Chapter 428: Chapter 143 If You Can Accomplish It, Your Contribution Will Be Greater Than Newton!_4

This math problem can easily be answered by any child who has attended kindergarten.

However, within the axiom system designed by Qiao Yu, because N(1) = {N_α,β(1) ∣ (α,β) ∈ all modal spaces}, N(2) = {N_α,β(2) ∣ (α,β) ∈ all modal spaces}.

Therefore, the equation becomes: N_α,β(1) ⊕ α,β N_α,β(1) = N_α,β(2)

If modal parameters are substituted, it can further transform into: N_α,β(1) ⊕ α,β N_α,β(1) = N_α,β(2 + δα,β)

Once in a periodic modal space, a conclusion can be drawn that N_α,β(1) ⊕ α,β N_α,β(1) = N_α,β(0).

Because this means that 1+1 returns to a modal value of “zero,” forming a closed structure in the modal space.

Wait a moment…

So if one must provide a general solution for 1+1 within this axiom system, it is: N(1+1) = {N_α,β(1) ⊕ α,β N_α,β(1) ∣ (α,β) ∈ all modal spaces}

To the average person, this seems like complicating a simple problem.

But for a mathematician, especially one studying number theory, it feels incredibly flexible!

Different expressions directly represent different hierarchical structures and the meanings mathematicians wish to assign them.

This means that in future papers, there’s no need to define a host of mathematical symbols with special meanings, unifying all mathematical constructions.

In traditional number theory research, authors often have to create a set of symbols or definitions for specific structures to describe a phenomenon or problem, which increases understanding difficulty and hinders broad dissemination.

That’s how traditional mathematical analysis operates. It even has the fancy name of custom frameworks.

But if Qiao Yuzhen can create this framework, it would define a highly flexible and unified mathematical language for number theory and even future algebraic geometry research.

No need to redesign a set of symbols for a particular problem; just select the appropriate expression from this comprehensive framework!

Whether it solves the Twin Prime Conjecture isn’t even relevant anymore, because if this framework is successfully created and popularized, it would provide future mathematical research with something akin to a programming language.

Clearly, Tian Yanzhen has also realized this and looks at Qiao Yu with an inspecting gaze and a hint of confusion.

“Could you tell me the purpose of designing this axiom system?” Zhang Yuantang, after a moment of silence, asked his first question.

“Wasn’t it you who said we should start from classifying numbers for prime number research? I am categorizing all numbers, don’t you think it would facilitate subsequent research on prime numbers?

The ultimate aim is, of course, prime number research. Though it may seem complex now, I’ve considered it thoroughly; under this framework, analyzing symmetry and invariance would be much more convenient.

Especially considering if I can develop this system, the Twin Prime Conjecture becomes the modal distance relationship between prime pairs in different modal spaces.

Can’t we then build a bridge between number theory and geometry? This way, when conducting conjecture research, those geometric tools can also be included.

Using geometric tools to analyze number theory problems, symmetry, invariance, periodicity, curvature…

Imagine, geometric, topological, differential geometric tools can be used directly for number theory analysis, broadening the perspective for analyzing number theory problems all at once?”

Qiao Yu said enthusiastically and somewhat proudly.

Indeed, Qiao Yu also had personal motives for designing this axiom system.

Qiao Xi will be focusing on geometry under her grandmaster’s guidance in the future. He’s already decided to pursue research in number theory. So how can both work together?

Of course, a unified framework is needed.

By breaking down a complex number theory problem into multiple geometric problems for analysis, he could justifiably incorporate his mother into his research team.

This way, if they achieve results, no one could criticize it. After all, his framework allows for solving number theory problems using geometric methods.

Just thinking about it, it’s quite exciting. Qiao Xi would be the most supportive assistant in his future number theory research.

Clearly, for Qiao Yu, climbing the peak with another person is more interesting than climbing alone. Not to mention, it would be more fulfilling.

However, after saying all this, Qiao Yu was somewhat puzzled by Tian Yanzhen and Zhang Yuantang’s exchange of glances.

He couldn’t help but ask suspiciously: “Uh, am I wrong, or is there something wrong with the design of my system that makes you skeptical?”

Zhang Yuantang took a deep breath and said: “Based on the simple definitions and few examples you’ve given so far, there’s nothing apparent at the moment, but…”

Qiao Yu hastily interrupted: “Sorry, Professor Zhang, let me interrupt for a moment. Indeed, the examples I showed are somewhat simple due to time constraints; I haven’t had the chance to incorporate more elements.

But I actually have many ideas. And I’ve considered that this framework can fully encompass group theory, graph theory, and other theories.

For instance, if we define a modal group, it can also include all possible modal mappings, with group operations defined as compositions of mappings.