My IQ has been increasing year by year.

Chapter 281 Beginning

The morning breeze in Boston carries a hint of Atlantic moisture.

The corridors of Harvard University's Science Center echoed with the sound of hurried footsteps.

Today, no one lingered at the coffee bar in the lobby. Those who bought coffee quickly walked towards the large lecture hall at the end of the corridor, paper cups in hand.

Chen Zhuo followed Pierre and Arthur.

They each held an envelope issued by Harvard's logistics department, containing the conference schedule and several sheets of white paper.

The doors to the lecture hall were wide open.

The room was already full of people.

This is not the kind of public lecture that's packed with undergraduates just for the spectacle.

Those sitting here are all colleagues who have come from Princeton, Columbia, MIT, and various universities in Europe.

There were elderly professors with gray hair, and young scholars in suits.

The classroom was well-heated, and the air was filled with the bitter smell of coffee and the hushed conversations.

Pierre led Chen Zhu down the steps and stopped at a row of empty spaces towards the back of the middle.

Arthur sat down first, took off his coat and draped it over the back of the chair. Pierre sat in the middle, and Chen Zhuo sat down in the empty seat to Pierre's right.

Chen Zhuo placed the envelope on the table, untied the string, and pulled out the few sheets of white paper inside.

Then, he took a pen out of his pocket and gently placed it next to the white paper.

Pierre turned his head and glanced at the white paper Chen Zhuo had placed on the table.

"You don't need to calculate it yourself today."

Pierre's voice wasn't loud, just loud enough for Chen Zhuo to hear.

"Just watch from the stands."

Chen Zhuo nodded.

"It's nothing, I'll use it as a notebook."

He raised his head, his gaze passing over the heads of the scholars in the front rows, and landing on the area at the very front of the lecture hall.

The scene in front was completely different from the crowded conditions in the middle and back rows.

A large space was deliberately left empty between the first row of seats and the podium.

This physical distance made the people in the first row stand out.

There were only six chairs there.

Sitting in the middle was Taubes, the head of the Harvard Mathematics Department.

To his left was Shing-Tung Yau, and to his right and several other seats were occupied by several academicians of the US Academy of Sciences specializing in geometric analysis.

None of the six people spoke to each other.

In front of each of them lay a stack of photocopied manuscripts, more than three hundred pages of A4 paper, thicker and heavier than a brick.

Several markers were scattered next to the manuscript.

No one was drinking coffee or looking at their watches. They leaned back in their chairs or leaned slightly forward, staring at the podium, exuding a cold and stern sense of scrutiny.

On the podium was a blackboard that occupied the entire wall.

It is divided into four sections that can be pulled up and down. The blackboard is clean and tidy, and a row of white dustless chalk is neatly stacked in the long chalk tray below.

The minute hand of the wall clock pointed to twelve.

Nine o'clock sharp.

The door on the side of the classroom was pushed open.

Zhu Xiping and Cao Huaidong walked in one after the other.

The previously hushed conversations in the lecture hall vanished completely within seconds.

The space, which could accommodate hundreds of people, was so quiet that the only sound was the faint rustling of the air from the heating pipes.

There was no applause.

No one stood up, took the microphone, or gave an opening introduction.

Cao Huaidong walked to the side of the podium.

There was a separate wooden table and a chair. On the table was a microphone connected to a wire.

Cao Huaidong pulled out a chair and sat down.

He placed the original manuscript, which he had been holding close to his chest, on the table, opened the black cover, and turned to the first page.

He picked up a pen with his right hand and glanced between the manuscript and the academicians in the first row of the audience.

Zhu Xiping did not walk towards the table.

He walked straight to the huge blackboard.

He picked up a brand new white piece of chalk from the chalk trough, without turning to face the audience or saying "Good morning".

With his back to hundreds of the world's top mathematicians, he raised his hand and the chalk landed on the leftmost blackboard.

The chalk tip touched the blackboard, making a crisp tapping sound.

A series of partial differential equations describing the initial state of the manifold moved smoothly against the black background along his wrist.

The letters and numbers were written very large and with great force.

White chalk dust dripped down the surface of the blackboard.

Chen Zhuo sat in the middle or back row, his eyes fixed on the blackboard.

This is the foundation of all the deductions. The initial conditions of the Poincaré conjecture under the Ricci flow are listed line by line.

Zhu Xiping wrote slowly, but very coherently.

After writing the first line, he made a heavy dot with chalk at the end, then started a new line and wrote Hamilton's classic inequality on the evolution of curvature.

Fifteen minutes have passed.

The first blackboard was half full.

No one in the audience was taking notes.

Everyone was staring at those lines of equations, comparing them to the preprints they had seen in their minds.

Just as Zhu Xiping was preparing to write down the third lemma.

On the far left of the first row, a professor from MIT leaned forward slightly.

He didn't raise his hand, but spoke directly, his voice echoing in the quiet lecture hall.

"Zhu".

The chalk stopped on the blackboard.

Zhu Xiping did not turn his head.

"The third line of the first blackboard."

The MIT professor looked at the writing on the blackboard, his tone devoid of any politeness.

"Regarding the initial manifold smoothness condition, did you directly borrow Hamilton's lemma from 1995, or did you implement your own scaling?"

This is a very detailed, but extremely fatal, boundary issue.

If the initial conditions are not determined, all subsequent evolutions will be castles in the air.

The students' eyes instantly shifted between the questioner and the podium.

Zhu Xiping remained with his back to the audience, the chalk in his hand suspended in mid-air, motionless.

Cao Huaidong, who was sitting to the side of the podium, moved.

His gaze never left the manuscript in front of him.

He didn't even turn the pages; he simply leaned forward slightly, getting closer to the microphone on the table.

"We've done a scaling down."

Cao Huaidong's voice was amplified and carried steadily throughout the classroom.

The MIT professor stared at him.

"Where is the boundary?"

"The specific boundaries have been broadened to formula 4.1 on page 12 of the manuscript."

Cao Huaidong speaks at a steady pace and enunciates clearly.

"Because in subsequent deductions, we need to leave enough space for the singularity to handle curvature bursts. Hamilton's original lemma is too tight here, which will cause the flow to fail to converge in a finite time."

The MIT professor lowered his head and opened the manuscript in front of him.

The sound of the pages turning was very loud.

He flipped directly to page twelve and glanced at the two lines on the page.

He picked up a red pen and drew a circle at point 4.1 on the formula.

"I saw it."

The professor looked up.

"The scaling is within the allowable error range, continue."

Cao Huaidong leaned back and moved away from the microphone.

The chalk that had been lying still on the blackboard started moving again.

Chen Zhuo looked at Cao Huaidong on the side of the podium, fiddling with a pen in his hand.

The manuscript, hundreds of pages long, detailing which page each formula was on and why it had to be changed, had its underlying logic like a net, completely enveloping Cao Huaidong's mind.

The simulation continues to move forward.

The equations on the blackboard became increasingly complex, and the evolution of the Ricci tensor began to involve the handling of nonlinear terms.

Ten minutes later.

Harvard's mathematics department chair, Taubes, leaned back in his chair with his hands crossed over his chest.

He looked at the line of equations about the lower bound of eigenvalues ​​that Zhu Xiping had just written.

"Wait a minute."

Taubes spoke up.

The chalk stopped again.

Taubes stared at the blackboard, his brow slightly furrowed.

"Why is the lower bound of that eigenvalue a constant C, instead of depending on time t? The volume changes during curvature evolution."

This time, Cao Huaidong did not approach the microphone.

Zhu Xiping put down the chalk in his hand, turned around, and faced the audience.

A thin layer of chalk dust had settled on the cuffs of his suit as he looked at Taubes, who was sitting in the middle.

"Because on this connected component, the Ricci curvature has been locally controlled."

Zhu Xiping's voice had a heavy southern accent, but his English pronunciation was very clear and articulate.

"Look at the inequality above. We have already given the cutoff using the maximum principle. In the local region, the evolution of t no longer affects the structure of the fundamental group, so the lower bound can be an absolute constant C."

Following the direction Zhu Xiping pointed, Taubes looked at the maximum value cutoff condition circled in red chalk on the previous line.

He pondered for a few seconds.

"Reasonable."

Taubes nodded.

Zhu Xiping didn't say a word more. He turned around, picked up the chalk again, and continued writing.

Pierre sat down next to Chen Zhuo and gently adjusted his posture.

"They've rehearsed countless times backstage."

Pierre looked at the stage and muttered something under his breath.

"This level of proficiency can't be acquired just by looking at manuscripts."

Chen Zhuo turned his head, looked at Pierre, paused for a moment and thought about it.

"Ten years of being sidelined," Chen Zhuo replied softly.

Pierre glanced at Chen Zhuo, said nothing more, and continued to stare at the blackboard.

Time passed little by little.

This high-frequency, intensive reconnaissance fire occurred five times in the first forty minutes.

The top experts in the first row took turns firing their shots, but the real problems were the devil in the details.

Each time, either Cao Huaidong would instantly recite the page number and formula number of the manuscript, or Zhu Xiping would turn around and give an extremely basic logical explanation.

Interrupt, answer immediately, continue writing.

The pace is so fast it's breathtaking.

Many foreign scholars in the audience were secretly alarmed.

They originally thought it would be a one-sided lecture, but the front row of Harvard turned it into a thorough interrogation.

The two Chinese scholars on the podium defended themselves flawlessly.

Forty-five minutes.

The first blackboard on the far left is already full.

Zhu Xiping gripped the metal frame at the bottom of the blackboard with both hands and pushed it upwards forcefully.

With a loud clang.

The blackboard, covered with partial differential equations, slid up to the top along the slide rail, revealing the clean blackboard underneath.

Zhu Xiping picked up the chalk and began to process the topological changes of the manifold in a finite amount of time.

This is the most difficult and error-prone part of proving the Poincaré conjecture.

Singularity.

Hamilton was stuck on this point for over a decade. Perelman offered a seemingly disjointed approach, but left numerous logical gaps.

Zhu Xiping and Cao Huaidong's work over the past ten years has been to gradually weld these gaps shut.

The letters on the blackboard became denser.

When Zhu Xiping wrote down the convergence conditions of the metric tensor before and after topological changes, the air in the entire lecture hall seemed to become heavy.

On the far right of the first row sat an academician of the American Academy of Sciences, whose hair was almost entirely white.

He remained silent, the manuscript in front of him turned to page forty-five.

He stared at the manuscript for a while, then looked up at the conclusion that Zhu Xiping had just written on the blackboard.

The old academician stretched out his withered fingers and tapped twice on the solid wood table.

knock!knock!

The sound wasn't loud, but it had extremely strong penetrating power.

"Wait a minute, Zhu, stop."

The old academician spoke, his voice somewhat hoarse.

The chalk left a short white line on the blackboard and then stopped.

Zhu Xiping did not turn around, but remained facing the blackboard.

The old academician picked up a red pen from the table and touched the manuscript with the tip.

"How did you determine the convergence bound of the metric tensor in your description of manifold topological transformations?"

The old academician looked at the podium with sharp eyes.

"On page 45 of the manuscript, there are only two lines of conclusion; you directly state its existence."

The classroom fell completely silent.

Even the occasional sound of turning over papers disappeared, and everyone's eyes were instantly fixed on the podium.

"You skipped the intermediate limit derivation steps."

The old academician spoke very slowly, emphasizing each word.

"We are examining the Poincaré conjecture, not listening to a regular academic report. There can be no skipping steps, and I cannot assume your conclusion is valid."

This is the fatal interception.

Without any preamble or pleasantries, it goes straight to the heart of the matter.

If, during this level of review, the speaker is found to have used unproven assumptions, even just once, the credibility of the entire argument will collapse instantly.

This is a hundred times more dangerous than confirming the boundary conditions we just discussed.

Side of the podium.

Cao Huaidong's back lifted off the chair back.

He sat up straight, and his right index finger instantly pressed against the edge of page forty-five of the manuscript.

He was indeed prepared to explain.

The reason for skipping steps in this section is that the derivation process was too complicated. When they were organizing the manuscript, in order to make the layout coherent, they put the specific limit estimates in the appendix and only kept the conclusions in the main text.

Cao Huaidong parted his lips slightly, preparing to announce the page numbers of the appendix into the microphone.

"it is good."

A calm voice interrupted Cao Huaidong's actions.

Zhu Xiping spoke up.

He didn't look at Cao Huaidong to the side, nor did he turn around to look at the thick manuscript.

He put the half-worn piece of chalk back into the chalk tray, turned around, and looked at the old academician in the first row.

Zhu Xiping showed no anger or panic at being challenged.

"I will write out the entire derivation," Zhu Xiping said.

Cao Huaidong shut his mouth, leaned back in his chair, and withdrew his fingers from the paper.

He knows his old partner too well.

Zhu Xiping turned around.

He did not continue writing on the blackboard that he had only half-written on.

He walked to the second sliding blackboard, gripped the frame with both hands, and pulled it down forcefully.

Bang~

A completely clean blackboard appeared in front of everyone.

Zhu Xiping picked up a whole piece of white chalk from the chalk trough.

Without pausing or closing his eyes to recall, the chalk tip landed directly on the upper left corner of the blackboard.

A purely brute-force display of computing power has begun.

The sound of chalk hitting the blackboard became extremely frequent and rapid.

Zhu Xiping acted very quickly.

Partial differential equations, integral symbols, and convergence coefficients flowed from his hands like a stream.

He did not use any written explanations, only the purest mathematical symbols.

The first line is finished.

second line.

Third line.

He began to estimate the limit of the metric tensor near the topological singularity.

This is a tough battle to forcibly establish order in a continuous space.

There are no tricks involved, only an enormous amount of computation and an extreme mastery of partial differential equations.

Chen Zhuo sat in the middle or back row, leaning slightly forward.

His right hand, which was placed next to the white paper, unconsciously tapped the table lightly with his fingers.

His brain was working at lightning speed, trying to keep up with the progress on the blackboard and build a model of the convergence boundary in his mind.

The first step was to introduce a time variable, and Chen Zhuo followed suit.

The second step was to expand the Ricci tensor in the local coordinate system, and the corresponding matrix appeared in Chen Zhuo's mind.

The third step is to substitute Hamilton's extremum domain conditions into the integral scaling.

Chen Zhuo's thinking paused for less than a second because the scaling coefficients needed to be recalibrated. Just as he had aligned the initial conditions of the coefficients in his mind and was about to continue the deduction,

He raised his head and looked at the podium.

Zhu Xiping had already written up to the sixth step on the blackboard. He had not only finished calculating the limit, but had even begun to use this limit conclusion to derive the next lemma about connected components.

Chen Zhuo stopped tapping his fingers on the table.

He looked at the figure standing in front of the blackboard, the fabric of the suit back tugging as the arm swung wildly.

A look of utter awe appeared in Chen Zhuo's eyes.

He can't outsmart him.

It's not a matter of intelligence, but rather the kind of memory that's been ingrained in your very being, a gap that no amount of talent can bridge instantly.

"Smack."

A crisp sound.

The white chalk in Zhu Xiping's hand broke in the middle because he used too much force while writing.

The broken piece of chalk fell to the ground and rolled to one side.

Zhu Xiping didn't even lower his head.

He continued to scribble on the blackboard with the remaining half of the chalk in his hand.

Without any hesitation, without any movement of flipping through the manuscript paper.

This is a complex derivation that was written on a public basis without any preparation.

If you rely on rote memorization, your mind would go completely blank when faced with the intense, oppressive gaze of hundreds of top peers.

The only explanation is that he has written, calculated, and overturned these equations countless times over the past ten years.

They had long since become a part of his body.

ten minutes.

The entire huge blackboard was completely filled with densely packed partial differential equations.

At the end of the last line, Zhu Xiping heavily drew a symbol of absolute convergence.

He stopped.

He casually tossed the last bit of chalk in his hand into the chalk bin.

Zhu Xiping turned around, clapped his hands together, and white chalk dust scattered in the air, landing on his suit and leather shoes.

He didn't wipe the sweat from his forehead, nor did he gasp for breath.

He walked to the edge of the podium and looked down at the old academician on the far right of the first row.

"This limit."

Zhu Xiping pointed to the blackboard behind him covered with equations, his voice calm and even.

"Is it established now?"

Everyone's attention shifted from the blackboard to the first row.

The old academician kept staring at the derivation process on the blackboard.

His gaze swept from the first line to the last.

I watched it for a full minute.

The old academician lowered his head and picked up the red pen on the table.

He drew a very obvious checkmark next to the two lines of conclusion on page 45 of the manuscript.

He looked up at Zhu Xiping and placed the red pen on the table.

"No skipping steps."

The old academician's voice was still hoarse, but there was a new sense of agreement in his tone.

"The logic is complete, okay, continue."

The moment those four words were uttered, the atmosphere in the entire lecture hall seemed to instantly deflate by more than half.

Someone in the back row let out a long sigh.

Pierre sat down next to Chen Zhuo, slowly leaning back until his entire back was pressed against the chair back.

He looked at the Chinese scholar on the stage who was turning to walk toward the third blackboard, and then glanced at Cao Huaidong, who remained calmly seated to the side.

Pierre turned his head and whispered something to Arthur beside him.

"There are no unnecessary steps."

Pierre's tone conveyed the purest sentiments among colleagues.

"Extremely terrifying analytical skills."

Arthur nodded, looking at the equations on the blackboard, without saying a word.

On the platform, Zhu Xiping picked up a new piece of chalk from the chalk trough.

The chalk fell onto the blackboard again, continuing to echo in this lecture hall that brought together the world's most brilliant minds.

The time was 10:30.

The review is still ongoing.