A genius? I just love studying.

Chapter 144 Inspiration is Fleeting

Chen Hui put down his paper, walked to the blackboard, took the chalk from the bald professor, and wrote a series of formulas on the blackboard. "First, we need to find the Lagrange and self-dual conditions of the BPST instantaneous solution..."

"In five-dimensional gauge field theory, the construction of the gauge potential Aμ(x) must satisfy..."

Chen Hui wrote with lightning speed; he already had a clear idea of ​​what to do long before he came up here.

"As x approaches infinity, the expansion of the gauge potential is... This expansion shows that A_μ approaches the pure gauge form at infinity and satisfies the boundary conditions. However, by calculating the number of instants in the curvature integral, we can find that the integral result is 32π^4ρ^2, which needs to satisfy 32π^4ρ^2=8π^2ρ=1/4π. However, this condition cannot simultaneously satisfy compactness and topological constraints in a four-dimensional manifold."

"The homology group of the three-dimensional sphere S3 satisfies H^4(S^3, Z)=0, which means that there is no nontrivial SU(2) bundle structure, the candidate solution cannot satisfy the global topological condition, so there is no such gauge potential."

After writing down all the formulas on the small blackboard, Chen Hui put down the chalk and returned to his seat.

The students from Saclay University, sitting around the lawn, were still intently staring at the blackboard, deep in thought.

The IMO participants, who were watching the excitement from the lawn, felt their brains go blank. Chen Hui was speaking English, so they could understand each word individually, but when put together, they had no idea what it meant.

Is this something a high school student should be doing?

They were starting to question the meaning of life.

At this moment, the fair-skinned, blue-eyed girl sitting next to Chen Hui had turned her gaze away from the blackboard and looked at Chen Hui with curiosity in her eyes. She understood Chen Hui's proof and found no flaws.

That's why she was curious about this young Chinese man. Others might not know, but she knew that this guy wasn't even a student in their class, and that he hadn't been listening to the teacher's lecture at all; instead, he was looking at a paper.

Even so, this guy solved a problem that would have taken them some effort to understand without even thinking about it.

Who is he?

When did such a talented little guy appear in our school?
They were graduate students in the physics department at Saclay University, but this kid was clearly much better than them. Could he be a doctoral student?
Soon, the students sitting around the lawn gradually came to their senses. Many of them had already understood Chen Hui's proof and looked at him with the eyes of someone looking at a top student.

After most people had understood the proof, the bald professor finally spoke, "Good job!"

"This student did a very good job, demonstrating excellent geometric intuition and solid fundamentals, but missed a crucial point: overlooking the topological differences between four-dimensional manifolds and three-dimensional spheres!"

These words were like a wake-up call. Chen Hui looked at the blackboard and suddenly realized the problem.

At this point, the bald professor continued, "The correct construction should use the compactification technique of instantaneous modulus space. By embedding four-dimensional Euclidean space into a five-dimensional manifold, the problem is transformed into spectral analysis of self-adjoint operators using the Nahm transformation. This cross-dimensional topological correspondence establishes a mirror symmetry of the differential topology of gauge field rain, which is a prime example of the deep integration of Yang-Mills theory and differential topology!"

Although he pointed out Chen Hui's shortcomings, his gaze towards Chen Hui was full of smiles. He felt an overwhelming talent from this little guy, a talent he had only ever felt from genius mathematicians.

The last time I felt that way was probably with Peter Schultz.

"Mirror symmetry?"

Like a thunderclap exploding in his mind, the problems that had been troubling him for days suddenly surfaced in his mind. A jumble of images and complex symbols crowded together in his mind, which had previously been chaotic and without any clue.

But now, Chen Hui suddenly saw a clue among them that could link these graphics and symbols together in an orderly manner.

Your math level has improved from 7% to 8% (Level 3, Math).

……

Your math level has improved from 9% to 10% (Level 3, Math).

"perhaps……"

"Boss, that's awesome!"

Li Zehan came to Chen Hui's side. He couldn't understand Chen Hui's answer either, but didn't he see that the professor was praising him? So what was there to hesitate about? He just had to flatter him!
Wow!

The clues that had been gathered together suddenly scattered like water spilled on the ground, becoming countless splashes that could never be gathered again. The glimmer of inspiration that had just emerged also completely dimmed and could no longer be found.

A huge sense of regret welled up inside me.

For many people, this may be a once-in-a-lifetime opportunity.

But Chen Hui was different. After a brief moment of disappointment, he recovered and was able to find a clue today. Once his math level improved, he would definitely be able to seize this inspiration again!
Looking at the data panel, a sense of disappointment welled up in my heart again.

Even a fleeting spark of inspiration boosted his Level 3 math proficiency by 3%. If he were to actually solve the problem, he couldn't imagine the spectacular results.

"Stop making such a fuss in the future; you're thinking about the problem."

"You may escape the death penalty, but you can't escape punishment," Chen Hui said sternly. Even though he could disregard it, the feeling of having his inspiration interrupted was still very unpleasant.

"Oh."

Li Zehan looked at Chen Hui with innocent little eyes. He had known Chen Hui for so long, but this was the first time he had seen Chen Hui speak with such a serious expression, so he naturally realized the seriousness of the problem.

It's a pity the bald professor couldn't understand Chinese, otherwise he would have definitely asked a few more questions out of curiosity.

At this moment, Xu Zhiyuan also walked over. Instead of going to Chen Hui, he went to the bald professor and greeted him with a smile, "Professor Kong Nie, it's been a long time."

"Hello."

The bald professor responded politely, then bluntly expressed his confusion, "Excuse me, may I ask who you are?"

"Xu Zhiyuan from the Department of Mathematics at Jiangcheng University in China is here to bring Chinese contestants to Saclay University to participate in the IMO. My teacher is Faltings, and I have met Professor Kohn at the International Congress of Algebra."

Xu Zhiyuan wasn't angry. The man in front of him was Alain Connie, the 1982 Fields Medal winner. It was normal for people not to recognize him. He got his doctorate from Princeton, and his teacher was indeed Faltings. Unfortunately, like father, like son, he had embarrassed his teacher.

"Oh, I'm sorry, Mr. Xu, as people get older, their brains don't work as well."

Konney responded politely with a smile, not because Xu Zhiyuan had brought up his teacher Faltings, as Konney's own standing in academia was no less than Faltings'.

Kong Nie!

Upon hearing this name, the other IMO contestants standing nearby suddenly realized who it was.

They certainly knew who Konne was.

Those who can participate in the IMO are, of course, students with a great interest in mathematics. Many of them have already aspired to become mathematicians in the future, so they naturally yearn for the Fields Medal, which represents the highest award in mathematics. Many of the past Fields Medal winners can be recited by heart, so how could they not know about Connie?

However, there is a huge difference between the real person and the photo, and they did not recognize him at first. It was not until Xu Zhiyuan called out his name that they realized who he was.

For a moment, everyone looked at Kong Nie with starry eyes, feeling the happiness of successfully meeting their idol.

"I apologize for disturbing you, sir. If there's nothing else, we'll be leaving now."

After Xu Zhiyuan apologized on Chen Hui's behalf, he said to Chen Hui, "Let's go eat."

He didn't want to stay there any longer. He didn't know what had just happened or why Chen Hui was attending Kong Nie's class, but he didn't want a genius like Chen Hui to be poached by Kong Nie.

Chen Hui nodded and apologized to Kong Nie, feeling sorry for disturbing the class. He also said that Kong Nie's words had given him inspiration, and although he hadn't grasped it in the end, he was still grateful for the guidance.

Kong Nie was somewhat puzzled. Xu Zhiyuan had just said he was leading a Chinese team to the IMO, and the student he had just spoken to had come with Xu Zhiyuan. Did that mean the guy was still a high school student?!
No wonder he thought this little guy was so young!
Now, he feels that the little guy looks more like Schultz!

A bold idea popped into his mind, and he quickly stepped forward to Chen Hui and the others.

It's quite remarkable that he can still move at such a speed at his age.

"Hey, Chen Hui, would you be interested in being my student?"

Westerners are just that direct.

Not only the IMO participants and team leaders from various countries, but even the students from Saclay University looked at Chen Hui with envy when they heard this.

They all knew, of course, that the students Connie spoke of were different from the teacher-student relationship they were in now.

The thought of a Fields Medal winner as your teacher is incredibly exciting!

"I'm sorry, I already have a teacher."

Chen Hui responded politely; he had a fairly good impression of the old man.

"What a pity!"

Kong Nie made no attempt to hide his disappointment, then demonstrated his magnanimity to everyone, saying, "We can exchange ideas more often in the future. If you have any good ideas, feel free to email me!"

After saying that, he turned and left, leaving behind a group of IMO contestants and students from Saclay University looking at Chen Hui with strange eyes.

That was an invitation from a bigwig at the Philippine Awards, and you just turned it down like that?
They nodded frantically, wishing they could replace Chen Hui.

In the island nation's team, Gao Zhen, who had just regained his confidence, became lost again.

Isn't it said that these guys from China have already reached the pinnacle of their mathematical abilities by participating in the IMO? How come a Philippine Nobel Prize winner wants to take him on as a student?

It was only then that he realized that the question Chen Hui had answered, which they couldn't understand at all, must have been quite valuable.

Isn't it said that education in China is no good?
How come that guy can handle things he doesn't even understand with such ease?

This time, he was truly lost.

Not only Gao Zhen, but also the American player who once criticized Li Zehan was somewhat bewildered. They are all geniuses, but why is there such a big difference?

Compared to Chen Hui, their participation in the IMO is as childish as children playing house.

Of course, some people looked at Chen Hui with envy, such as Yilang, the contestant who was measuring directions at the hotel.

As for Deng Leyan and Wang Xiao, although they were equally surprised, they had experienced too many such things and were now somewhat immune to them. Even if Chen Hui did something earth-shattering, they would not be surprised.

Li Zehan and Chen Ling'er were genuinely happy for Chen Hui.

Even Xu Zhiyuan was only just coming to his senses. He admired Chen Hui's choice, which was the answer he had hoped for. He was also happy for Yuan Xinyi, but when it actually happened, he suddenly wondered if Chen Hui's choice was correct.

The students that Kong Nie was referring to were not quite the same as his relationship with Faltings; they were closer to the Chinese concept of a disciple. China values ​​lineage and mentorship, and the West does the same. Ordinary students could certainly enjoy some of this benefit.

Professor Connie is not only a Feynman Prize winner himself, but his teacher, Jean-Pierre Serre, was also a Feynman Prize winner. The influence of their lineage in the academic world is self-evident.

Becoming Kong Nie's student would be a huge boost to Chen Hui's future development.

The group, which had been chatting and laughing, fell silent. They walked into the cafeteria in silence, ate in silence, and left in silence, their feelings quite complicated.

……

A Provençal stew with a crisp baguette satisfied Connie greatly; he preferred this dish, full of the flavors of his hometown, to seafood and other delicacies.

Although he felt a little regretful about what had just happened, he didn't take it to heart. There are so many geniuses in the world, and it's not necessary to recruit them all under his command.

"Teacher, I met a very interesting Chinese student while proctoring the IMO today!"

As soon as he entered the lab, a student came up to him and chatted with him enthusiastically. "He finished the first day's three problems in just nine minutes. That speed is probably no less than that of Schultz and Tao back in the day. And I checked his age, he's only sixteen, just as young as Schultz was back then!"

"Another Chinese person?"

Kong Nie was taken aback, feeling that the proportion of Chinese people had been unusually high lately, whether in other fields or mathematics.

But he quickly realized that the little guy he had met seemed to be there to participate in the IMO as well. "What's his name?"

“hui chen”.

Sure enough it was him!

Hearing this name, Kong Nie was not surprised at all. If it weren't for it, he would have been even more surprised, because it would mean that China had produced two extraordinary individuals.

"It's a pity he's Chinese. Otherwise, with the talent he's showing now, he would definitely make a name for himself in the field of mathematics in the future. Even if he can't compare to Schultz and Tao, he won't be an unknown figure."

The student shook his head regretfully.

Kong Nie was puzzled, "Isn't Terence Tao also Chinese?"

"No, it's not the same."

The student immediately explained, "Although Tao was Chinese, he grew up in the West and received a Western education. He was not cursed by that land, which is why he was able to achieve such success."

Kong Nie understood what his student meant, and this view is also circulating in Western academic circles.

China is indeed a magical place.

But he soon had some doubts. The little guy's performance in class that morning was at least at the level of a mathematics doctoral student. He found it hard to imagine that such a person would be unknown in the mathematics world.

He is only sixteen years old!

If that's the case, perhaps he can only conclude that China is indeed a place cursed by the god of mathematics.

At the same time, he once again had the idea of ​​taking on apprentices, wondering if this would save a mathematical genius.

But now the problem isn't whether he wants to take on apprentices or not.

Shaking his head to banish these distracting thoughts, Kong Nie looked at his student and asked, "How's your research on cubic Diophantine equations going lately?"

He's full of energy when gossiping, but becomes listless when it comes to studying.

The student's face immediately fell, utterly dejected. "That's exactly what I was about to say! Look at the latest issue of the *Journal of Pure and Applied Mathematics*. Damn it, someone has already given a simplified solution to the cubic Diophantine equation!"

(End of this chapter)