A genius? I just love studying.

Chapter 264 A New Challenge, The Beginning of a World Change

At Carnegie Lake, Chen Hui, who had finished running five kilometers, slowly stopped and took a walk along the lake.

Inhale...exhale...

He tried to regulate his breathing with deep breaths to calm his wildly beating heart.

Your athletic rating has increased from Level 2 (4%) to 5%.

Seeing the barrage of comments, Chen Hui sat down contentedly on a nearby bench, admiring the view of Carnegie Lake. He unscrewed the energy drink that had been placed on the bench beforehand and gulped down a small mouthful.

His training these past few days has begun to show results. His sports proficiency is increasing at a satisfactory rate. What surprised him was his Chinese proficiency. As he focused his attention on this, his Chinese proficiency improved dramatically every day. It has now reached 89%, and he is about to reach level 3.

This far exceeded Chen Hui's expectations; his plan to improve his biological proficiency had not yet been put on the agenda.

Your Chinese language proficiency has increased from 89% to 90%.

Another barrage of comments lit up, and Chen Hui finally got up and returned to his apartment.

After taking a shower, I went to the office Fefferman had assigned to me with my thesis. As I passed the coffee machine, the long line of people waiting for coffee cups had disappeared.

He stepped over to grab a coffee and a donut, only to be told he needed to make a reservation. Apparently, their amusing discussion on the blackboard on the second floor had now been brought to life on this coffee machine.

It seems to be working quite well.

"Professor Chen!"

As Chen Hui turned to leave dejectedly, a girl with long brown hair called out to him, "If it's you, of course there's extra coffee!"

As she spoke, she handed Chen Hui a steaming cup of coffee and a freshly baked donut.

"Thank you."

Chen Hui readily accepted.

"It's my honor to save a few minutes for a genius mathematician!" The girl smiled sweetly, turned around, and went into the coffee shop to get busy.

I walked into the office, turned on my computer, and it was 9:00 AM Princeton time.
He logged into the interview software; today was the interview time he had scheduled with Fefferman.

These interviews usually go through several rounds. If Chen Hui is not selected, the resumes of those who are not selected can still be used to choose other professors.

Chen Hui left behind three resumes, including one for Deng Leyan.

The first interviewee was also a Chinese student. As a Chinese person, Chen Hui would naturally prefer to choose his compatriot under the same conditions.

Soon, a video call invitation popped up on Chen Hui's computer screen.

After entering, a very capable-looking girl with her hair tied up appeared on the screen.

"Yang Jingyuan, is that right?"

Chen Hui compared the photo on the resume and asked.

This girl on the resume is quite remarkable. She achieved a GPA of 3.85 out of a possible 4. Although she has no experience in competitions, this undoubtedly places her among the very top students in China.

Yang Jingyuan smiled slightly, showing no fear despite being facing a Philippine Academy Award winner. "Yes."

Why did you choose to pursue a master's degree in mathematics?

"I have had a strong interest in mathematics since I was a child. After completing my undergraduate studies, I want to pursue a master's degree to absorb scientific research knowledge on a higher platform, realize my life's value, and dedicate my youth to scientific research..."

Yang Jingyuan's smile remained unchanged, but a hint of smugness flashed in her eyes. Clearly, she was prepared for this question being pointed at her.

"..."

Chen Hui's expression was somewhat strange, but he still continued to ask, "So, if you successfully get into Princeton, have you thought about which field you would choose as your main focus?"

"Mathematical Physics!"

Yang Jingyuan said firmly, "I have heard about Professor Yang's achievements since I was a child and have a strong interest in the four fundamental forces of physics. When I was in college, I heard that you had completed the proof of the Yang-Mills equation and become the first mathematician in my country to win the Fields Medal, bringing this honor to China. I was very excited. From that moment on, I decided to explore the mathematical mysteries of the physical world with you!"

"Alright, since you're interested in mathematical physics and have decided to explore the mathematical mysteries of the physical world with me, then tell me your thoughts on the proof of the Yang-Mills equation."

"Ah, this... oh... I..."

For a moment, Yang Jingyuan was thrown into a panic, her face turning pale. This was clearly an unexpected problem.

"It's okay, just say whatever you want."

Chen Hui wasn't really expecting her to say anything specific, but since she spoke so confidently about her interest in mathematical physics and her admiration for Professor Yang and him, she must at least have read their papers.

"Professor Yang's paper achieved the unification of the three fundamental forces, which is a huge step forward for the field of fundamental physics. Your proof of the Yang-Mills equation is an epoch-making achievement that will directly impact..."

It must be said that this student had a remarkable ability to remain calm under pressure, and he quickly regained his composure and began to speak eloquently.

Unfortunately, her answers were all empty metaphysical summaries, without a single mathematical formula or physical theorem.

Chen Hui sighed, "Well, this question is indeed a bit difficult for you. It's okay, that's all for today's interview. You'll be notified of the results within a week."

Yang Jingyuan's eyes lit up. She felt that she had done a good job. She had answered all of Chen Hui's questions, and some of them she had answered very well because she had prepared in advance.

"Then thank you, teacher."

She felt very confident, so she decided to ask her teacher for help.

Chen Hui then exited the interview interface and clicked the "x" in the upper right corner of her resume.

He could roughly guess what the girl was thinking. She was simply trying to use her Chinese identity to play the emotional card and get a spot. After graduating and returning to China, she could leverage Chen Hui's influence to get a job in administration and rise through the ranks.

But Chen Hui didn't want to waste this precious spot paving the way for such a person. Princeton's master's degree spots are already valuable, and giving them to such a person would undoubtedly be disrespectful to those who truly love mathematics.

The second interviewee was from the University of California, and also had a recommendation letter from Terence Tao, so his resume was impressive enough.

"Hey, Professor Chen, it's great to finally meet you in person! You're even younger than I imagined!"

The moment the video call connected, the young Black man on the other end flashed his pearly white teeth and excitedly exclaimed, "The youngest winner of the Philippine Philharmonic Award in history! It would be so cool if I could become your student!"

The child's words were so captivating that Chen Hui could barely get a word in edgewise.

Fortunately, he knew this was an interview. "Have you thought about your master's research area?"

"Analytic number theory".

Michael answered without hesitation, "I studied the Mersenne prime conjecture during my undergraduate studies. One of the mathematicians, Zhou, proposed a conjecture that the distribution of Mersenne primes follows a specific pattern. Previously, conjectures proposed by mathematicians such as the French mathematician Shanks and the German mathematician Berlihart were mainly based on approximate formulas, while Zhou's conjecture was the first to describe the distribution of Mersenne primes with a precise expression..."

The combination of the exponential function and prime numbers in the formula may implicitly suggest the symmetry of prime numbers on the exponential scale…

“周氏猜测认为，当 2^2n<p<2^2n+1时，梅森素数 Mp=2^p1的数量为2^(n+1)1，想要证明这个猜想，我们或许可以结合素数定理与梅森数的特殊结构，推导其分布密度……”

When it came to his strengths, Michael became even more talkative. The ten-minute interview was far from enough for him to finish expressing himself. Chen Hui didn't interrupt him and let him continue. It wasn't until more than twenty minutes later that Michael remembered he was still in an interview. He then shut up and quietly looked at Chen Hui.

"Okay, that's all for today's interview. You can go back and wait for our notification."

Chen Hui nodded slightly, ending the interview.

After closing the video, Chen Hui hesitated for a moment while looking at Michael's resume. He glanced at his own judgment, which had reached level 7, and was not very satisfied. It seemed that his judgment needed to be improved further.

Michael and Yang Jingyuan are completely different people. Michael is genuinely passionate about mathematics, but Chen Hui thinks he is too outgoing.

To do mathematics well, you need to be able to calm down and focus on research. This kind of personality is not helpful for mathematical research.

But he felt that this little guy was really good, and the direction of his research was exactly the number theory that he was planning to enter.

In the end, he didn't immediately reject Michael's resume. He thought he could take another look, since Fefferman had said he would send him another batch of resumes later.

The last interviewee was Deng Leyan, Chen Hui's classmate from that year.

When the interview video started playing, the two looked at each other, Deng Leyan's expression was so complex that it was impossible to describe in words.

"Hello, long time no see."

Chen Hui was the first to start talking.

"haven't seen you for a long time."

Deng Leyan knew before the interview that the other person was Chen Hui, but he still chose to accept the interview.

After some pleasantries, the interview officially began.

It had been several years since they last met, and Chen Hui didn't know if this former child prodigy would disappoint him. Some necessary investigation was still needed.

Once the interview actually began, Deng Leyan's slight embarrassment vanished, and she became completely absorbed in Chen Hui's questions, answering them one by one.

The more questions he asked, the more satisfied Chen Hui became.

Deng Leyan's love for mathematics may not seem as fervent as Michael's, but it is deeply ingrained in his bones. Because he has already made mathematics an indispensable part of his life, he has become accustomed to it and his emotions are naturally not expressed too enthusiastically. But Chen Hui knows that he cannot live without mathematics and will not leave it.

This is a natural talent for studying mathematics!
His talent greatly pleased Chen Hui; he was undoubtedly the most talented student he had ever encountered.

The only pity is that Deng Leyan chose mathematical analysis, which leans towards the field of measure theory, and does not overlap much with Chen Hui's research field.

Of course, with Chen Hui's current mathematical expertise, teaching Deng Leyan is no problem.

After a morning of interviews, Chen Hui had already made up his mind about the final list.

Elena had already arrived at the office and was waiting. She saw Chen Hui conducting an interview, so she didn't disturb him. When Chen Hui finished the interview, she looked over nervously.

Have you ever thought about applying the Navier-Stokes equations to weather forecasting?

Chen Hui looked at the girl with some Slavic ancestry and said with a smile.

"I don't need an interview anymore?"

A fleeting look of surprise crossed Elena's eyes.

"You finished your interview yesterday, didn't you?" Chen Hui said with a smile.

The joy in Elena's eyes spread across her face.

Originally, Chen Hui wanted to study the application of the Navier-Stokes equations in controlled nuclear fusion, specifically the construction of plasma motion models. However, he clearly lacked the necessary conditions, so he turned to this direction.

However, he now needs to focus on solving the Riemann Hypothesis and working towards the next free attribute point, so entrusting this task to Elena is undoubtedly a good choice.

Weather forecasting models simulate airflow by discretizing the atmosphere into a three-dimensional grid and based on the Navier-Stokes equations. The European Centre for Medium-Range Weather Forecasts (EFSM) model uses a 9-kilometer grid and a 137-layer vertical structure to iteratively calculate the weather evolution over the next 10 days.

However, since directly solving the equations is computationally infeasible, meteorological models need to parameterize small-scale processes, such as cloud microphysics and turbulence, which results in only an approximate result.

Current weather forecasts can only show the probability of rain at a certain time, not the exact amount of rain at a specific time, minute, second, and location.

Furthermore, due to the nonlinear nature of the equations, the butterfly effect occurs, and the initial error amplifies exponentially over time. For example, the path prediction of Hurricane Sandy in 2012 showed significant discrepancies due to small deviations in the initial pressure field, with the final error exceeding 24 hours.

Theoretical studies have shown that even with perfect initial conditions, the singular limit of weather forecasting is 14 days due to turbulence and error accumulation.

However, the global existence and smoothness of the Navier-Stokes equations have now been rigorously proven.

One of the core contradictions in past weather forecasting was that while the existence of local solutions to NSE has been proven, the existence and smoothness of global solutions remain unsolved mysteries.

This means that, theoretically, there may be certain initial conditions, such as violent airflows corresponding to extreme weather, that cause the solution of the equation to "explode" within a finite time (resulting in an infinite velocity or pressure gradient), thus rendering the numerical simulation invalid.

Now, the legitimacy of the model will be fully established, meteorologists will no longer need to worry about the theoretical risk of sudden solution collapse, and the simulation results of all NSE-based numerical models will have strict mathematical reliability.

The current 10-14 day effective window for weather forecasting is due to the chaotic effect, also known as the butterfly effect, which leads to an exponential amplification of errors. However, the existence of smooth solutions means that fluid motion remains structurally stable over large timescales, which may extend the predictable time range, for example, from 2 weeks to 1 month or even longer.

Chen Hui's goal is to accurately predict the weather and extend the predictable time frame.

For example, if a series of calculations predict that a high-intensity earthquake will occur in a certain area in six months, then corresponding relocation work can be carried out in advance to avoid losses.

"Interesting!"

Elena's eyes were bright. She was already interested in partial differential equations, and being able to apply them to such an interesting topic was undoubtedly a cool thing.

Especially with such an excellent teacher to guide her, what reason would she have to refuse?

(End of this chapter)