CHAPTER 409: CHAPTER 139 ALWAYS SOMEONE OVERJOYED_5

Professor Tan frowned and asked.

"It’s very simple. If I can prove that the Galois representations of every pair of twin primes can be defined through the characteristics of modular forms, then the Galois representations can automatically possess the uniqueness of the number pairs without the need to reconstruct them each time."

Qiao Yu said casually.

Professor Tan was stunned for a moment, then frowned even more and subconsciously asked, "Are you saying to directly define the matrix of a Galois representation using modular forms?"

Qiao Yu nodded and replied, "Yes, of course, I haven’t figured out how to define it yet. I’ll just give a simple example:

For instance, we can use the Fourier coefficients of modular forms as characteristic parameters for the Galois representations. Then theoretically, their trace could reflect the structure of the Fourier coefficients.

If successful, I can find a universal construction rule for the Galois representations of prime pairs. If it fails, I’ll look for other patterns.

If you want to ask more, I can only say I haven’t thought it through yet. After all, Director Tian just assigned me this task yesterday, and I’ve only thought about it for a day. This is just a rough idea that I think might work."

In fact, Qiao Yu had quite a few ideas, but he found the others even less reliable, so he didn’t mention them at this time.

Anyway, this wasn’t an academic discussion; he was just trying to earn some face for his mentor.

Looking at Professor Tan’s furrowed brows as he contemplated, he felt that Director Tian should be quite satisfied.

"Haha... Brother Lu Yuan, what do you think of my student’s idea?" Tian Yanzhen asked with a smile.

"Phew... if he can achieve this result by the end of this year or early next year, by the way, Qiao Yu, you’re sixteen this year, right?"

"Mm..."

"Then we can look forward to a seventeen-year-old Fields Medalist." Tan Lu Yuan sighed, glancing at Tian Yanzhen.

"No rush, no rush. If it can’t be done in one year, then two years. Qiao Yu, don’t feel pressured. There’s no difference between seventeen and twenty-one."

Elder Yuan glared at Tan Lu Yuan and then looked at Qiao Yu, speaking loudly.

Obviously, he didn’t like Tan Lu Yuan’s statement, suspecting it could be harmful praise.

Tan Lu Yuan was first astonished and then smiled wryly.

He understood Elder Yuan’s concerns but couldn’t argue. He genuinely didn’t mean it that way; he just couldn’t help but express his amazement.

After all, this idea is not something an average person could come up with. Even for those who do think of it, the difficulty remains enormous.

Just thinking about it reveals its complexity. If truly accomplished, this would mean that using characteristic matrices to directly describe the structure of number pairs would become a brand-new tool for number theory research.

Moreover, it would significantly expand the application boundaries of the Langlands Program. If this doesn’t receive a Fields Medal, it wouldn’t make sense.

But just from the old man’s reaction, it’s clear how much they value Qiao Yu.

Any word potentially disadvantageous to the child is something they don’t want to hear. What else could they do?

Fortunately, Qiao Yu quickly reacted and immediately said.

"I’m not in a hurry at all, Grandpa, did you forget? You said you’d definitely see me win the Fields Medal yourself. At the time I replied that I plan to win it in my thirties."

As Qiao Yu spoke, he glanced at Xia Keke at his side.

The tacit understanding between the two was remarkable. Xia Keke promptly picked up the juice-filled cup in front of her and, smiling warmly, said to the two elders, "Grandpa Yuan, Grandpa Tian, I toast you with a glass of juice, wishing you both to grow younger with each passing day.

This way, twenty years later, when my brother wins the Fields Medal, Grandpa Yuan and Grandpa Tian can join and see my brother receive the award together."

"Good, good, good, you little girl, really clever. Come, come, come, together, together."

The words of the two children left Tan Lu Yuan initially stunned, then suddenly realizing he had been somewhat foolish, not as eloquent as the two kids.

He looked somewhat resentfully at Tian Yanzhen, whose smiling face seemed all the more annoying!

...

After Xia Keke toasted with her juice, she naturally caught the attention of Elder Yuan and Tian Yanzhen.

Especially Elder Yuan.

He began asking Xia Keke about her purpose for visiting, and upon learning she was here for the Yanbei University summer camp, he showed concern for Xia Keke’s studies...

After understanding Xia Keke’s situation, he made a decision.

"Before you leave, pick a day to visit Qiuzhai with Qiao Yu, and I’ll test you. If you pass Grandpa’s test, don’t go to Yanbei anymore; come to Huaqing with us."

"Alright, Grandpa, I’ll toast you with another cup of juice."

"Good, good, good."

Tian Yanzhen and Qiao Xi sat on the side, smiling at this scene, without saying a word.

In short, the meal ended with hosts and guests both delighted. It felt like getting drunk on the atmosphere rather than the wine...

...

"Tomorrow, you don’t need to rush to submit your report to me. The summer camp should be starting tomorrow, and Xia Keke will be participating in camp activities, so take your mom around Beijing.

If you need to go far and require a car, let me know, and I’ll arrange it for you."

Returning to Yanbei University, Tian Yanzhen reminded Qiao Yu before leaving.

"Okay, Director Tian. But I’ll definitely need a car; otherwise, it’ll feel too inconvenient to go anywhere," Qiao Yu replied without reservation.

"Alright, I’ll give you a phone number later, just call it for arrangements."

"Thank you, Director Tian."

"Alright, go keep them company; they’re waiting for you."

Qiao Yu’s guess was correct; his performance today had made the mentor quite satisfied, reaching a level of satisfaction that couldn’t be surpassed.

Strutting over to the two women, even before he could speak, Qiao Xi spoke first, "I see why you could recognize one as a grandpa; you’ve inherited quite the skills in charming your grandpa."

"What do you mean by charming? Isn’t it about having a good foundation first? First, I have to study hard, right, Keke?"

"Mm-hmm, everything brother says is right!" The little girl nodded her head vigorously, appearing very well-behaved.

"Haha... Qiao Yu, see? You’ve even managed to corrupt Keke!"