From child prodigy to chief scientist

But considering Xu Xiao's terrifying learning speed, how he seems like a completely different person every few days, it seems perfectly reasonable for him to do anything.

Xu Xiao then mentioned that she needed to transfer money to the thesis database service provider.

Upon learning of this, Wang Ze readily agreed:

"My bank card has online banking, so I should be able to transfer the money online."

Hearing Wang Ze say this, Xu Xiao was also pleasantly surprised. She thought to herself that Wang Ze truly deserved to be the director of Yucai Children's Class, having such advanced technology as online banking back in 2004.

After some attempts, Wang Ze successfully helped Xu Xiao recharge her account.

"I've topped up your account with 1,000 yuan now. If that's not enough, I'll top it up for you later."

"That's enough, that's enough. We shouldn't need that much. Director Wang, could you please give me your bank account number? I'll transfer the money to you when I get back."

"Alright, don't be so polite with me. We're all so lucky to have a student like you in this year's junior class!"

At this time, Xu Xiao didn't have much cash on him, so he could only keep the matter in mind and think about finding an opportunity to pay it back later when he got the money.

After downloading these papers to his computer, Xu Xiao printed them out and bound them using the office printer.

Over the next few days, Xu Xiao studied these papers carefully, especially those concerning "Kloosterman and".

This allowed him to gain a much deeper understanding of the relevant knowledge and to basically grasp the research progress in this direction.

Over the years, some mathematicians have indeed conducted related research, but there are still many unexplored areas of research.

Relying on his strong mathematical intuition, Xu Xiao made an inequality assumption related to the "Kloosterman sum"—

"For odd prime numbers p, when (a, b) are not all 0 modulo p, |T(a, b)|≤2√p.

This inequality was not something Xu Xiao wrote casually. For example, the bound 2√p is a classic upper bound for many exponent sums.

However, because Kloosterman and Legendre have an additional weight, the situation here is more complicated than with other indices.

But at least, this is much easier to handle than the Gaussian solution problem that Xu Xiao had thought of three or four times before.

"I never imagined that just finding a research topic would be so difficult."

It must be admitted that doing academic work and preparing for competitions are two completely different things.

It is certainly not easy to achieve good results in a competition, but the competition questions are readily available, and you just need to solve the problems according to the questions.

However, when it comes to academic research, you not only need to find your own research topics, but you also need to ensure that the topics are not researched by others and that the difficulty level is appropriate.

If the topic is too difficult, it is very likely that no results will be achieved even after several years.

A topic that is too simple, even if solved, will not have much academic value.

Being able to finalize the topic is a big step forward.

For some time afterward, Xu Xiao devoted most of his time and energy to proving this inequality.

According to Xu Xiao's own assessment, this problem is much more complicated than the one he had previously asked Yuan Jiyang.

To complete this proof, Xu Xiao specifically bought several books related to algebra, number theory, exponents, and so on to enrich his knowledge base.

At the beginning of the research, Xu Xiaoxian started with numerical experiments and tried to use some elementary methods to verify the results.

However, none of these methods were very effective, especially after variable substitution, which resulted in double summation, making the whole problem more complicated.

However, subsequent research also brought some good news. After decomposing the sum, Xu Xiao discovered that the Kloosterman sum satisfies a variety of symmetry properties.

Some of these symmetries have not been shown in related papers, which means that Xu Xiao is likely the first person to discover these properties.

…………

Before we knew it, it was already 2005.

With winter break approaching, Xu Xiao was also preparing to return to the steel city.

Before leaving, Xu Xiao sent Yuan Jiyang another email, telling him about her recent research project, including its progress and the problems she had encountered.

After sending the email, Xu Xiao couldn't help but shake his head and sigh.

"Just as I predicted, the first entry task is almost complete, but there's still no hope for the second task."

Even now, Xu Xiao still has no clue how to prove this inequality and can only hope that Yuan Jiyang can give him some pointers.

the other side.

In his office at the School of Mathematics at Yenching University, Yuan Jiyang was sitting in front of his computer, carefully reviewing the progress reports of graduate students' research projects.

Although it is now winter break, Yuan Jiyang has no intention of resting and is busy handling various tasks every day.

In addition to his own research projects, he also tries to check the progress of the graduate students' projects regularly and provide guidance to the students.

After reading a student's report, Yuan Jiyang's expression became somewhat serious.

"You're already a second-year graduate student, how come your research project is still so immature?"

In Yuan Jiyang's mind, a second-year graduate student in the Department of Mathematics at Yenching University, although not yet a full-time researcher in the strict sense, should at least possess basic research capabilities.

However, Yuan Jiyang was far from satisfied with the content presented in the students' reports.

He had clearly provided a detailed research topic, but by dealing with only a problem of medium difficulty, he exposed many problems in the students.

"I haven't read enough academic papers, and my foundation isn't solid enough."

Yuan Jiyang is not usually a very strict person, but he is quite demanding when it comes to scientific research.

Of course, these students just didn't meet Yuan Jiyang's requirements; compared to their peers, they were already quite outstanding.

At that moment, a new email pop-up message suddenly appeared on Yuan Jiyang's computer screen.

Normally, Yuan Jiyang wouldn't process email messages immediately; he would only process them once a day in the evening.

When work is particularly busy, it's normal to only process emails every few days.

However, after seeing the sender information of the email, Yuan Jiyang temporarily stopped his work and opened the email directly.

"Xu Xiao... finally emailed me again."

Yuan Jiyang's level of attention to Xu Xiao was unusual.

Even towards the students in his lab, Yuan Jiyang had never shown such enthusiasm.

Xu Xiao is not even a student at Yenching University now, and it's hard to say whether he will actually come to my lab in the future.