, stood up, and looked at Li Jianming with some concern.

Li Jianming ignored Wu Tao.

He turned his head and looked at Chen Zhuo, who was standing at the other end of the blackboard.

Chen Zhuo also looked at him.

There was no wild joy on the boy's face. He patted the chalk dust off his hands, his expression still gentle and calm, but there was a hint of understanding of the boundaries of knowledge in his eyes.

"Chen Zhuo".

Li Jianming spoke, his voice terribly hoarse.

"Let's stop."

Chen Zhuo nodded and placed the last piece of chalk in his hand into the blackboard slot.

"Do you know what this is?"

Li Jianming leaned against the lectern, looking at Chen Zhuo.

Chen Zhuo remained silent.

He actually had a vague feeling when he was halfway through the deduction.

That feeling of suddenly touching a seabed fault in the deep sea.

"This is not a polynomial approximation."

Li Jianming gave a self-deprecating laugh, a laugh tinged with an almost trembling helplessness.

Li Jianming pointed to the core area in the center of the blackboard.

"This is a special case of Hodge's conjecture."

Wu Tao's notebook fell onto the coffee table with a thud.

He stared blankly at the blackboard, his mind going blank.

Hodge's conjecture.

These four words are like an insurmountable mountain for anyone who studies mathematics.

That was one of the seven Millennium Prize Problems with a $1 million reward from the Clay Mathematics Institute.

It is the holy grail of algebraic geometry and topology.

Wu Tao felt his legs go weak. He slowly sat back on the sofa, staring at the blackboard. Suddenly, he felt that every word and phrase exuded a suffocating sense of oppression.

Li Jianming looked at Chen Zhuo.

He wanted to see shock, fervor, or fear on the thirteen-year-old boy's face.

But nothing.

Chen Zhuo simply tilted his head slightly, glanced at the formulas on the blackboard, and then looked away.

"The wall is too thick."

Chen Zhuo gave a very fair assessment.

He looked at Li Jianming, his tone calm.

"With my current brainpower, even with the fastest computing power, I can't get past this wall. There's too much theoretical foundation and underlying mathematical tools required. I still haven't learned enough."

Chen Zhuo readily admitted his limits.

He doesn't assume that just because he's a genius, he can solve the Millennium Problem by intuition alone.

Intuition can lead him to the door, but to open that door, he needs an extremely large and systematic foundational framework.

Hearing Chen Zhuo's words, Li Jianming felt a weight lifted from his heart.

What he feared most was that Chen Zhuo was too arrogant and would insist on crashing his head against the wall and dying.

A genius who goes astray can destroy himself faster than anyone else.

"It's good that you can see it clearly."

Li Jianming sighed, his tone filled with indescribable complexity.

"My knowledge base has reached its limit. I can't help you get over this wall. At most, I can only shamelessly ask someone for help when you don't understand something."

Li Jianming looked at Chen Zhuo as if he were looking at a peerless piece of uncut jade, but he was troubled because he did not have a carving knife in his hand.

The atmosphere in the office became unusually heavy.

It was a sense of powerlessness after hitting the ceiling of human intelligence, mixed with a hint of resentment.

Wu Tao sat on the sofa, even his breathing became soft.

In this almost frozen silence.

"Gurgle."

A very clear, very untimely voice rang out in the office.

Li Jianming was stunned.

Wu Tao was also stunned.

Both of them turned their gaze toward the source of the sound.

Chen Zhuo stood in front of the blackboard and glanced down at his stomach.

He reached out and rubbed his stomach through his clothes.

Then, he looked up at Li Jianming and Wu Tao, who were somewhat taken aback, and smiled helplessly.

"Teacher, this wall really can't be pushed down, and..."

Chen Zhuo paused for a moment, then his expression regained its youthful vibrancy, tinged with a hint of complaint.

"I was at the physics department at noon, and I was so focused on watching them run data that I didn't get enough food from the cafeteria. Now I'm actually a bit hypoglycemic."

The heavy academic atmosphere instantly crumbled upon this sentence.

The oppressive feeling brought about by the Millennium Problem was shattered by this crisp gurgling sound.

Li Jianming looked at the boy in front of him, who was covered in chalk dust and whose stomach was growling with hunger.

One second they're conquering the abyss of algebraic geometry, the next they're rubbing their stomachs and yelling that they're hungry.

The old professor finally couldn't hold back any longer.

He pointed at Chen Zhuo and laughed loudly. The laughter echoed in the spacious office, making the windowpanes tremble slightly.

"You brat!"

Li Jianming laughed and cursed.

He walked to the boss's chair, picked up the gray knitted vest, put it on, and buttoned it up one button at a time.

"No problem is bigger than eating! Let's go eat!"

Li Jianming waved his hand and strode towards the door.

Halfway there, he suddenly stopped and turned to look at Wu Tao, who was still sitting on the sofa in a daze.

"Wu Tao!"

"Yes, teacher!"

Wu Tao quickly stood up.

"Check everything you just wrote down against the last thing left on the blackboard, character by character! Produce a clean draft. Figure out any skipped steps yourself. If you get even one wrong symbol, you can forget about your defense!"

Wu Tao glanced at the blackboard covered in wild cursive writing with a bitter expression, then looked at the watch on his wrist.

8:30 p.m.

Looking at his messy dozen or so pages of notes, and then at the blackboard covered in wild cursive, Wu Tao felt utterly hopeless.

"Teacher, you two were jumping around too much just now... If I need to sort out the logic in this and make a copy that I can understand, the cafeteria will definitely be closed."

Chen Zhuo walked over and patted Wu Tao on the shoulder.

"Thank you for your hard work, senior brother. Take your time."

Chen Zhuo smiled gently.

"The Physics Department just gave us some payment for our work. My teacher and I are going to the stir-fry section of the second canteen to eat. Come over when you're done copying, and I'll treat you to sweet and sour pork ribs."

Wu Tao's eyes lit up when he heard this.

"Did the Physics Department pay your stipend? How much? Can I order some braised ribbonfish?"

The image of the bank card containing two million yuan flashed through Chen Zhuo's mind.

He nodded, his tone very sincere.

"Plenty of ribbonfish."

Li Jianming listened to the conversation between the two students at the door and urged them impatiently.

"Hurry up! Chen Zhuo, come with me, don't disturb him while he's working."

Chen Zhuo responded and followed Li Jianming out of the office.

The two walked down the stairs side by side.

"Chen Zhuo".

Li Jianming walked ahead with his hands behind his back and suddenly spoke.

"Um?"

Chen Zhuo responded.

"If the acceptance letter for that paper in the Journal of Mathematics arrives, I will ask the department to handle it discreetly and not push your name out for the time being."

Li Jianming did not turn around; his voice echoed in the empty corridor.

Chen Zhuo raised an eyebrow.

Why?

He didn't actually care about becoming famous; he was just curious about Li Jianming's decision.

"A tree stands out in the forest."

Li Jianming paused.

"You're only thirteen years old. A top-tier graph theory journal article is enough to make you famous both domestically and internationally, but that's not a good thing. All sorts of conferences, social engagements, and titles will overwhelm you, and you won't have time to focus on your studies."

Li Jianming turned a corner, stopped, and looked back at Chen Zhuo.

"What's more, what we encountered tonight was enormous."

The old professor's eyes appeared somewhat profound under the incandescent light.

"Hodge guessed that once a word of this leaked out, saying that we had made some progress in this area, whether it was true or not, we would be under intense scrutiny both domestically and internationally, and we would become a target of the academic community."

Chen Zhuo nodded, indicating his understanding.

"The Fang Academy made me sign a confidentiality agreement, probably to avoid causing me trouble."

Chen Zhuo casually mentioned it.

"What do those rough guys in the physics department know?"

Li Jianming gave a soft hum.

"They did it for the sake of Tibetan technology, I did it for the sake of Tibetans."

Li Jianming continued walking down.

"There's not much I can teach you back home. What you're lacking is top-level algebraic geometry knowledge and thinking. You can't learn this from books; you need someone to guide you."

Li Jianming sighed.

"I'll keep an eye out for opportunities abroad for you. For this level of problem, you need to go to a place with a solid foundation."

Chen Zhuo followed behind without saying a word.

He actually understood what Li Jianming meant.

I walked out of the math department building.

The cool autumn night wind blowing on my face invigorates me.

Not far away, the lights of the second canteen looked especially warm in the night.

Occasionally, groups of two or three students would walk by after their evening self-study sessions, carrying freshly bought sausages or milk tea.

Chen Zhuo took a deep breath of the air, which smelled of fallen leaves.

"teacher."

Chen Zhuo turned his head and looked at the stubborn old man next to him who had been stubborn all his life.

"Actually, besides sweet and sour pork ribs, we can also add steamed sea bass today."

Chen Zhuo smiled gently.

"The fee that Dean Fang gave us today was quite substantial; it's a small token of their appreciation from the School of Physics to our School of Mathematics."

Hearing this absurd talk, Li Jianming was so angry that he wanted to hit him on the head with the teacup in his hand.

"Useless! All you can think about is those spare ribs and sea bass!"

Li Jianming cursed, but quickened his pace.

"Hurry up, or the chefs at the stir-fry shop will be off work."

Chen Zhuo smiled and shook his head, then put his hands in his pockets.

Through the fabric, the bank card lay quietly against his chest, while in his mind, fragments of Hodge's conjectures continued to collide unconsciously.

The two hardest things in the world.

What we eat determines what problems we resolve.

We have to take it one step at a time.

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