Chapter 422: Chapter 142: On the Generalized Modal Number Theory Axiomatic System in Multiple Transcendental Spaces_4
Qiao Yu nodded and said, "Yes, Professor Zhang, I’ve always been interested in the distribution of prime numbers."
"Oh?"
Zhang Yuantang smiled and asked, "You’re interested in the distribution of prime numbers, so why were you so focused on the Geometric Langlands Conjecture before? I’ve also read your papers and always thought you might be more interested in algebraic geometry."
Without hesitation, Qiao Yu responded, "Because I studied your papers and then realized that with the current tools, whether it’s sieve methods or autonomous forms, we can’t completely prove the Twin Prime Conjecture or the Riemann Conjecture.
I think the Langlands Program might be a breakthrough for solving this problem. By starting from the properties of symmetry and invariants, I try to construct a new algebraic geometry framework and even use geometric language to express the characteristics of prime numbers.
So if you look at my previous research, it’s actually laying the groundwork to ultimately solve issues related to prime numbers. As for helping Professor Dennis’s team complete the proof of the Geometric Langlands Conjecture, that was an accident."
"An accident?" Zhang Yuantang paused, then shook his head and nodded.
He then looked at Tian Yanzhen, who was sipping tea, realizing what it means to be "fearless like a rookie calf."
Involuntarily, he asked, "Do you know what a new framework represents?"
Qiao Yu nodded and replied, "I know, for example, it means I have to construct an entirely new axiomatic system from scratch. I also need this system to at least be recognized by the mainstream mathematical community."
These days of learning made Qiao Yu more confident when discussing these topics with Zhang Yuantang.
Zhang Yuantang glanced at Tian Yanzhen, who was silently sipping tea, smiled, and continued to ask, "So are you planning to do this work alone—construct an entirely new axiomatic system, then prove the Twin Prime Conjecture?"
Noticing Zhang Yuantang’s smile, Qiao Yu also smiled and replied, "Why not, Professor Zhang? Well, maybe not entirely alone. If needed, I might invite my mom to join my team."
"Your mom?" Zhang Yuantang was taken aback, probably somewhat puzzled about where Qiao Yu’s confidence came from.
In fact, if he hadn’t been involved in Twin Prime research all this time, he might not have had such doubts.
"Qiao Yu’s mother, Qiao Xi, is currently a student of Mr. Yuan Zhengxin," Tian Yanzhen explained.
Then Tian Yanzhen glanced at Qiao Yu.
If he hadn’t explained, Zhang Yuantang might think Qiao Yu was just messing around.
"Oh?" Zhang Yuantang glanced at Tian Yanzhen, a bit confused. He had heard of Qiao Yu, but Qiao Xi...
Wait, Zhang Yuantang suddenly remembered a paper recently published by Qiao Yu in Ann.Math. It seemed there was a second author by that name.
A mother-son collaboration on a paper?
"Well... if it’s a new axiomatic system..."
After a long silence, Zhang Yuantang shook his head and said seriously, "Since you have this idea, you must have researched it, and this will be a huge project. Moreover, if you actually accomplish this, I even feel that compared to your new system, the Twin Prime Conjecture becomes less important."
Qiao Yu nodded earnestly and said matter-of-factly, "Yes, solving the Twin Prime Conjecture is just the beginning. Because everyone says I have the potential to solve the Riemann Conjecture.
So if I can build such an axiomatic system, I surely hope it can help me prove that all non-trivial zeros of the ζ function are on the critical line in the complex plane."
Zhang Yuantang glanced at Tian Yanzhen, who was also seriously watching him. At that moment, he seemed to sense the ambition hidden in the room, and couldn’t help but laugh.
"Godel once said that before proving the Riemann Conjecture, a new cornerstone for mathematics needs to be found. I always thought Grothendieck was the closest to resolving this cornerstone. If he hadn’t gone astray back then.
Well, Qiao Yu, I also think highly of your ability and admire your courage. But I hope you can maintain a more balanced mindset. The Riemann Conjecture has led many mathematicians researching it into a state of obsession.
I hope this won’t happen to you. Of course, I can also share some of my research insights with you, though I don’t know if they’ll be useful to you."
Qiao Yu said seriously, "Don’t worry, Professor Zhang. I understand everything you’ve said. And to be honest, I’m very interested in your research insights.
Because honestly, I’ve been thinking of many approaches lately. However, I haven’t figured out a specific entry point yet."
Zhang Yuantang nodded, noticing Qiao Yu’s seriousness, he decided to open up.
"If you want to hear my advice, it’s that when you can’t find an entry point, maybe it’s better to set aside the question of prime numbers for a while. Don’t focus on primes, but instead study the structure of numbers themselves.
For example, the distribution patterns and interrelationships of integers within a larger structure. After all, your focus is on an axiomatic system, which means you need to find a relatively universal structural principle, not just limit yourself to the specific properties of primes.
Primes are just one phenomenon within the numerical structure, and you first need to understand more general number behavior, distribution patterns, and their interrelationships within different structures.
Once you’ve done this, when you return to the problem of primes, maybe you can find a natural path within this axiomatic framework to explain their distribution and properties..."