Top Student at Their Peak

"Haha... alright, I'm heading out!"

...

This birthday was fairly pleasant. After Yu Yanjiang left, both Director Tian and Elder Yuan only advised Qiao Yu not to let his mind be occupied with other nonsensical matters.

He also had to focus on mathematics, especially theoretical aspects.

Qiao Yu naturally agreed. However, the daily routine from then on would likely be a mix of play and tutoring.

The tutoring was at Qiao Xi's request.

After all, Old Xia's family trusted them enough to send Xia Keke over, and ensuring her safety was not the only concern.

She couldn't come to Beijing just to play, and then return with worse grades.

So, every morning, Qiao Yu had to get up by 7:30, wash up and have breakfast, and then start doing exercises with Xia Keke at eight...

While Xia Keke worked on problems, he read articles and brainstormed for his computing platform.

When Xia Keke finished, he was also responsible for grading and explaining her mistakes.

This time he truly became a 'father'... As the saying goes, once a teacher, forever a father.

But Qiao Yu was happy to do so. In the afternoons, he would take Xia Keke to Yanbei University for a confidential class. After all, learning more things is always useful.

After class, they would stroll around nearby, casually chatting. If it was too cold in the evening, they would either watch a movie or stay home to continue working through problems and reading books.

Life was carefree and pleasant.

Time flew by, and before they knew it, the Lunar New Year arrived. On the eve of the New Year, they didn't have class in the afternoon, and the family went shopping. Afterwards, they secretly celebrated Qiao Yu's lunar birthday, just the three of them...

They had New Year's Eve dinner with Elder Yuan. There wasn't much to say about the couple of days during the New Year.

Qiao Xi after taking the two little ones to pay respects to their two mentors, then they had some free time.

Then, at Qiao Xi's request, they resumed doing homework and problems starting on the fourth day, with Qiao Yu responsible for explanations.

There was nothing much to do during the New Year; especially since Qiao Yu wasn't keen on joining the crowds, and Qiao Xi and Xia Keke didn't know where to find any festivities.

But Xia Keke didn't mind at all. After all, being able to stay with Qiao Yu every day already made her quite happy.

Even doing exercises was okay, and just like that, time moved to the sixth day.

As usual, Xia Keke was working on her exercises, but she was feeling a bit down and distracted. After all, the enjoyable winter break was about to end.

Early in the morning, her mom even called to remind her to remember to go to the station on time tomorrow...

They might not see each other for another half a year. Thinking about this, Xia Keke couldn't help but sneak a glance at Qiao Yu beside her.

Unfortunately, he was seriously thinking about something, continuously writing and drawing with a pen on paper.

"Huh?"

Hearing this sound from Qiao Yu, Xia Keke quickly withdrew her gaze.

Then she quickly realized it was unusually not to react, so she openly turned her head to look at Qiao Yu and asked, "What's up?"

"What does this formula look like to you?" said Qiao Yu, pointing at his draft paper.

Xia Keke moved her gaze to the draft paper.

There were a total of three formulas written on the paper that Qiao Yu pointed at...

Xia Keke glanced at it and asked, "Which formula are you talking about?"

Qiao Yu replied, "Of course the third one. Don't you think the third formula looks a lot like another formula? Oh... right, you probably haven't encountered that formula yet."

Xia Keke curiously asked, "What formula?"

"The Riemann Zeta Function!" said Qiao Yu, quickly writing down the Riemann Zeta Function next to the third formula.

Xia Keke carefully compared them several times, then asked in an uncertain tone, "These two... um, do they really look similar?"

"Absolutely! One is the cumulative sum of natural numbers n, and the other is the cumulative integral of the disturbance parameter α. Both functions also introduce power factors, where one represents the distribution characteristic of frequency, and the other the distribution characteristic of density."

Qiao Yu casually explained.

"Hmm..."

Xia Keke wanted to say something but Qiao Yu turned his head and said, "Oops, I got carried away. Don't feel bad if you don't understand. Let me tell you, even Senior Brother Chen, Director Tian's Ph.D., might not understand the connection here."

"Oh!" Xia Keke indeed felt a lot better.

If even a Ph.D. couldn't understand it, then it was fine for her not to...

"Is your discovery useful?" Xia Keke couldn't help but ask.

"Yes, it's indeed very useful and quite interesting. The periodicity and symmetry of the orbital disturbances show behaviors similar to the Fourier series expansion, which is the first formula.

From this, a form of integral was defined to analyze the modal density of the orbital disturbance, which is the second formula you saw. When it is normalized, it results in the relationship of the third formula.

The third formula turns out to closely resemble the Riemann Zeta Function. If it's not a coincidence, there must be a mathematical connection. Let me put it this way, if it's not a coincidence, Americans will soon owe me a million, in US Dollars!"

Qiao Yu said with an air of seriousness.

"Are you talking about the Riemann Hypothesis?" Xia Keke suddenly realized, as Changjun Middle School's math teacher had once mentioned the seven Millennium Prize Problems.

"Yes, because this implies that the symmetry between the two is closely related. This means, it doesn't require complex tools to reformulate the zeroes problem of the Riemann Zeta Function into a geometrical problem in the modal space.

As for translating the geometrical problem into a number theory one, my first paper has already proven it. So if the two aren't a coincidence, it means you can complete the proof with a rather simple method."

Qiao Yu confidently said.