A genius? I just love studying.

Chapter 151: Even the sea of ​​questions was tackled.

In the next dormitory room, Zeng Yiyuan, who was originally going to sleep, ultimately didn't go to sleep because Yin Piao was also awake. He just stood in front of the computer, staring at the average score displayed on the rankings.

brush!
The webpage flickered, and the average score for Class 1 of Theory changed to 8.2!

Zeng Yiyuan knew that the rankings were refreshed every five minutes. In other words, in those five minutes, that guy from Class 1 got 48 points, which was truly terrifying!
We're all math majors, so we all have some mental arithmetic skills.

"He's conquered the fifth sea of ​​practice questions!"

Yin Piao suddenly spoke, his tone resolute, a hint of fighting spirit flashing in his eyes. Finally, something in this world had appeared that could pique his interest.

As Zeng Yiyuan observed, he hadn't put in his full effort when solving the problems. If he had been serious, getting through the fifth section of the problem wouldn't have been a problem.

He now regrets it a little. If he had taken it seriously back then, he could be competing against that guy now, seeing his limits and seeing where his own limits really are.

Zeng Yiyuan nodded slightly. 48 points. Although it could be due to other circumstances, judging from the current score, it is highly likely that the guy got 48 points by passing the fifth section of the sea of ​​questions and answering three questions correctly.

Each question in the sixth section of the "Sea of ​​Questions" is worth 32 points. If that guy gets two more questions right, the average score of the first-grade theory class will surpass theirs.

Hope not!
Zeng Yiyuan prayed silently.

If that guy only gets one question right, his average score is only 9.36, which is just a little lower than theirs. You can imagine how difficult it is to get two questions right. The score increases exponentially with each sea of ​​questions, and the difficulty is the same.

If the third set of problems was already so difficult, how difficult would the sixth set be? Zeng Yiyuan was genuinely curious and the thought of going to see for himself arose for the second time.

In dormitory 908,
The students in the first theory class fell silent again.

This time, they weren't worried about disturbing Chen Hui while he was doing his problems; they were simply amazed by his incredible speed at solving them.

Five-minute speedrun through the fifth section of the sea of ​​questions!

It's like they're doing elementary school math problems. Is this the level of the IMO champions?

"Perhaps, we really do have a chance to get first place?"

The dormitory was so quiet that Yin Hao could hear his own heartbeat, and a bold idea popped into his mind.

Looking at these jaw-dropping guys, Li Zehan proudly raised his head, a sense of superiority welling up inside him. He was already used to this kind of scene.

While everyone was lost in their own thoughts, Chen Hui had already answered the three questions in the sixth section of the sea of ​​questions and entered the seventh section.

Let M be a compact, smooth manifold, and E→M be a smooth vector bundle of rank n, whose structure group can be reduced to SO(n). Consider the following two propositions:

1. E has an existence metric (i.e., a smooth section g∈Γ(EE) satisfies that gp is a positive definite inner product at every point p∈M).
2. The Euler class e(E)∈H^2n(M;Z) of E is zero.

(a) Prove that proposition 1 is equivalent to proposition 2 (details required).

(b)若进一步假设M为闭定向流形且n为偶数，证明存在唯一的度规g使得对应的曲率形式Ω满足i/2πΩ∈A^(1，1)(M)且其积分∫M^(i/2π)Ω=c1(E)，其中c1(E)为E的第一陈类。

(c) Provide examples to illustrate that the above uniqueness may not hold when n is odd, and explain its relationship to characteristic class theory.

This was a question that combined algebraic topology, differential geometry, and functional analysis. Chen Hui didn't know why there was such a question on the college entrance exam, but coincidentally, he knew the answer.

These questions were quite easy for him.

Yin Hao and the others stood blankly behind Chen Hui. They no longer cared about the rankings, because when Chen Hui passed the sixth section of the sea of ​​questions, he scored 96 points in just three questions, completely surpassing the theory class and rightfully standing at the top of the rankings.

The outcome of the next problem-solving session was no longer relevant; they just wanted to know how far this prodigy could go and whether this sea of ​​problems would ever end.

……

School of Mathematics
Gong Haitao walked out of the office and strode into the office next door without knocking.

In the office, a sprightly old man with gray hair was working at his desk. He glanced at Gong Haitao briefly before burying himself back in his work.

"Old Liu, what are you doing?"

Gong Haitao walked to the desk and peered over the shoulder at the old man's desk.

"What else can I do? I'm bored, so I'll give those kids some practice questions."

Since Gong Haitao had spoken, Liu Ming couldn't ignore it, so he stopped writing, looked up, and leaned back in his chair.

"If you ask me, you should stop setting questions. The questions you set are probably impossible for anyone to solve in their lifetime."

Gong Haitao was both amused and exasperated. "These questions are so difficult that even doctoral students might not be able to solve them completely. Giving them to a bunch of freshmen is just asking them a lot of trouble."

“Those who can do this will not find it difficult, and those who cannot do it will not find it difficult either.”

Liu Ming looked impatient. "Speak up, what do you want to brag about? Hurry up and finish, I still have more questions to give you."

"..."

Gong Haitao felt somewhat uncomfortable.

However, this was to be expected, as the two were too familiar with each other. Just by seeing Gong Haitao's smug expression, Liu Ming knew what he was going to do.

"One of my graduate students published a Q1 SCI paper!"

Even if your awesomeness is punctured, it's still awesome. You still have to brag about it. Gong Haitao quickly adjusted his mood and said proudly, "JOURNAL OF DIFFERENTIAL GEOMETRY, JDG!"

"Oh, I know."

Liu Ming responded and continued to work on the questions. He knew that if he showed any other expression, Gong Haitao would nag him for half an hour.

Feeling somewhat bored, Gong Haitao prepared to find another old friend to brag to when he saw Liu Ming, who was setting questions, suddenly asked, "By the way, how did the kids from the math department fare this time?"

"not bad!"

Liu Ming, equally pleased, said, "The second theory class has produced a promising student who has made it to the fifth section of the sea of ​​questions."

"Oh?"

"That's really great!"

Gong Haitao also became interested, so he went around to the desk and stood next to Liu Ming, ready to see the ranking of this entrance test.

He also participated in setting the entrance exam questions. Every professor and teacher in the School of Mathematics, and even many doctoral students, participated in setting the questions; otherwise, the sea of ​​questions could not have been formed. Of course, he knew the difficulty level of the fifth sea of ​​questions.

Unfortunately, Liu Ming didn't have the rankings open on his computer, leaving Gong Haitao empty-handed. He didn't stop talking, though, "But I heard that those little geniuses from Class One who participated in the IMO are back, so the rankings might have changed."

"That's not necessarily true. Class 2 is much stronger than Class 1 as a whole. It's not something that three people can reverse. Besides, Class 2 also has a promising talent. I don't know how someone like that ended up at Jiangcheng University."

Liu Ming shook his head, but his eyes were filled with excitement. As the administrator of the sea of ​​questions, Liu Ming could directly check everyone's answers, and Yin Piao's achievement of entering the fifth sea was naturally eye-catching.

"Oh? So you're thinking of taking on a disciple?"

Gong Haitao became even more interested.

"Let's observe it for a while longer."

Liu Ming did not deny it. At the same time, he reached for the mouse and opened the official website of the School of Mathematics at Jiangcheng University. As an old friend of many years, he knew exactly what Gong Haitao had come to see.

"Haven't you heard about the big news in the industry lately?" "Teacher Tian and Xin Yi had a falling out over a student. Now that kid is in Class 1. A kid who can make Teacher Tian interested must have some skills."

Gong Haitao stared at the computer screen, looking excitedly like he was watching a spectacle.

"That's not the case; it's a complicated matter."

Liu Ming probably knew some of the inside story, and knew that Tian Yang was angry because Yuan Xinyi had concealed the progress of the research project.

Given that Tian Yang wholeheartedly helped Yuan Xinyi complete the project, Yuan Xinyi's actions were indeed somewhat disheartening.

As for that little guy, he was indeed the catalyst. Being noticed by two big shots meant he must have some talent. He believed that the little guy was stronger than Yin Piao and wouldn't stop at the fifth level of the sea of ​​questions. But to lead Class One to surpass Class Two and take first place was just too far-fetched.

At this moment, the rankings were finally displayed on the computer screen, and the first place was none other than Class 1 of Theory!
"?"

Both of them were stunned.

Looking at the average score at the bottom of the rankings, it's 11.64?

Even Gong Haitao, who had confidence in Chen Hui, was stunned when he saw the score.

The average score suddenly increased by nearly seven points, which means that the three little guys got nearly two hundred points together.

In other words, everyone is at least at the fifth level of the "sea of ​​questions" level, and no one is worse than Yin Piao, whom Liu Ming has his eye on.

"No wonder he's an IMO gold medalist!"

Gong Haitao clicked his tongue in amazement, "Take a look at their answers."

Without Gong Haitao's prompting, Liu Ming had already clicked on the webpage, entered the administrator interface, and checked the answers, sorting them by time.

Li Zehan and Chen Ling'er's names appeared at the very top.

However, upon seeing the two scores, a hint of doubt flashed in Liu Ming's eyes, followed by surprise.

These two only scored 29 and 17 points respectively, which means that there was another person who scored more than 150 points!
Without even calculating, Liu Ming knew that this meant someone had entered the seventh sea of ​​questions!

He knew very well the difficulty of the seventh set of practice questions; it was something a freshman could never do.

Even his doctoral students might not be able to do it.

That person wasn't on the list, so there's only one possibility: he's still doing the questions!
The seventh sea of ​​practice questions is simply not his limit!
"No wonder Elder Tian and Xin Yi value him so highly, he truly lives up to his reputation!"

Liu Ming sighed.

"I wonder if he can maintain this level now that he's started doing scientific research."

Gong Haitao muttered to himself, "Many competition geniuses are first-rate at solving problems, but their transition from problem-solving to scientific research is not ideal. In many cases, they are even worse than those students with average competition results or those who have never participated in competitions."

Gong Haitao was also puzzled. He wondered why he suddenly couldn't do many mathematical problems, since many mathematical studies were essentially problem-solving exercises.

Although there are no standard answers to research topics, mathematicians need to find the correct answers.

“You can doubt those competition students, but you can’t doubt Xin Yi and Professor Tian’s judgment. I heard that the young man has already achieved good results and is waiting for review.”

Liu Ming closed the webpage. He wasn't interested in the final score. Chen Hui had already proven his talent in problem-solving, but his talent in scientific research still needed time to prove.

"I think I should go back and focus on nurturing my graduate student. He's so young and already publishes in Q1 SCI journals; he might actually become a mathematician in the future!"

Gong Haitao said proudly that he had more faith in his student, who had already proven his research abilities, than in Chen Hui, who had not yet proven himself in scientific research.

Of course, that was also because he knew he couldn't beat Yuan Xinyi; otherwise, he would have given his all to such a genius, no matter what.

"Get out of here."

Liu Ming rolled his eyes, too lazy to pay attention to this guy.

But in his heart, he was planning to take Yin Piao as a student so that Yin Piao could start real mathematical research as soon as possible.

Mathematicians, especially young mathematicians, have very precious time.

……

Jiangcheng University, male dormitory
Yin Piao and Zeng Yiyuan were still looking at the computer screen.

As expected, when the five minutes were up, the average score of the theory class soared again, from 8.2 to 18.5.

"What."

"Is there a bug in the system?"

Zeng Yiyuan laughed. In just five minutes, the average score had increased by nearly ten points, bringing the total score close to three hundred points. Was this something a human could do?
"It's not a bug."

Yin Piao shook his head, "After finishing the sixth and seventh sets of practice questions, I got exactly 288 points!"

His eyes were also filled with shock after he finished speaking.

He was very confident in his abilities. If he got serious, he might be able to pass the fifth set of questions, but he definitely wouldn't be able to do the sixth set.

The difference in difficulty between each set of practice problems increases exponentially.

But that guy has already conquered the seventh sea of ​​questions!

Where are his limits?
He wasn't the only one with this question; everyone in room 908 had the same idea.

They looked at Chen Hui as if he were a monster, a monster on a completely different level from them.

However, when Chen Hui clicked to continue answering questions, a new sea of ​​questions did not appear; instead, his paper was automatically submitted.

The sea of ​​practice questions has come to an end!
Chen Hui was somewhat unsatisfied. After spending a long time thinking about difficult math problems, doing some simple problems like this occasionally was a good way to relax his mind.

The questions had been completed, but everyone was still standing in room 908, feeling lost.

"The world has given me what I possess..."

The singing broke the silence of the dormitory. Yin Hao looked blankly in the direction from which the singing came before realizing that it was his cell phone ringtone.

Upon seeing the caller ID, Yin Hao realized it was his class advisor, Zhang Lei, calling, and quickly answered the call.

"What's going on with your class? None of you went to military training? What were you doing?"

Cold sweat instantly broke out on Yin Hao's forehead, and he was drenched in sweat. He checked the time and realized it was already past 2:20 in the afternoon. Only then did he remember that he still had military training in the afternoon.

"Let's go to the playground right away. Um, Teacher Zhang, you can check the entrance exam rankings on the official website."

After hanging up the phone, Yin Hao called out, "Class One, come with me. It's time for military training. Hurry up and get to the parade ground."

Zhang Lei was initially furious, but Yin Hao's seemingly random and incoherent words made her temporarily suppress her anger. She went to the School of Mathematics' official website, where she saw the top-ranked Theory Class 1 and its exaggerated average score.

(End of this chapter)