From child prodigy to chief scientist

"Those science subjects are okay, but I really can't get into the humanities. Sigh, I guess I'll just have to memorize them by rote."

Yang Dun was a child who was very dependent on his interests. He would study the subjects he liked with great enthusiasm, while he would strongly resist the subjects he didn't like.

He hates memorizing English words the most, so much so that his current English level is not necessarily better than that of his classmates in the junior class, let alone reaching the high school level.

But in order to go to Yenching University next year, after chatting with Xu Xiao for a while, Yang Dun still had to take out his vocabulary book and start memorizing.

Xu Xiao wasn't too worried about the academic exam and continued studying the materials Yuan Jiyang had sent her.

Thanks to the effects of the terms "focus" and "mathematical intuition," Xu Xiao learns very quickly.

He not only acquired a lot of new knowledge, but has even begun to try reading some academic papers.

Among these, one mathematical concept that particularly interested Xu Xiao was the "Gauss sum".

This is a concept proposed by Gauss when he was studying the quadratic reciprocity law, which roughly refers to the summation of specific complex exponential terms.

Of course, this is not the simple "summation of an arithmetic sequence from 1 to 100" that people are very familiar with, but a concept involving more complex modular arithmetic and complex number distributions—

"For an odd prime number p, we define G(1, χ) = ∑(k=0)^(p-1)χ(k)e^(2πik/p)."

It is essentially a weighted sum of roots of unity and is often used to connect complex analysis and number theory problems.

With his brain highly active, Xu Xiao's thoughts began to wander rapidly.

"If... we replace the most classic quadratic form of Gauss's sum with a cubic or even a fourth term, could it be studied as a new research topic?"

Since this entry task requires Xu Xiao to solve a complex problem on his own, problems that have already been studied by predecessors are probably not feasible.

However, after some deduction, Xu Xiao realized that the problem was not as simple as he had imagined.

However, when the problem progresses from two to three or four times, the complexity of the problem also increases exponentially.

This is clearly a problem that Xu Xiao cannot solve at his current level. Even if he were given a year, he might not be able to achieve any breakthrough.

"Since increasing the number of attempts isn't working... let's try a slightly different approach."

This time, Xu Xiao kept the quadratic term unchanged, but made adjustments elsewhere.

After some experimentation, Xu Xiao constructed a completely new form of exponent sum with feature weights—

"For an odd prime number p, define T(a, b) = ∑(x=1)^(p-1)(x/p)ζp^(ax+bx^(-1))..."

Xu Xiao thought that this index was something that no one had studied before.

If that's really the case, I can define it as "Xu Xiaohe" and then conduct more in-depth research.

However, just to be on the safe side, Xu Xiao still searched for relevant information in case her ideas really did coincide with those of her predecessors.

Among the books Yuan Jiyang sent was one called "Mathematical Terminology".

This book contains nearly 10,000 mathematical terms, making it a very comprehensive book on basic mathematical concepts and professional vocabulary.

Xu Xiao quickly flipped through the contents, thinking it was unlikely that she would run into such a thing by chance.

But when he came across the terminology related to number theory, Xu Xiao's expression turned to one of astonishment.

"Isn't this... just like 'Kloosterman'?"

This concept was proposed by a Dutch mathematician as early as 100 years ago.

Although the form constructed by Xu Xiao is slightly different from that of "Kloosterman and", it is essentially the same thing.

"Sigh... Creating something new is really not that easy."

Xu Xiao swore that he had indeed come up with this idea himself, and that he hadn't seen it before, accidentally memorized it, and then reproduced it.

However, upon closer reflection, this outcome is actually quite normal.

He himself was a new form derived from the transformation of "Gauss and". Since he could think of it, it was entirely possible for his predecessors to have thought of it as well.

Seeing that it was getting late, Xu Xiao had no choice but to put the matter aside for the time being and go to wash up and rest.

The next day, after waking up, Xu Xiao did not go to class first, but went straight to Wang Ze's office.

That night, Xu Xiao thought carefully about her research topic and gradually realized a misconception she had.

In fact, to complete a research project, it is not necessary to construct a completely new concept. Instead, one can delve into existing concepts and find new research directions from them.

For example, cubic equations have been constructed by predecessors, and the general solution of the equations in the real number system has been found.

However, when the intermediate steps involve taking the square root of a negative number, the old theoretical framework is insufficient to solve the problem.

At this point, solving the problem of finding the square root of negative numbers can be considered a new research direction.

Xu Xiao could also adopt a similar approach, such as delving deeper into the "Gauss sum" or "Kloosterman sum" to see if he can find a suitable research entry point.

It was still early, and Wang Ze hadn't arrived at work yet, so Xu Xiao took out her keys, opened the door, and went inside.

"Search for relevant papers for reference, and see which directions have not been studied before."

The materials Yuan Jiyang sent me before included some journal articles, but the number was still too small and the coverage was very limited.

If you want to better understand the academic achievements in a certain field, it is definitely more convenient to search on academic paper websites.

Digital academic resources in this era are far less abundant than in the past, but fortunately, academic websites such as CNKI, VIP, and Wanfang have been established.

Xu Xiao searched on different academic websites and found quite a few relevant papers.

"It's a pity that most of them require payment to download, but I'll just have to spend some money."

Xu Xiao didn't mind paying to download the paper, after all, she had received quite a few scholarships before.

The current payment method is very inconvenient; you can't just scan a QR code with your phone, you have to make a recharge through a bank counter.

Just as Xu Xiao was thinking about whether to call Xu Lang and ask him to help transfer the money, Wang Ze arrived at the office.

"Xu Xiao, you're here so early today?"

"Well, Director Wang, I wanted to look up some papers online, so I came early."

"Checking academic papers? No... have you reached the point of researching academic papers already?"

This is something that students in their senior year or above would normally do. Even though Xu Xiao has already proven himself in the CMO, he hasn't even gone to university yet.