CHAPTER 425: CHAPTER 143: IF YOU CAN COMPLETE IT, YOUR CONTRIBUTION WILL BE GREATER THAN NEWTON’S!

Online, a celebrity popularized a line.

"You simply don’t understand dad’s happiness."

The essence of the meaning is just a playful version of the Emperor using a golden hoe, expressed in a more humorous way.

It’s hard for the poor to understand the happiness of the rich, just as it’s hard for ordinary people to grasp the joy of high-IQ individuals.

Yet, from time to time, the world produces several extraordinarily talented individuals, repeatedly shaming the intelligence of regular geniuses.

It’s like in those technologically backward times, people couldn’t fathom how Einstein figured out the constancy of the speed of light and his conclusions on the relativity of time and space.

After all, the core idea of this great physicist’s special relativity directly challenged Newtonian classical mechanics’ intuitive understanding and common sense.

How could time, which is eternally unchanging, possibly expand?

And how could the speed of light remain constant? It even led to the introduction of the mass-energy equivalence!

The most baffling part is that mass could actually convert to energy?

It’s important to note that in classical physics at the time, mass and energy were considered completely different physical quantities, each conserved in their own right. This was common knowledge!

However, a series of subsequent experiments gradually verified Einstein’s views.

Especially when human scientists discovered nuclear fission and fusion, research on the atomic nucleus revealed that Einstein really understood this!

After a boy and a fatty demonstrated immense power, the mass-energy equivalence became an undisputed fundamental formula in physics.

In some sense, Qiao Yu wanted to do something similar. But mathematics, unlike physics, allowed Qiao Yu’s ideas to be freer.

To save time when consulting Professor Zhang tomorrow, Qiao Yu fell into a state of excited creativity.

He needed to give Professor Zhang some examples.

For instance, the number 1.

This basic number, in the system Qiao Yu designed, the modal number of 1 would no longer be a fixed value, but would display different modal characteristics as the modal space (α,β) changes.

It is denoted as N_α,β(1). Moreover, within this fixed axiomatic system, it possesses some unique properties.

For example, the self-consistency of the modal unit number.

Expressed with a formula as:

This means that despite changes in the modal space, the modal unit number always behaves as a unit element in any mode.

In other words, no matter how the mode changes, the modal unit number consistently retains the conceptual nature of 1, albeit existing in different forms.

Additionally, due to the changes in mode, different modal spaces need to show different modal dependencies.

For example, in the complex number field:

This essentially introduces the concept of the self-consistent representation space in the Langlands Program. Or rather, structures the corresponding self-consistent representation space.

Similarly, if one continues to manipulate the number 1, the concept of modal convolution can also be applied. In Qiao Yu’s construction, modal convolution Gm is an extremely important operation.

The modal unit number serves as the neutral element of the modal convolution, for any modal number N_α,β(n):

Additionally, for future operations, the modal unit number must also possess self-referentiality.

A simple 1, within this framework, can be a complex phase modal unit number, an exponential recursive unit number, or a unit number of a multidimensional representation.

With these definitions, some concepts in classical number theory can be transformed.

For example, in classical number theory, the formula for an arithmetic sequence is expressed as: a_n = a_1 + (n−1)d.

When this formula is extended into the modal space, allowing the common difference and terms of the sequence to depend on changes in the modal parameters (α,β), the modal arithmetic sequence would be denoted as:

The purpose of doing this is actually quite simple.

Since current tools fail to solve a series of problems with prime numbers, simply elevate the problems of number theory to the dimension of modal space.

This allows Qiao Yu to utilize a series of tools he defines within this axiomatic system to resolve those unsolved problems in number theory.

Qiao Yu thinks he can call this the modal Langlands Program.

Honestly, this feeling of creation is quite exhilarating. It’s like actually constructing a new digital universe, even directly immersing Qiao Yu in it.

Of course, while this feeling is thrilling, much work is still needed to establish a corresponding connection between these tools, operations, and classical number theory.

But for now, Qiao Yu doesn’t need to think about all that. He only needs to construct this multilayer structure incorporating different modal spaces.

Then, tomorrow, he will discuss with Professor Zhang, who suggested this idea, further refinement which will be an immense undertaking.

By the time Qiao Yu feels sleepy, it is already three in the morning.

Usually, Qiao Yu lives quite regularly, going to bed at eleven.

He can even refrain from glancing at his phone before sleeping.

Only during these rare moments of vibrant mathematical passion, because of heightened focus, does he forget about tiredness and accidentally stays up till dawn.

But it doesn’t matter. When he finally feels sleepy, it truly means he can’t hold on for another second.

At that moment, even washing up becomes a luxurious task.

He simply stands up, wobbling into his bedroom, collapses on the bed, and falls asleep within thirty seconds, emitting a slight snore.