A genius? I just love studying.

Chapter 275 Everything is ready
A squirrel leaped down from a tall ginkgo tree and landed on a thick oak branch that stretched between an oak and a maple tree, right next to the classroom wall outside the window. It ran along the branch, its movements swift and unpredictable.

Sometimes it would accelerate and sprint for a while, sometimes it would suddenly stop, stand up straight, and look around warily...

Michael sat by the window, captivated by Chen Hui's description of the "randomness of the zero-point distribution," yet finding it somewhat elusive. The shadow of a squirrel swaying by the window inadvertently entered his field of vision. Initially a distraction, as he watched, a strange association exploded in his mind.

"This branch...doesn't it resemble the critical line Re(s) = 1/2? And those points where the squirrel stops...aren't they like nontrivial zeros in a random distribution? It accelerates, decelerates, hesitates, and changes direction..."

Doesn't this precisely simulate the spacing between zeros—a spacing that is neither perfectly uniform nor completely chaotic, but rather conforms to specific statistical laws?

He was shocked by his seemingly absurd yet incredibly strong intuition. Almost without thinking, he pointed to the squirrel's projection outside the window and blurted out, "Teacher! Look, doesn't it look like... doesn't it look like a zero-point sequence walking on a critical line? Its 'stopping point' distribution is just like GUE correlation!"

The whole class was stunned. Their gazes shifted from Chen Hui to the squirrel hopping carefree outside the window, then back to Chen Hui's face, a mixture of confusion and amusement on their faces. Elena also raised an eyebrow with interest.

Chen Hui's train of thought was interrupted, and he instinctively frowned and looked out the window.

Just then, the squirrel performed a classic move: it sprinted from a tree scar (point A) to a fork in the road (point B), stopped, and instead of going straight, it circled the fork for half a turn before continuing to run toward the next target (point C).

This path is clearly visible on the projection: A->B (sprint)->circling around B->C.

In that instant, Chen Hui's mind was as if illuminated by a bolt of lightning!
He didn't think Michael was being silly; on the contrary, he captured the most vivid interpretation of abstract randomness from this concrete, dynamic image.

The sprint path simulates short intervals between zero points, occurring at high frequency.

The squirrel's circular circling at point B vividly illustrates the avoidance effect. Just as the eigenvalues ​​of a random matrix repel neighbors that are too close, isn't the squirrel's circling and hovering at point B precisely an attempt to avoid directly colliding with the fork in the road, a potential gathering point?

This perfectly corresponds to the scarcity of small intervals in the GUE distribution!
The overall unpredictability is not entirely random. The squirrel's movement is constrained by the tree structure, i.e. the critical line, and its own habits, forming a constrained random walk. This is very similar to the Riemann zeros, which are constrained by analytical conditions on the critical line but exhibit the characteristics of a random matrix!
A surprised and radiant smile spread across Chen Hui's face, and he slammed his hand on the podium.

"Brilliant!"

His voice was filled with excitement as he pointed to the squirrels outside the window, “Look, everyone, our distinguished visiting professor is giving us a master-level demonstration lesson on stochastic processes!”

He walked quickly to the window and sketched the outline of the squirrel's shadow on the edge of the blackboard with chalk.

A horizontal line represents a tree branch, i.e., a critical line.

Draw points at the locations where the squirrel stops, A, B, and C.

A small circle was drawn around point B to mark the avoidance zone.

Connect A->B (short and straight) and B->C (with a loop) with arrows.

"Look!" Chen Hui explained excitedly, "The squirrel's trajectory inadvertently visualizes for us the core of Montgomery's conjecture: the repulsiveness of zero-point distribution!"
Its lingering and detouring at point B is precisely to avoid getting too close to that fork node; this behavior pattern is exactly the same as the sharp decrease in the probability of small gaps predicted by GUE!

His eyes scanned the students intently. "Michael has keenly grasped the topological intuition of this spatial distribution pattern. Although the squirrel's movement is limited by a one-dimensional branch, isn't the distribution of stopping points, turning frequency, and acceleration pattern contained in its path a vivid, discretized one-dimensional random field model?"
It reveals the hidden interconnected structures within randomness in an almost poetic, non-verbal way!

Chen Hui turned around and solemnly wrote on the blackboard: Sciurus Randomicus (Random Squirrel)!

"Let's temporarily name this teaching assistant Sciurus Randomicus! Its 'experiment' reminds us that the most profound mathematical ideas are sometimes hidden in the most ordinary natural dynamics. The mysterious rhythm of the zeros of the Riemann zeta function may be encoded in the rhythm of this squirrel's leaps, in the trajectory of these falling autumn leaves."

Chen Hui suddenly understood. After so many days of contemplation, he finally broke free from his cocoon. The inspiration brought to him by the squirrel tore through the thick cocoon, and rays of light shone in from the outside. He felt that he was about to grasp the key to the Riemann Hypothesis.

Your math grade improved from 78% to 79%.

The barrage of comments arrived as expected, all within Chen Hui's expectations. He knew that this was still the result of his not fully digesting this epiphany, and that his math proficiency would continue to grow rapidly for the next few days.

As the class ended, Chen Hui walked towards his office, while the students chattered excitedly about the lesson. Such a lively teaching method was still something to talk about even at Princeton.

The squirrel by the window was already famous enough, but now it's shrouded in an aura of mystery.

It is foreseeable that before long, "Riemann's Squirrel" will become a new legend in Fein Building, and the squirrel seems to have realized its "academic status" as it leisurely lands on the windowsill and struts around with its head held high, just like an unofficial professor inspecting the classroom.

……

"teacher."

As soon as he returned to the teaching and research office, Deng Leyan called out to Chen Hui.

"?"

Chen Hui opened his mouth slightly, surprised by the title "teacher".

Because of his previous experience, Deng Leyan had never called him "teacher," and Chen Hui understood his awkwardness, so he didn't force him.

I don't know what happened today, but Deng Leyan actually put aside his pride.

"I've found a topic that interests me."

Deng Leyan blushed slightly, but still insisted on finishing what he was saying.

"Oh?"

Is it harmonic analysis?

Chen Hui asked with interest, Elena and Michael were both graduate students, so they had naturally decided on their research topics when they enrolled. Deng Leyan, after all, was still an undergraduate and did not know much about the world of mathematics. Therefore, after choosing the general direction of analysis, Chen Hui did not let him decide on his topic immediately.

However, he had already prepared many alternative directions for Deng Leyan to choose from.

Harmonic analysis is a strength of Princeton, stemming from the legacy of the great mathematician Elias Stein, whose four-part series on analysis, namely "Real Analysis," "Complex Analysis," "Functional Analysis," and "An Introduction to Fourier Analysis," are all his works.

Deng Leyan shook his head.

"Multiscale analysis and additive combinatorics?"

This is the direction Chen Hui plans to recommend: using harmonic analysis tools, such as the circle method and discrete constraint estimation, to solve additive number theory and combinatorics problems.

In particular, the most famous problem in additive number theory is Goldbach's conjecture.

If Deng Leyan can solve this problem, his fame in China will probably be no less than Chen Hui's.

Deng Leyan shook his head again.

"Complex Analysis and Geometric Function Theory?"

Chen Hui had long considered Deng Leyan's future and prepared many directions for him, such as studying dynamical systems through complex analysis, which is also a popular field today.

"I plan to join Elena's team to study weather forecasting models."

Instead of asking Chen Hui to continue recommending directions, Deng Leyan took the initiative to speak.

Studying the existence, uniqueness, regularity, long-term behavior, and possible singularity formation of solutions to the Navier-Stokes equations and Euler equations is a highly challenging core problem in analysis.

Deng Leyan was also very good at partial differential equations.

Chen Hui was silent.

He didn't really want Deng Leyan to get involved in this matter; in fact, he had a premonition that researching this project might be somewhat dangerous.

Elena is an American, and Michael is working with her on the Riemann Hypothesis, so Deng Leyan's identity is quite sensitive. "You should work with Elena on the data first."

Chen Hui did not stop him. Interest is the best teacher, or you could say that interest is also part of talent. He did not want Deng Leyan to be in a dangerous situation, nor did he want to bury his talent.

After explaining some things to Elena, Chen Hui returned to his seat and began to summarize what he had learned in class that day.

His hunch was right. Although Michael seemed uneducated, he had an amazing talent for analytic number theory. Today, working with the squirrel gave him the inspiration to solve the Riemann Hypothesis.

……

On December 24th, a light drizzle fell over Princeton, the sky was overcast, and it looked like the end of the world was about to come.

Chen Hui was running along the shore of Carnegie Lake, sweating profusely.

Professor Adams of the Institute for Advanced Study was running alongside him.

There were quite a few people running along the lake; the wind and rain couldn't stop their love for health.

"Phew...Professor Chen, wait for me...Phew..."

Adams followed Chen Hui breathlessly. This athlete, who had trained for decades, was now struggling to keep up with Chen Hui's pace.

And this guy has only been running for less than six months!
Ten kilometers, thirty-five minutes!
This speed has surpassed that of many professional athletes. Adams was secretly amazed. He had personally watched this little guy transform from a chubby, fleshy young man into the fit and healthy man he is today.

call.

Chen Hui let out a long breath, and after stopping, he wasn't even too out of breath.

During his nearly six months at Princeton, his physical condition has improved dramatically.

With a thought, he brought up the data panel.

[Host: Chen Hui
Chinese Level 4 (15%)

Mathematics Level 5 (97%)

English Level 4 (30%)

Physics Level 4 (96%)

Chemistry Level 3 (99%)

Biology Level 2 (0%)

Physical Education Level 4 (18%)

Geography Level 2 (0%)

History Level 2 (0%)

Politics Level 5 (33%)

In three months, Chen Hui's various attributes have improved significantly. His Chinese language skills have reached level 4 thanks to his deliberate practice. He has also tried publishing a few articles on the Endpoint Chinese website and easily reached 10,000 subscribers.

After reaching level 5 in mathematics, each 1% improvement requires a lot of effort and even a certain amount of luck. To this day, he has not yet reached level 6.

After reaching the CET-4 level in English, Chen Hui stopped paying attention to it, but because he lived in Princeton, his improvement rate was not too slow.

Physics, on the other hand, only saw a slight increase of a little over ten percent in three months, as he only occasionally helped Elena with some questions about Navier-Stokes equations and weather forecasting models.

With his return to training, Chen Hui's athletic proficiency has increased at an astonishing rate. Now, his physical condition is comparable to that of an Olympic champion, and even compared to some champions who specialize in only one area, Chen Hui is a well-rounded athlete.

His speed is comparable to Usain Bolt's, and his weightlifting is comparable to that of Olympic champions in the same weight class...

This is only level 4. Chen Hui doesn't even dare to imagine how monstrous his physical abilities will become if he advances to level 5 or 6.

Sometimes Chen Hui wonders if he had focused on improving his physical fitness from the beginning, would he have become a superman? Especially now that he is in such a situation, his desire to exercise is even stronger.

As for politics, Chen Hui has never paid attention to this subject, but it is growing at an astonishing rate every moment.

Even after reaching level 5 in mathematics, the growth rate has slowed down significantly, but politics seems unaffected. At this rate, it will probably surpass mathematics soon.

Seeing such a promising upward trend, Chen Hui also started to continue studying chemistry two months ago. Now he is only 1% away from upgrading his chemistry to level 4. When all six subjects reach level 4, he will gain another free attribute point.

My math skills will soon reach level 6, and I'll also get a free attribute point.

The future looks bright.

Chen Hui wiped his sweat, drove the Dodge Challenger he had bought more than two months ago back to his villa, parked the car in the yard, took a shower at home, and then went out again.

"I made you breakfast."

Lin Xiaotang, with her hair down and wearing pajamas, stood at the door, rubbing her eyes, and pointed to the beef noodles on the dining table.

As Chen Hui's nominal girlfriend, Lin Xiaotang naturally moved in when Chen Hui moved. Of course, Chen Hui specially prepared a separate room for her.

As for the bowl of beef noodles, Chen Hui curled his lip. Based on his understanding of Lin Xiaotang, it was most likely a pre-made dish. He might as well go to the club and eat some bread.

Woohoo...

The Dodge Challenger roared to life as Chen Hui sped away.

Lin Xiaotang glanced at the beef noodles on the table, picked up a mouthful, and thought it tasted alright. Without being polite, she sat down at the table and finished the noodles in one go. Then she threw the bowl into the sink, wiped her mouth, and walked out of the room toward another Porsche 911 parked in the courtyard.

Of course, it was just a used 911, but given the 911's high resale value, the price she got was still not low, since she bought it herself.

Chen Hui drove his Dodge Challenger into the Princeton campus and arrived in front of a brand new building.

This is the supercomputing building for the mathematics department!
Youwei Group was indeed very efficient. They said it would take three months, and they actually built a supercomputing cluster with a computing power of 10 quadrillion calculations per second for Chen Hui.

The relevant model calculations are already underway, and Chen Hui is very satisfied with the efficiency.

Unfortunately, complete meteorological data is not yet available; otherwise, we could proceed with full-scale model building and validation.

“Teacher, I knew you’d be here. Lend me your Dodge Challenger for a few hours; I need to go buy some things.”

Michael flashed a smile, revealing his white teeth, and said to Chen Hui, "Tomorrow is Christmas, and I'm going to throw a huge party. You absolutely have to come, teacher!"

"Christmas?"

Chen Hui was slightly bewildered, not expecting that he had been away from home for so long. After Christmas came New Year's Day, and after New Year's Day, the Lunar New Year would come soon.

It looks like I won't be able to go home for the Chinese New Year this year.

(End of this chapter)