Chapter 8 What kind of monster is this?!

The private room quieted down instantly.

At this moment, the curiosity of the professors was also fully aroused as they silently waited for Zhang Chunlei to pose the question.

After all, Group Theory is a separate branch of mathematics. Even if one has systematically self-studied Advanced Mathematics, facing a Group Theory problem would still be like groping in the dark.

They had all heard of mathematics prodigies in high school who advanced to study calculus and linear algebra early.

But for a high school kid to understand Group Theory...

That really was like a revelation—an eye opener.

A moment later, Zhang Chunlei had thought of a problem and began to speak, "Hmm, listen carefully, kid. This is a proof question: In a finite group \(G\), for any two distinct elements of order two that are not conjugate, there exists another element of order two that commutes with the former two."

As the question was posed, all the professors in the private room privately admired Zhang, thinking that he really had a level of expertise—what an excellent question he had given.

How should I put it?

It wasn't considered a difficult problem in Group Theory, and could even be seen as a basic question, yet it was very interesting.

But to solve this problem, one must thoroughly understand several extremely important concepts in Group Theory.

Concepts like finite group, conjugacy, commutativity, the order of a group, elements...

One also needed an innovative mathematical mindset because to solve this problem quickly, one could actually use methods indirectly encountered in high school mathematics.

It indeed was a clever problem.

To say it was difficult—well, for someone who had systematically studied and understood Group Theory, it wouldn't take too much time to figure it out.

But to say it was not difficult—even if the world champion of the Math Olympiad came, they probably wouldn't even understand the question.

Watching Qiao Ze, who had fallen into deep thought, Zhang Chunlei said with a smile, "Haha, kid, don't rush. Take your time thinking. As long as you come up with the solution before we finish drinking tea today..."

"I've already thought of how to prove it, with induction." Qiao Ze suddenly interrupted Zhang Chunlei.

"Huh?" Everyone was simultaneously stunned.

That was damn fast, wasn't it?

No exaggeration, many professors at the scene still only had a vague idea...

"Suppose there is an element of order two \(m\), \(mm = 1, mx = xm, my = ym\)."

"Let \(mk = (xy)^k\), if \(mk = (yx)^k\), then we are done.

"If \(mk \neq (yx)^k\), then for \(j

"If \(j+k\) is even, then there exists \(h\), such that \(2h = j+k\), \((xy)^h \neq (yx)^h\),"

"If \(j+k\) is odd, then there exists \(h\), such that \(2h+1 = j+k\), taking \(z = (xy)^{h + 1}\), \(zy \neq xz\)"

"Then \((yx)^h \neq (xy)^{h + 1}\), from this we can prove that \(mk \neq mj\)."

"Finally, because \(G\) is a finite group, this process will definitely terminate."

"Proof complete."

Li Jiangao silently took a cup for himself from the tea set that Zhang Chunlei had just prepared, and then drank it in one gulp.

As long as one is not the one being shocked, it feels quite entertaining.

Especially when he saw that dazed and complicated expression on Zhang's face across from him, he really felt like laughing.

Now everyone knows this kid is defying the heavens, right?

"Cough cough...you really understand Group Theory?"

After recovering, Zhang Chunlei made a remark, then turned toward the still-distracted professors and said, "Look at that, who says our Huaxia generation is not as good as the past? Now we have high school kids who have already mastered Group Theory! When I was in high school, I hadn't even heard of the term 'Group Theory'."

"Isn't that the truth? Professor Li, where did you find this kid?" someone couldn't help but ask.

"Hehe, drink tea, drink tea, we agreed not to talk about these things," Li Jiangao said with a smile, playing coy.

Because he knew, the more mysterious he made it sound, the more interested these people would definitely be in Qiao Ze.

"It's your turn to tell me what your research topic is," Qiao Ze didn't pay attention to the crowd's admiration and continued to seriously look at Zhang Chunlei and asked.

"Alright, but first you need to tell me, why are you so concerned about my Yangtze River Scholar topic?"

"Because I want to become a Yangtze River Scholar and then an academician with Li in the future, so I want to know how difficult it is to become a Yangtze River Scholar."

"Pfft…"

As soon as Qiao Ze finished speaking, Li Jiangao sprayed the tea he had just sipped straight out. Luckily, he reacted quickly and turned his head in an instant, spraying it outside; otherwise, that pricy tea worth at least a thousand yuan would have been wasted.

"Sorry, my apologies, kids say the darndest things, kids say the darndest things..." Putting down his teacup, Li Jiangao explained with a flushed face.

Qiao Ze, curious, looked at Li Jiangao and asked, "Don't you want to become a Yangtze River Scholar?"

"Haha…" This time, everyone in the private room burst into laughter.

Qiao Ze didn't understand what they were laughing about and just felt a bit unhappy.

Sensing something, Zhang Chunlei waved his hand to quiet the laughter, then seriously said, "Okay, okay, now it's my turn to keep my promise. The topic I submitted is the application of Group Theory in designing molecular structure computation models.

More specifically, it's about using the models built on Group Theory to completely replicate the molecular orbital calculation model and results of the hyperconjugation effect in toluene. Do you understand? Of course, I can't take all the credit for the success of this topic; the professors from the chemistry department provided a lot of help.

But this topic itself has no value for mere reference. However, when you and your Li really want to apply for a Yangtze River Scholar topic in the future, you could consider starting from my point of combining academia and application, choosing topics that can solve some real-world problems. This has been a more favored direction for Yangtze River Scholar and Jieqing topics in recent years."

Zhang Chunlei's words sent Qiao Ze back into silence.

However, this time the professors no longer had any expectations for Qiao Ze.

In fact, a high school student, even if they understood some Group Theory, could not possibly fully comprehend the significance of this achievement from the few words of Zhang Chunlei. Mathematics is a fundamental discipline. When it comes to choosing a research topic, if you're going to solve practical problems, it requires collaboration with other disciplines.

Only pure number theory research is exempt from this.

But these days, to stand out by doing pure number theory research is extremely difficult. It's even fair to say that the paths have nearly been sealed off.

But on the other hand, Qiao Ze's performance had already surprised the math professors who were used to seeing geniuses.

Self-studying Group Theory in high school, that's something only a truly crazy person would do, given that it's not even on the college entrance exam.

The scary part was, he seemed to have actually understood it.

However, when the professors' inquisitive gazes started to focus on Li Jiangao, wanting to inquire more about the kid's background, Qiao Ze spoke up again: "If that's the case, then using Group Theory to construct a self-supervised feature decoupling framework should also count as a practical application of Group Theory, right?"

"In my concept, this framework can allow computers to perform downstream causal inference tasks, giving programs the ability to perform causal reasoning, as well as unsupervised representation learning capability. It might even create an AI program smarter than chat GPT and reduce the current reliance artificial intelligence has on big data. Moreover, there's no need to collaborate with other departments, since I also know a bit about computers."

"If this topic were submitted to the Yangtze River Scholar review panel, they'd acknowledge it, right?"

After speaking, Qiao Ze, observing the professors' strange looks, added another sentence: "This was just an idea I had before; it's not certain that I can actually do it."