Chapter 450: Chapter 148 This Isn’t Paranoia, It’s Confidence_2
Zhang Yuantang’s words immediately made the expressions of the three become much more serious.
Whether it’s integrating the existing tools for research in Number Theory or completely combining Number Theory with Geometry, both can be considered major breakthroughs in Mathematics.
Especially the latter.
Undoubtedly, if Qiao Yuzhen succeeds, it would be a Fields Medal-level achievement.
Naturally, it also piqued the interest of the three big figures. Research in prime numbers has always been a problem in Number Theory, and if the theory proposed by Qiao is indeed useful, it means their research will gain a completely new set of theoretical tools.
Especially if geometric methods can be seamlessly used to solve number theory problems, as it’s already an important direction and key area in the development of modern mathematics.
After all, Geometry provides many highly abstract and powerful tools for Number Theory.
"Well... can you tell us about this theory?" James Maynard asked cautiously.
After all, in the entire academic field, learning about someone else’s unpublished research is somewhat frowned upon.
However, if it’s just a general direction and doesn’t involve the details of the proof, it’s not an issue.
So Zhang Yuantang nodded quite naturally.
He didn’t participate in Qiao Yu’s subsequent work, and he didn’t know the details.
"Qiao Yu proposed a generalized modal axiomatic system in Number Theory. Specifically, every natural number can be mapped into a modal space. This process is called modal mapping.
He defined the structure corresponding to conventional numbers, which includes sets of basic numbers, integers, fractions, and real numbers. It possesses the dependencies and self-referential nature of modal numbers. Let me give you an example using an arithmetic sequence..."
With that, Zhang Yuantang spent over twenty minutes to explain a rough outline of Qiao Yu’s idea.
A very general framework.
After listening, the three professors simultaneously furrowed their brows, deep in thought.
There’s no way around it; it’s just a rough outline, and it’s quite difficult to understand the content through a simple explanation.
But everyone understood the significance within it.
"Wait a moment, I can understand this modal mapping. But since Qiao Yu’s ambition is so grand, this framework is surely a multidimensional modal framework, which leads to a problem.
Many modal mappings would be nonlinear and irreversible, which means that classical number theory methods cannot be directly applied within the framework. How is this problem solved?"
Tao Xuanzhi pondered for a moment and then posed his question.
Zhang Yuantang shrugged and replied, "I don’t really understand the details of how he dealt with it, and it’s not appropriate for me to ask in detail. However, Qiao Yu should have a solution.
I remember him simply explaining that he built a supermodal operator matrix, which is different from traditional matrices where the elements are not just arrays or linear operators.
Instead, it’s a modal operator composed of multiple mappings and self-referential relationships. Thus, each operator matrix has dual dimensions, ordinary dimensions, and modal dimensions.
Where the modal dimension can represent the matrix’s mapping in different modal spaces, even if this mapping is nonlinear and irreversible."
Zhang Yuantang’s answer wasn’t very detailed; he knew Qiao Yu constructed such a matrix, but he indeed didn’t know anything more specific.
On that day, Qiao Yu presented his idea, and after a simple discussion, he left Huaxia the next day and returned to the Western Hemisphere.
It’s not that he didn’t want to stay a few more days, but Yanbei University didn’t request him to stay longer, so naturally, he was too embarrassed to continue staying there.
Actually, Tian Yanzhen had talked to him once, suggesting that he could teach at Yanbei University or take a position at the Yanbei International Mathematics Research Center, but Zhang Yuantang had not made up his mind.
"This idea... is very bold and indeed seems effective. The holistic integration of number theory and geometry... it could even be more than just number theory and geometry, of course, if he really succeeds."
After careful consideration for a while, James Maynard spoke up.
The emotions were complex, just as mentioned before; if Qiao Yu were to succeed, it would undoubtedly be another Fields Medal achievement.
These gifted individuals always manage to be so unreasonable like this.
"No wonder Peter Schultz and Qiao Yu get along so well; they’re walking the same path." Tao Xuanzhi remarked.
The sentiment was quite fitting.
Undoubtedly, both Tao Xuanzhi and Peter Schultz are brilliant figures of the young generation. However, the reasons why they were recognized by the Fields Medal are completely different.
Peter Schultz relied on establishing an entirely new system, while Tao Xuanzhi solved an important mathematical problem. They walked different paths, and now it seems that Qiao Yu also intends to walk Peter Schultz’s path.
"Actually, not necessarily. As far as I know, Qiao Yu designed this framework to be able to prove the Twin Prime Conjecture. Perhaps after this framework is constructed, he will take on the challenge of the Twin Prime Conjecture.
In other words, he might build a programmatic system that can guide mathematics while solving a series of number theory problems; perhaps he could combine both of your paths.
And that’s quite possible. After all, he has already made significant contributions to the proof of the Geometric Langlands Conjecture. Really, I’ve considered facing challenges, but I didn’t expect the challenger to be so young."
Zhang Yuantang expressed a different opinion.
He had spoken with Qiao Yu face-to-face and felt more acutely the pressure when discussing academic issues with Qiao Yu. Initially, he could quickly come up with answers to some superficial questions.