From child prodigy to chief scientist

Chapter 97 Mathematics is our language of communication

"Then, let's work together and see if we can solve this problem?"

"No problem, it's settled then."

Since both of them had already scheduled classes for the afternoon, they decided to conduct their research in the evening.

"Let's meet at the library entrance at 6:30 pm and then go to the study room together."

"Yes, I should be able to do it at the right time."

"Do you have a cell phone? If anything else happens, we can contact you directly by phone or text message."

"I haven't bought a phone yet, so please give me your phone number. I'll call you if anything happens."

After making their agreement, the two said goodbye and parted ways temporarily.

In the afternoon class, Xu Xiao was noticeably less focused than before, constantly thinking about the topic Pan Hong had raised.

After all, this topic was indeed more interesting than what the teacher had taught. Since he was already itching to get started, Xu Xiao decided to start researching it on his own ahead of time.

What Xu Xiao didn't know was that in another classroom, Pan Hong was also not paying attention to the lesson and was researching her own topic.

Around 6:30 p.m., Xu Xiao walked to the library entrance and found Pan Hong already waiting there.

When she saw Xu Xiao coming over, Pan Hong smiled and waved to him.

The two then went into the library study room together and found two empty seats next to each other.

"Xu Xiao, I thought about it this afternoon. A cycle graph Wm = K1 + Cm is equivalent to having one more fully connected central vertex than a regular cycle Cm. We can apply the existing Ramsey number results for cycles to obtain a trivial upper bound."

C

While speaking in a low voice, Pan Hong demonstrated her derivation process from the afternoon to Xu Xiao.

Seeing what Pan Hong had written, Xu Xiao smiled helplessly and took out her own draft paper.

Xu Xiao had thought of the same things as Pan Hong that afternoon.

Although there are some differences in the details of their derivation, their overall ideas are very similar.

Upon seeing the contents of Xu Xiao's draft paper, Pan Hong finally understood why Xu Xiao had reacted that way.

Not only did they both start their research ahead of schedule without permission, but their research approaches were also remarkably similar.

However, they both know that what they are doing now cannot solve the problem immediately and still has certain shortcomings.

"Xu Xiao, I feel that this 'Ordinary Upper Realm' is still too loose, and the error between it and the actual value is probably quite large."

"Yes, that's what I think too. Let's do an actual test first and see how big the error really is."

"Actually verifying this? The computational load is just too huge!"

Pan Hong naturally knew how complicated the calculations were; if she were to calculate them purely by hand, she didn't know how many days it would take to finish.

Xu Xiao naturally didn't have this concern; for him, it was just a matter of writing a program.

"That's simple. You can just write a C program. Verification of vertices up to 1000 can be completed quickly."

"C Programming Language — You can program too?"

This is indeed a blind spot in Pan Hong's knowledge. The previous CMO did not test her on programming knowledge at all, and Pan Hong had not systematically studied related content.

"Yeah, I do know a little bit. Come on, let's go to the computer lab."

Upon arriving at the computer room, Xu Xiao turned on a computer, opened Microsoft Visual C++ 6.0, and began writing programs proficiently.

This program wasn't too complicated for Xu Xiao; he could simply use brute force enumeration.

Pan Hong felt like she was reading a book written in heaven, unable to understand what Xu Xiao was doing. She wanted to ask, but was worried about disturbing Xu Xiao.

Xu Xiao finished writing the program in just a few minutes.

"Okay, now let's run the program and wait for the computer to finish the calculation."

Pan Hong stared intently at the changes on the screen, and then a look of surprise appeared on her face.

Although she didn't quite understand the programs, she could at least understand the output.

Pan Hong had already calculated the first few simpler values ​​herself, and the numbers on the screen were exactly the same as those results.

This proves that Xu Xiao wasn't just making things up, but genuinely understands programming.

In that instant, Pan Hong finally understood that Xu Xiao's abilities were far greater than she had imagined.

His mathematical talent is indeed very strong, but that's not the whole story of his abilities.

Pan Hong secretly made up her mind that she must study programming well in the future and absolutely not fall behind Xu Xiao in this area.

As the computer continued its calculations, one result after another appeared on the screen.

Comparing the difference between the ordinary limit and the upper limit of actual values, Xu Xiao frowned slightly, clearly the result was not so satisfactory.

"The overall scaling error has exceeded 150% — the accuracy is indeed far too poor."

He had anticipated the issue of insufficient accuracy, but he hadn't expected the actual accuracy to be this bad.

Such a sparse and ordinary upper realm obviously has no academic value.

Pan Hong was also somewhat surprised by the result, but she quickly found the reason behind it.

"It seems to be an issue with overall scaling. The degree constraints of the central vertex and the degree constraints of the cyclic vertices are bound together, resulting in a significant loss of accuracy."

"Yes, I think that's the problem too. I think we should consider decoupling and splitting the degree constraints, which should further improve the accuracy."

Xu Xiao then explained his thought process in detail.

His idea was to divide the vertices of the wheel graph into two categories and apply different Ramsey number constraints to each category.

In this process, the neighborhood derived subgraph cycle Cm of the central vertex J is controlled by the cycle Ramsey number r(Cm, Kn).

而圈J顶点的邻域导出子图路Pm—1，则是用路Ramsey数r（Pm—1，Kn）=（m—2）（n—1）+1控制。

Pan Hong also expressed her strong agreement with the method proposed by Xu Xiao.

Back in the study room, they didn't rush to continue working, but instead divided up the tasks.

Pan Hong was mainly responsible for the construction of the combinatorial layer, such as the neighborhood structure of the split graph, the derivation of degree constraints, the proof of mathematical induction, etc.

Xu Xiao was responsible for the optimization at the analysis level, including the construction of integral scaling functions, as well as various programming and verification tasks.

The next day, neither of them went to class and spent the whole day in the study room.

Given the quiet environment of the study room, they couldn't communicate loudly and often had to express their thoughts through formulas.

Fortunately, mathematics naturally fostered a tacit understanding between them, and even without any language or writing, mathematics itself could serve as a means of communication.

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