Actually, Zhang Zhou didn't quite fancy making friends with classmates who liked to brag.
But, recalling the counselor's instruction, he decided to bite his tongue for now.
He had thought that, after saying such things, Qiao Ze might continue to utter even more astonishing bombast to showcase his uniqueness.
After all, the show-offs Zhang Zhou had encountered before all behaved like this.
He was also afraid that Qiao Ze's remarks might provoke Gu Zhengliang to utter something unpleasant.
However, to his surprise, after calmly discussing the professors in the school who specialized in geometry, Qiao Ze stood up, naturally picked up his lunch box, and didn't ramble on any further.
This again made Zhang Zhou feel a little uncomfortable...
Is that all? Just like that?
So brief and unassuming?
"Aren't we going to eat?" Qiao Ze asked with a perplexed look at the class president with the complicated expression.
"Yes, yes, let's go eat. To the third cafeteria."
...
On the way, the three walked together, and Qiao Ze, as usual, had little interest in talking.
So Zhang Zhou could only chat idly with Gu Zhengliang about the content of today's class.
It's not that they didn't want to talk about something else.
Mainly, with a Qiao Ze beside them, whose thoughts they couldn't quite grasp, they really couldn't find a better topic.
"Did you understand the second example problem in today's math analysis class?" Zhang Zhou asked.
"More or less," Gu Zhengliang pushed his glasses up and said, "I think the difficult part is still the Riemann Integration; it's too confusing. By contrast, Lebesgue Integration is much easier to understand."
"Yeah, anyway, I think math analysis is really hard!"
Zhang Zhou lamented, then, subconsciously glancing at the quietly accompanying Qiao Ze, he couldn't help but ask, "By the way, Qiao Ze, have you encountered the course Math Analysis before?"
Qiao Ze nodded and answered, "Self-studied it."
"Um... self-studied?" Zhang Zhou blinked and asked again for confirmation.
"Yes!" Qiao Ze responded briefly again, but feeling that it seemed too aloof, he added, "Lu Ding's Principles of Mathematical Analysis."
"Could you then give us a simple analysis of the difference between Riemann and Lebesgue Integration?"
Gu Zhengliang couldn't help but ask, the impetuosity of youth evident in his voice, but still controlled.
"Riemann Integration partitions the domain of a function, while Lebesgue Integration partitions the range of a function," Qiao Ze replied casually, "I don't know the example problems your teacher explained in class, so I'm not sure what you find difficult. However, I guess it probably has to do with the interchange of order of integration and limits."
Zhang Zhou and Gu Zhengliang both paused, especially Gu Zhengliang, who instinctively pushed his glasses and asked, "You could guess that? Why?"
Qiao Ze looked at the class leader, remembering how he had helped make his bed earlier, and began to explain, "Mathematical analysis often requires interchanging the order of two limit processes, especially the interchange of integration and the limits of a sequence of functions. Under Riemann Integration, the uniform convergence of a sequence of functions is required to ensure the interchangeability of integration and limit operations.
Meanwhile, the Lebesgue Dominated Convergence Theorem dictates that only very weak conditions are needed to interchange the operations of integration and limits. Hence, if you find Lebesgue Integration easier to understand and Riemann Integration confusing, I believe it's probably because of this."
Zhang Zhou and Gu Zhengliang exchanged glances, then realized that the guy walking alongside them was likely not one of those fake show-offs who knew nothing but rather someone genuinely skilled.
Just from a few casual remarks, he could identify what sort of example problems were discussed in class that day and even analyze the reasons behind them. Zhang Zhou felt that this person must be one of those with a high IQ and intelligent logical analysis abilities described by postgraduate exam tutor Zhang Gaofeng, the kind who could leave everyone astonished without anyone being able to track down how it was done.
No wonder this guy could parachute in out of nowhere.
It's terrifying!
Zhang Zhou suddenly had a flash of inspiration and guessed, "Qiao Ze, were you from a different major before? And then a mathematics teacher discovered your talent and snatched you up?"
Qiao Ze shook his head and said, "No, I'm a senior in high school this year. Li said the high school environment wasn't suitable for me, so he let me start at the university early."
"Senior high..." Zhang Zhou looked at his own bowl of rice and suddenly felt a little ashamed to eat.
"What were you thinking? If you had the energy to self-study mathematical analysis in senior high, why didn't you compete in the Olympiads and go to Yanbei? The Yanbei University School of Mathematics is the NO.1 in the country. Why come to our school?" Gu Zhengliang said somewhat excitedly.
Qiao Ze paused, having never considered this question. After all, before coming to Xilin University of Technology, he hadn't had much expectation for university life.
However, an image of a person soon emerged in Qiao Ze's mind, and then he naturally said, "Because Li is here, I came. He's the first person I've met with some intelligence, and he's also a really good person."
Zhang Zhou blinked his small eyes hidden in fat and suddenly understood what this guy meant by saying if he talked too much, it was easy to offend people.
"You mean, before you met Li, you hadn't encountered a single person with some intelligence?"
"Yeah." Qiao Ze nodded.
"What about me?" Zhang Zhou asked subconsciously.
Qiao Ze pursed his lips and said nothing.
After all, in his view, classmates who found even the most basic Riemann integration tricky really weren't those he could rightfully praise for their intelligence. Wasn't this something one could understand by just watching a few minutes of a video?
Maintaining silence was the biggest concession he could make, thanks to the education he had received from Li Jian.
But seeing Zhang Zhou's gradually forlorn face and thinking of the class president's enthusiasm, the inherently kind-hearted Qiao Ze decided to say something after all. He thought for several seconds and then managed to eke out, "I think you're a really good person."
"Pfft... Hahaha..."
Gu Zhengliang next to him couldn't hold back his laughter at that statement, losing all composure and patting Zhang Zhou on the shoulder, "Qiao Ze, you've nailed it. Our class president really is impeccable in character, explosively good. I must give this good guy card a full score!"
"Damn, I'm not treating you to dinner tonight! Gu, you're heartless!" Zhang Zhou pushed away Gu Zhengliang's hand, resentfully declaring.
"No worries, I'll treat today," Gu Zhengliang cheerfully said.
Seeing Zhang Zhou's deflated look at that moment, he was genuinely happy.
See how smart he is, he certainly won't disgrace himself.
But obviously, Gu underestimated Zhang Zhou's threshold for shame.
And Zhang Zhou was clearly not stupid; at least he could tell that this new classmate was genuinely disdainful of saying insincere flattery.
"Qiao Ze, why don't you also comment on Gu's intelligence while you're at it?"
"Qiao Ze, don't mind him! Damn, Zhang Zhou, you're really too vile!"
Qiao Ze looked at the two squabbling and suddenly thought that university life indeed seemed much more interesting than high school life.
It also made him feel more cheerful, truly rare for him to want to say a heartfelt word. Thus, the next moment, the warm words coated in utmost sincerity reached the ears of both men: "Although you're not smart, you're really not that stupid either!"
The two who were just tussling suddenly fell silent.
Maybe they were touched by the warmth?
Probably so.