From child prodigy to chief scientist

Chapter 100 Your attention span is a bit too much

"Is this another effect of the thought entry?"

In addition to permanently enhancing thinking skills, thinking terms may also stimulate additional thinking abilities.

According to the system's description of this term's effect, it only has a small probability of being triggered and is not a regular ability.

However, shortly after acquiring this entry, Xu Xiao successfully triggered the passive effect. He didn't know if it was because the probability was higher than he had imagined, or because he had a stroke of good luck.

Xu Xiao didn't have time to think too much and quickly took advantage of the fact that her brain was at its peak to focus on the problem at hand.

This state lasted for a few minutes, after which the strange, lightning-like feeling in my brain quickly disappeared and did not last long.

But even just those few minutes of extra mental stimulation were enough for Xu Xiao.

At this moment, the corners of his mouth curled up slightly, as if he had found a solution to the problem.

"This problem is really nothing special!"

With his brain working at near overclock, Xu Xiao suddenly noticed something.

By optimizing the lower bound of the integral into a weighted logarithmic lower bound, the divergence factor caused by odd cycles can be precisely offset.

Even Xu Xiao himself found it difficult to explain how he came up with this idea so quickly.

For Xu Xiao, this seemed to be just a natural thing.

In fact, those students who have the best grades in school often do not necessarily become excellent teachers.

One reason for this is that they feel many issues are so simple that they don't need to be explained, and that they can see the answer at a glance.

Now, Xu Xiao can finally understand how those geniuses feel.

Another point that satisfied Xu Xiao was that the rapid processing of her brain had not caused any obvious side effects.

Because the effect of thinking terms is an essential improvement in thinking ability, rather than overdrawing his brain capacity.

Even if it's a rare instance of an extra boost in cognitive abilities, the impact on the brain is relatively manageable given the short duration of its effect.

In the following time, Xu Xiao began to deduce the solution in detail according to his new approach.

As he had anticipated, using a weighted logarithmic lower bound did indeed help to counteract the divergence factor.

The logic behind this lies in the fact that the new lower bound utilizes the convexity of (1—t)^(1/m) to completely absorb the divergent secondary principal terms into the logarithmic factor of the principal term, thereby obtaining a tighter integral estimate.

Although the formula for the new lower realm doesn't seem particularly complicated, its actual effect is surprisingly good.

Xu Xiao tried to calculate and compare the previous values, and found that the error was significantly smaller than before, and it was visibly more compact.

If you run the program again with numbers up to 1000 to determine the overall error range, there shouldn't be any major problems.

The next day, after getting up, Xu Xiao told her parents and then went to Yanda University with her schoolbag on her back.

He wanted to continue working on the project with Pan Hong, but he quickly realized a problem.

"Sigh—Pan Hong doesn't have a cell phone either, so we can't contact her directly."

He couldn't keep waiting for Pan Hong to contact him, so after thinking about it, he went to the library study room they used to frequent.

To Xu Xiao's relief, he actually found Pan Hong inside.

At this moment, Pan Hong was sitting in her seat, engrossed in studying something, completely unaware of Xu Xiao's appearance.

Pan Hong only belatedly noticed Xu Xiao after he sat down next to her.

"Hey, Xu Xiao, you're here."

"Hmm. You're here so early today, why didn't you call me?"

"Your parents are here, and I was worried about bothering you, so I thought I'd come and work for a while first."

As she spoke, Pan Hong shared some of her latest ideas with Xu Xiao.

After Xu Xiao left yesterday, Pan Hong has not rested and is still thinking about the divergence problem of odd numbers m.

Although she hasn't made any substantial progress yet, she has at least come up with some new ideas that she can try.

Xu Xiao was somewhat surprised to learn about Pan Hong's thoughts.

Although Pan Hong's method is not yet fully mature and can only be considered a preliminary plan, it is getting closer and closer to the ideal solution.

"Xu Xiao, what do you think of these methods? I feel like they're worth a try."

"Well, I actually thought about it last night too, and I think our thinking is quite similar —"

As he spoke, Xu Xiao showed Pan Hong his newly optimized formula for the lower bound of integrals.

Upon seeing the formula, Pan Hong's face immediately showed a look of surprise.

「fm（）≥[（1—1/m）×1og（/m）—（1/（2m））×（1og（/m）^2—（1+1/（m×（m—1））]/——你是怎幺想到这幺一串式子的？」

Regardless of the actual effect of Xu Xiao's formula, Pan Hong was somewhat at a loss when faced with this complex sequence of words.

Faced with Pan Hong's question, Xu Xiao was also a little unsure how to answer.

He couldn't very well say that he noticed it directly; such attention would be far too astonishing.

Xu Xiao had no choice but to analyze the derivation of the formula from a relatively objective perspective.

"Initially, my idea was to start with the convexity of (1—t)^(1/m), then I used a second-order Taylor expansion and made some modifications, and combined it with the properties of Jensen's inequality—"

Listening to Xu Xiao's explanation, Pan Hong felt like her brain was about to shut down.

It wasn't until she stopped and thought about it for a while that she finally seemed to understand a little.

"If you put it that way, then our thinking is indeed on the same general direction."

"That's right. If you push it a little further, you should be able to derive a similar formula."

Pan Hong disagreed with this, saying that she had only given a direction, while Xu Xiao had already derived the complete formula, and the difference between them was obvious.

Even now, Pan Hong still hasn't fully grasped Xu Xiao's reasoning; some details still need further careful consideration.

"Perhaps—this is the difference between Xu Xiao and me," Pan Hongxin said.

Although they both got full marks in CMO, she is four years older than Xu Xiao, which is enough to show the difference in their talents.

Often, the ideas of geniuses are difficult to understand, just as three-dimensional beings find it hard to comprehend four-dimensional space.

Pan Hong could only objectively acknowledge the existence of this gap, but she didn't feel frustrated because of it. She knew it wasn't her problem; it was just that Xu Xiao was too much of a supermodel.

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