Chapter 264: Chapter 114 I Want You to Stand on the Summit, Unable to See Any Face Below_2

Now, just thinking about these things makes me very happy. Qiao Yu, let happiness be a bit simpler. Your life should be joyful, and if mathematics brings you joy, then stand on the peak of the mathematical mountain. When you look down, where is he? You can’t see him.

Ha… If you could reach that level, just imagining it makes me happy! Believe me, this is the greatest punishment for someone like him; he sees you standing on the peak, yet gets no benefits, losing sleep every night.”

Qiao Yu thought for a moment and said, “Although what you said makes sense, I’ll only heed part of it. I’ll abandon those little tricks, but I want to use fair and open means to add difficulties to his life.”

Qiao Xi looked at Qiao Yu somewhat absentmindedly, suddenly asking, “And then? Can you reach the top, Qiao Yu? Like I said, stand on the highest peak where others can only look up to you, and when you look down, you can’t see any faces clearly.”

Qiao Yu nodded with certainty, “Of course, I will definitely make him personally see Grandpa’s statue, see the neighborhood that belongs to the Qiao Family, and then make him leave! To accomplish these, the first thing is to stand on the peak of the mountain!”

Qiao Xi said calmly, “Don’t just talk, you know, your Grandpa used to say, a man’s words must be honored.”

Qiao Yu raised his fist high with fighting spirit, “Just wait and see, I’ve decided to listen to you, treat this as a game, have faith in me, I’m awesome at games!”

Qiao Xi smiled, the corners of her mouth slightly raising, like a blossoming lotus…

“Alright, Qiao Yu, I’m waiting to see you standing at the peak.”

…

Shutting down the video, Qiao Yu took a deep breath.

It’s like there’s a fire burning in his heart.

Indeed, the Qiao Family is full of extraordinary people.

Qiao Yu remembered when Grandpa was still around, he was especially good at motivating him. Back then, Qiao Xi was always lazy.

Who would’ve thought that now Qiao Xi also awakened this motivating trait.

Standing at the peak, seeing no faces below clearly, including that man’s, just the thought of it made Qiao Yu shiver with excitement.

Qiao Yu looked at his computer, it was filled with downloaded papers.

Instinctively reaching for the mouse, he hesitated for a moment, then decisively deleted most of the papers.

Since Qiao Xi wants to see a peak duel game, all the past things can be set aside for now.

The news he got from Professor Pan is that the team of nine people highly value this result. Especially for a professor in his thirties, proving the Geometric Langlands Conjecture will be a stepping stone to winning the Fields Medal for them.

So now what Qiao Yu needs to do is to fully understand and analyze the entire process of proving the conjecture, then specifically study whether there are any loopholes in the proof process that the man is responsible for.

Undoubtedly, this is an enormous workload and extremely challenging task for Qiao Yu – acting as a peer reviewer role.

After all, the Langlands Conjecture is an area he has not yet delved into. And it is a broad and abstract proposition, in essence, its purpose is to build a bridge between different branches of mathematics and then unify them.

Specifically, for the Geometric Langlands Conjecture, it is about unifying algebraic geometry with representation theory, and it can even be said to be a junction between mathematics and physics.

The conjecture believes that there is a one-to-one correspondence between the spine on algebraic curves and representations of Lie groups. Specifically, it suggests that some geometric objects on algebraic curves can correspond to certain algebraic structures.

Specifically, for each spine defined on an algebraic curve, there is a corresponding Lie group representation, so that in the context of algebraic geometry and representation theory, this correspondence can be verified.

This means that the representation of Lie groups can be understood by studying geometric objects on algebraic curves, and vice versa.

Fortunately for Qiao Yu, he has researched algebraic curves and has some research on Lie groups, though not in-depth. The better news is that such a massive proposition is explained through five complete papers by the project team.

If the five articles are sorted logically, the man’s work mainly focuses on the first half, while Professor Pan from Huaqing and his advisor Danis focus mainly on the latter half.

Of course, this does not mean Qiao Yu only needs to study the first half, in fact, he needs to understand the logic of the entire proof and try to find possible logical loopholes in the proof process, he must understand all five papers.

This allows him to understand the entire team’s proof strategy and find its underlying structure.

During this process, he still needs to learn a lot, but Qiao Yu has an advantage.

A member of the paper team is a professor at Huaqing and has already added him on WeChat. He can ask for help anytime on WeChat, which saves a lot of time.

Such a life, so beautiful!

…

The next day, on the day before the first phase of the IMO special training, Xue Song visited Qiao Yu at eleven in the morning as usual, clearly feeling that today’s Qiao Yu seemed a bit different than usual.

For example, after opening the door for him, he didn’t engage in the usual warm small talk, just glanced at him blankly and then returned to his position.

Xue Song curiously took a look, then felt worried.

He pointed at a highlighted formula on the screen: D-mod(BunG)≃IndCohNilpglob(LocSys^G), saying, “What’s gotten into you? Isn’t this the Geometric Langlands expression? I remember Director Tian assigned you a project to establish a random prime number model? Or did you apply for this yourself?”

“Yes, but concepts from the new geometric theory like IndCohNilpglob I find interesting, so taking a look first.” Qiao Yu answered without even looking up.

“Interesting?” Xue Song shook his head and said, “Qiao Yu, I think you’ve become obsessed.”

“Of course it’s interesting, Mr. Xue, don’t you think this isomorphism relation might heavily rely on the specific choice of G? If the chosen G in a specific context leads to changes in some geometric objects’ properties, it might render this isomorphism invalid. Potentially misleading results?”

Qiao Yu suddenly asked.

Xue Song was baffled, pursed his lips, instinctively swallowed, and said, “Qiao Yu, please respect a professor who intends to devote his life to Diophantine equations. I can’t be a mathematical all-rounder, and the era of mathematical all-rounders is over. That last sentence was said by Jorn Nielsen.”

“Oh, then I’ll ask Professor Pan.” Qiao Yu casually replied, picking up the phone next to him.

Xue Song scratched his head, all the while Qiao Yu didn’t look up at him once during the conversation.

This state made Xue Song’s scalp tingle, he even doubted whether Qiao Yu realized he was standing behind him.

This gave Xue Song a headache, he considered whether he should let Tian Yanzhen take a look at his student, what exactly happened, wasn’t he still complaining about being too tired of studying some time ago, how did this sudden change happen?

On the other side, at Huaqing University, someone already took such actions.

…

In Qiuzhai, Pan Jingyuan hurriedly walked into Yuan Zhengxin’s office with a worried expression and said, “Elder Yuan, could you talk to that kid Qiao Yu, he shouldn’t push himself too hard, health is more important.”

“Hmm? What’s wrong?” Yuan Zhengxin looked at Pan Jingyuan with a puzzled expression, not understanding what he meant.

Professor Pan said nothing, handing over his phone with a wry smile.

Yuan Zhengxin took the phone, put on his glasses, oh, it’s the WeChat chat record with Qiao Yu.

Goodness, ever since they added Professor Pan on WeChat yesterday afternoon, the chat hasn’t stopped!

In the afternoon, it was fine, just some basic questions and some gossip, but by evening, the questions increased, initially coming every ten minutes, later not as frequently, but every one or two hours a question would pop up.

And they were the kind of complex questions just by looking.

The last question last night was already at 1:53 AM, and then another question popped up this morning at 6:57 AM…

Goodness? So dedicated?