A genius? I just love studying.

Chapter 251 First Steps into the Free Land, Breathing the Sweet Air

"Hey Han, I heard you're from Jiangcheng University. If I want to pursue a PhD there, what preparations do I need to make?"

On the Princeton campus, a blond teenager stopped Li Zehan and asked earnestly, "I heard that Professor Chen will be taking on some teaching duties and will also be recruiting students. How can I become his student?"

Li Zehan awkwardly touched his nose.

Well, he went to great lengths to transfer from Jiangcheng University to Princeton for graduate studies, but now others are starting to plan to go to Jiangcheng University.

Fortunately, these people only knew that he came from Jiangcheng University, and they didn't know his relationship with Chen Hui.

"All you need to do is pass the exam."

Li Zehan answered truthfully that in the past, there was no need for exams. Not to mention students from Princeton, even students from any random Western diploma mill could easily apply for international student positions and even receive scholarships.

However, Li Zehan is unaware of Wang Qiming's recent sweeping reforms, but if he wants to enter the School of Mathematics at Jiangcheng University, sorry, everyone has to pass an exam, and the difficulty of that exam is not low.

Of course, this guy should have no problem passing the exams to get into Princeton.

"However, if you want to become Chen Hui's student, you still have to pass his interview, so that depends on you."

Li Zehan didn't linger after finishing his sentence and strode towards his research office. Chen Hui had solved another Millennium Problem, and he couldn't afford to fall too far behind.

In Germany, at the Max Planck Institute for Mathematics, Faltings finished reading the paper and sighed. As proud as he was, he had to admit that the young Chinese man was indeed the reincarnation of Gauss and Euler.

He heard that the Institute of Chemistry also collaborated with Chen Hui and made groundbreaking progress in high-temperature superconductivity.

We have focused on both theoretical and applied mathematics, and have achieved world-class, no, even world-class, results in both.

What a scary little guy!
He also spent many years at Princeton and met many geniuses.

If Princeton is a constellation of stars, then that little Chinese guy is the moon shining brightly across the world, a figure on a completely different level from them.

At Yanbei University, Tian Gang took off his reading glasses and sighed again. He had many opportunities to take Chen Hui as his student back then, but he never expected that Chen Hui would end up as his grand-disciple. It was truly a pity.

At Tsinghua University, Qiu Chengwu looked at Yun Wei beside him and asked, "What do you think?"

"The argument is rigorous and the proof is concise."

Yun Wei stammered, “New talents emerge in every generation. I’m only in my thirties, and I’m about to be swept away by the tide.”

"I never expected that kid would actually use complex geometry to complete the proof."

Qiu Chengwu was all smiles, especially seeing the theory he had proposed years ago in Chen Hui's proof, which filled him with a sense of accomplishment.

His specialty is complex geometry, and Chen Hui can be considered to have learned it from him.

"Okay, okay!"

After praising him several times, Qiu Chengwu burst out laughing.

"Get me a plane ticket, I need to go back to my alma mater."

After his initial joy, Qiu Chengwu had a sudden impulse: "If I don't return home in glory, wouldn't that be like wearing fine clothes at night?"

"Is it the University of California, Harvard, Stanford, SUNY, or Princeton?"

Yunwei roughly guessed what the teacher was going to do and asked with some amusement. He knew that the teacher was a graduate of the University of California and had later taught at schools such as Harvard and Princeton.

"Of course we'll go to all of them!"

Chiu Cheng-wu didn't mince words, "It's been a long time since I've seen my old friends. The International Congress of Mathematicians is about to begin, so I'll go and join in the fun."

Chengdu Aircraft Industry Research Institute

Academician E Weinan was overjoyed, "This is wonderful! Chen Hui has truly given us a great gift!"

The fourth-generation engine has been developed and is ready for practical application. Their current research has shifted to the combustion efficiency of internal combustion engines. The breakthrough in the NS equation has undoubtedly made the path ahead clear to them.

Previously, all fluid simulations in engineering were essentially based on numerical solutions of the Navier-Stokes equations. However, regardless of whether the finite volume method, finite element method, or spectral method was used, there was always a hidden concern in its theoretical foundation—the inability to strictly guarantee the global existence and smoothness of the solution.

This means that when the Reynolds number is extremely high, such as in supersonic flow, hypersonic boundary layer, or complex flow, numerical simulations may fail due to decomposition (the appearance of an infinite velocity gradient), but engineers cannot theoretically distinguish whether it is a real physical phenomenon or a numerical error.

The mathematical description of turbulence has long relied on empirical models, whose rationality lacks rigorous mathematical verification. This results in the model parameter adjustment being highly dependent on experimental data, making it difficult to apply universally.

Now, Chen Hui has completed the proof of the Navier-Stokes equations, which means that the stability of numerical methods is mathematically guaranteed. As long as the initial and boundary conditions meet certain regularity, the error of the numerical discretization scheme can be strictly defined through consistency and stability analysis, without the need to verify through a large number of numerical examples to avoid theoretical risks.

This also makes it possible to theoretically modify turbulence models. Turbulence is essentially a high-dimensional nonlinear solution of the Navier-Stokes equations. The existence of smooth solutions means that the statistical average of turbulence can be modeled through rigorous mathematical expansion, reducing the dependence on empirical coefficients.

For example, the ε equation in the k-ε model may be upgraded from empirical assumptions to a first-order approximation with asymptotic expansion.

Especially in the design of hypersonic vehicles in the aerospace field, the prediction of boundary layer transition has long relied on empirical criteria. If a smooth solution to the Navier-Stokes equations exists, the location of the transition point can be rigorously derived from the global structure of the solution, which can significantly reduce the trial-and-error cost of wind tunnel testing.

The core logic of engineering fluid design, such as aircraft aerodynamic layout and engine combustion chamber optimization, is a cycle of design-simulation-experiment-correction. However, due to the theoretical uncertainty of the Navier-Stokes equations, many optimization objectives are essentially derived through a large number of experiments.

The existence of a smooth solution implies that the global optimal solution must exist. The minimum induced drag of the wing can be obtained by solving the stagnation line theory of the Euler equation and then combining it with the smooth solution of the Navier-Stokes equation to correct for the viscous effect, thus directly giving the theoretical optimal solution.

This means that the precise reconstruction of design boundaries goes from trial and error optimization to theoretical prediction!

Academician E Weinan was overwhelmed with excitement as he contemplated the various changes that the proof of the Navier-Stokes equations would bring. He felt that the breakthrough of the Yang-Mills equations had a tremendous impact on theoretical mathematics and theoretical physics, laying a solid foundation for the future.

So, the breakthrough in the Navier-Stokes equations has an impact that is happening now, and may even be happening tomorrow!
Unfortunately, Chen Hui's paper has already been published. Breakthroughs in basic theory are usually not kept secret, which is also the norm in academia.

But this means that everyone can enjoy the benefits brought by the Navier-Stokes equations, and those who want to reap the first wave of benefits need to act quickly.

Suddenly jolted awake, E Weinan strode toward the office of Zhao Yundong, the person in charge at Chengdu Aircraft Industry Group (CAC). “Professor Zhao, we should invite Chen Hui to CAC. If he can personally explain it, we will be able to digest this evidence more quickly. We need to hurry up with the research on the combustion efficiency of internal combustion engines and the design of the seventh-generation fighter jet.”

"Mr. E, please go ahead and make the contact. We will fully cooperate!"

Zhao Yundong was radiant. He understood, of course, that this was an unprecedented opportunity. With Chen Hui by their side, they were sure to gain the upper hand this time.

……

Dennis flew for more than ten hours before landing, transferring in Beijing to fly to Jiangcheng. He was quite familiar with this route.

However, during his layover in Beijing, he immediately saw Terence Tao's post and then logged onto arXiv, where he quickly found Chen Hui's paper.

Dennis found a print shop, printed out the paper, and began studying it on the plane.

Three hours later, the plane landed at Jiangcheng Tianhe Airport. Dennis got off the plane in a daze, but did not go to Jiangcheng University immediately.

Although he had been on a plane for more than ten hours and was feeling very dizzy and in poor condition, he had been studying the Navier-Stokes equations for many years and had also collaborated with Chen Hui for more than half a year. In fact, some of Chen Hui's proofs included some of his own work.

Three hours was enough time for him to understand Chen Hui's paper.

Of course, Chen Hui's statement in the email that he was right was merely to save face for Dennis. Dennis knew that if he continued his research in that direction, he would never find the final answer. Although Chen Hui's proof also used topology, it had absolutely nothing to do with his subsequent research.

With a sigh, after being stranded at the airport for several hours, Dennis finally bought another ticket back to Philadelphia.

The May Day holiday passed quickly, and Chen Hui had a few rare days of leisure before he was about to leave for the International Congress of Mathematicians.

This time, Chen Hui and Yuan Xinyi set off together again. Looking at his student, Yuan Xinyi had a complicated expression. Although Chen Hui was his student, he knew that he hadn't really taught Chen Hui much. Chen Hui's achievements today had little to do with him.

It's truly amazing that this little guy could replicate in just a few months what we've painstakingly researched our entire lives.

Not only Yuan Xinyi, but Dai Yafeng also followed Chen Hui to Philadelphia.

After leaving the airport, Dai Yafeng drove a car he had somehow found, taking Chen Hui and the other person straight to the Hilton Hotel.

This International Congress of Mathematicians was held at the Philadelphia Convention Center, and the official hotel was the Hilton Pennsylvania Hotel, located on the University of Pennsylvania campus, less than 5 kilometers from the Philadelphia Convention Center.

"Brother Feng, what is this?"

As soon as he got in the car, Chen Hui stared at Dai Yafeng's bulging waist. It was late May, and the weather in Philadelphia was quite hot, only slightly better than in Jiangcheng. Dai Yafeng was only wearing a simple shirt, so the unusual thing about his waist was very obvious.

Dai Yafeng didn't hide anything, lifting up his shirt to reveal his black member.

Yuan Xinyi's eyes widened, and he quickly stepped forward to shield Dai Yafeng. "Are you out of your mind?"

Dai Yafeng laughed nonchalantly, "Don't worry, I'm now an employee of a security company and I have a gun license. Not only can I legally carry a gun, but I can also fire it in an emergency."

Yuan Xinyi then remembered that they were in the free United States, where there were indeed fewer taboos.

"We're here to attend the International Congress of Mathematicians, not to take over territory."

He still couldn't help but laugh and complain.

"It's better to be prepared."

Dai Yafeng disagreed with Yuan Xinyi's statement, saying, "This place is different from China. If there is an emergency, having this thing will give us peace of mind and ensure everyone's safety."

Wei'erlong Wei'erlong...

As the three were talking, a car with lights suddenly approached from behind, signaling Dai Yafeng to pull over.

"Do you know why I pulled you over?"

A police officer knocked on Dai Yafeng's car window, cautiously observed the situation inside, and asked a question.

"I'm not sure, officer. Could you please tell me?"

Dai Yafeng rolled down the car window, calmly looked at the police officer, and spoke fluent American English.

After recognizing the three men, the officer's attitude became much ruder. "Put your hands on the steering wheel and get out of the car now. We suspect you have contraband in your vehicle and need to search it. Please cooperate."

"oh oh……"

Dai Yafeng laughed. "Do you have a search warrant? I don't agree to your search."

Normally, at this point, the other party should check the driver's license, vehicle registration certificate, and insurance certificate; directly searching the car is obviously not the standard procedure.

"Please get out of the car now. We suspect you have prohibited items in your vehicle."

The officer asked firmly, "Is there a gun in the car?"

"Have."

Dai Yafeng answered truthfully, "I have a certificate."

But the officer immediately drew his weapon, pointed it at Dai Yafeng, and said even more sternly, "Please get out of the car now."

At the same time, his companions also came to the back row and stared at Chen Hui and his companion.

"OK."

Dai Yafeng got out of the car with his hands raised and said, "May I film your law enforcement process?"

His proposal was unsurprisingly rejected.

Dai Yafeng didn't care. These police officers all had body cameras, unlike in China where surveillance cameras could just break down. Without body cameras, all their actions would be illegitimate.

However, Dai Yafeng still remembered the officer's badge number and name.

Fortunately, after a thorough search, no illegal items were found in the car, and all of Dai Yafeng's documents were valid. After the search, the officer allowed Chen Hui and the other two to leave.

What frustrated the three even more was that the reason the officer stopped them was simply because Dai Yafeng hadn't used his turn signal when he changed lanes.

This allowed the three of them to experience authentic American life.

Perhaps the bad luck was used up as soon as it landed, because everything went incredibly smoothly from then on.

The Hilton Hotel, being located within the University of Pennsylvania campus and surrounded by affluent neighborhoods, didn't offer Chen Hui and his companions much of an experience of everyday American life.

"Professor Chen, it's been a long time. Welcome to Philadelphia."

As soon as he arrived at the hotel lobby, Chen Hui saw Fefferman again. He really had a connection with the head of the Princeton Mathematics Department.

"Professor Fefferman."

Chen Hui responded politely, thinking that someone had already welcomed him in advance, and he had experienced the hospitality of Philadelphia.

"congratulations!"

Fefferman chuckled and joked, "Another Millennium Problem! With a million-dollar prize every year, you'll probably become the richest mathematician in the world!"

This is obviously an exaggeration. His annual salary at Princeton was $60, so a million-dollar bonus would be a lot for him, but definitely not a lot.

Have you decided how to spend this bonus?

"Um……"

Chen Hui hesitated for a moment, then said, "Let's pay off the mortgage first."

Hahaha……

Fefferman burst into laughter.

Chen Hui was just joking, of course. With his current wealth, he could easily buy a building in London as a birthday gift for his 20-year-old granddaughter who is still in university.

(End of this chapter)