CHAPTER 414: CHAPTER 140: THE POSSIBILITY THAT MY MOM IS ALSO A MATHEMATICS GENIUS_5

Tan Lu Yuan could only respond with a bitter smile: "Yes, you’re right, in this regard, I’m not as good as him."

Of course, he couldn’t help but have some complaints in his heart. If the circumstances were switched, even if Qiao Yu was his student, he could be more open-minded than Tian Yan Zhen.

Alright, hearing this, Elder Yuan felt it was about enough. He didn’t want to say anything more and was just about to rest when his phone vibrated several times.

Yuan Zhengxin picked up the phone and saw several messages from Qiao Yu pop up.

He clicked in and saw a photo, a manuscript with very neat handwriting.

However, the old man wasn’t in a hurry to look at the contents of the manuscript in the photo but first looked at the string of words that followed.

"Grandpa, are you asleep? Sorry to disturb you. If you’re asleep, you can reply tomorrow. The picture I just sent is a conjecture my mom made after reading my paper on the upper bound of rational points on curves."

"She thinks that in the algebraic curves that meet the specified geometric conditions, the function f(θ,g) may tend towards a limit, indicating that as the deficiency increases, the number of rational solutions gradually approaches a stable upper bound."

"I think if this conjecture can be proven, it means that as long as there’s an appropriate form of function, one can use f(θ,g) to describe this point, even if the curve may not have a clear closed-form. We can still estimate this upper bound based on the specific geometric properties of the curve."

"She can even understand Professor Schulz’s paper independently! You judge for me, I think this is a display of mathematical talent. But she refuses to admit it and says I’m making a big deal out of nothing."

"If you also think she has mathematical talent, please scold her for me! Even though if I seriously argue, she certainly can’t outtalk me, but you know, she is, after all, my mom! I can’t argue with her, so I’m counting on you!"

The old man could see that Qiao Yu was very emotional, otherwise, he wouldn’t have sent five text messages in just two minutes.

However, after looking at it, the old man was indeed interested. Not to mention anything else, being able to independently understand Schulz’s paper was already quite impressive.

As for this conjecture...

The old man opened the photo and then zoomed in to look at it very carefully.

Beside him, Tan Lu Yuan was a bit puzzled as to why the old man picked up his phone and suddenly seemed lost in thought.

Just as he was about to speak, Elder Yuan suddenly waved him over, saying: "Lu Yuan, you also saw Qiao Yu’s paper today, come over and take a look at this."

Tan Lu Yuan quickly stood up and walked over, took the phone handed by the old man, took off his glasses, and looked carefully.

"This... does it mean the upper bound is determined by the geometric properties of the curve? If that’s the case, even if it’s only a specific type of curve that can satisfy this condition.

It means as long as the geometric properties of this type of curve are analyzed, regardless of its complexity, an upper bound can be obtained. If it involves higher dimensions...

That is, if the expression of the function could be listed, that would be even better."

Tan Lu Yuan frowned and thought for a while, then looked at Elder Yuan with a puzzled face and said: "Is this thought up by Qiao Yu’s mom? The one who wasn’t very talkative today? I think this proposition could apply for a Natural Science Foundation grant, right?"

He really had a puzzled look. If this conclusion was something Qiao Yu’s mom came up with independently after reading Qiao Yu’s paper, then this mathematical intuition is terrifying.

Although now we can’t be sure if it’s correct. But coincidentally, we can first use a supercomputer for simple validation. If it’s roughly correct, this topic can indeed be proposed.

But... could mathematical talent be inherited? This really made Tan Lu Yuan question life.

After all, his son really hasn’t shown any talent in mathematics. He doesn’t even have much talent in science, only being able to choose the arts in high school. This may be one of his lifelong regrets.

Even though his son is actually doing quite well now. But he, a grand math professor, has a son who chose the arts, making him embarrassed to talk about this with others.

"Do you also find this conjecture very interesting? It should be real, my grandson wouldn’t lie to me. Besides, do you think he has any need to lie to me?

When it comes to mathematics, either you understand it or you don’t. A few simple questions will reveal it. So, I’ll give him a call, I’ll turn on the speaker, and you can listen in."

Tan Lu Yuan could hear that the old man was somewhat excited when he said this.

Then he suddenly thought of a possibility...

Could not help but feel a bit dazed again.

If it really happened, then this mother and son...

The call connected quickly, and Qiao Yu’s voice followed.

"Grandpa, you’re not asleep yet."

"Mm, not asleep. I was just chatting with Professor Tan. Let me ask you, is this conjecture really a conclusion your mom thought of independently?"

"Yeah, hang on, Grandpa, I’ll get her to speak with you now."

...

In the hotel room, Qiao Yu walked to the bedroom door and started knocking.

"Mom, Grandpa Yuan called, he wants to speak with you."

Soon the door opened, and Qiao Xi glared at Qiao Yu, just about to scold this troublesome kid, when she saw the phone in Qiao Yu’s hand, showing an ongoing call...

She could only take a deep breath and took the phone from Qiao Yu’s hand.

"Hello, Elder Yuan."

"Qiao Xi, right? Both Professor Tan and I thought your idea was very interesting. Could you tell us how you came to it?"

"Sure, Qiao Yu showed me his paper, and I felt that his handling of the impact of deficiency and geometric constraints on the number of rational points was a bit rough.

Especially the supercomputer validation report at the end of the paper, while the results are correct, some results still have discrepancies.

For instance, there’s a data point where θ^g equals 8, but the actual supercomputer calculation gives 6 rational points. Of course, 6 is indeed less than 8, which satisfies N(C)≤C(θ)=θ^g, this result.

So, you can’t say Qiao Yu’s proof is wrong. However, this is evidently not precise enough, so I wondered if I could make the results a bit more refined.

After carefully going through Qiao Yu’s paper several times, I speculated that there might be a connection between the geometric properties of the curve and the rational solutions. But I couldn’t figure it out, so I cleverly tallied all the data the supercomputer provided at the end of the paper.

Then I found that as the deficiency increased, the discrepancies between the supercomputer’s results and the theoretical formula gradually diminished, especially for curves with high deficiencies.

So it seems to show that although θ^g provides an effective upper bound, the actual number of rational points does not seem to grow according to this power function but tends towards a relatively stable number.

So I had this conjecture. Of course, I really don’t know whether it’s correct, I can’t prove it, nor do I know how to verify it, I can’t even think of what the expression of this function might be."

Qiao Xi explained slowly. She simply thought such a function might exist, if so, then mathematical geniuses might be as common as dirt, Qiao Xi thought.

"Okay, Qiao Xi, it’s quite late today, if you have nothing going on tomorrow morning, why don’t you come over to my Qiuzhai for a visit, how about that?"

"Ah... this... will it be too much trouble for you?"

"I have nothing scheduled for tomorrow morning, bring Qiao Yu along, we can chat casually, no pressure."

"Alright, Elder Yuan, I’ll bring Qiao Yu to visit you tomorrow."

"Mm, Qiao Yu knows where my office is. I’m usually there by eight. Rest well, I’m hanging up now."

"Goodnight, Elder Yuan."

...

After hanging up the phone, Qiao Xi glared at Qiao Yu in annoyance. Qiao Yu, on the other hand, held his head high and met Qiao Xi’s gaze head-on.

His face seemed to say the words "Unyielding."

"Is it appropriate for you to disturb Elder Yuan so late at night?"

"I’ve said, it was Grandpa who called me."

"But I really have no mathematical talent! And I still often zone out!" Qiao Xi said while rubbing her head.

"But what if you do? Let Grandpa verify it, just in case. If you do have it, I’ll support you in taking the field yourself to show up that jerk. Just think, he’s just a small math professor at Berkeley. There’s no cost in just trying!

And if one day you become a great mathematician yourself, able to give a plenary talk at the International Congress of Mathematicians, won’t he be so scared he’d pee his pants if he saw you then?"

Qiao Yu said carelessly.

Alright, Qiao Yu did have the confidence.

Probably, only he could so boldly take up a great academician’s valuable time.