Chapter 340

In Mochii Shinichi’s interuniverse Teichmüller theory, there is a word that is often mentioned.

That is - recovery!

In this new mathematical system constructed by Mochii Shinichi, he separated the addition structure and multiplication structure that were attached to the numbers at the same time, deformed them separately, and then restored them again.

In other words, in Mochii Shinichi's system, addition no longer represents addition, and multiplication is also not represented by the multiplication symbol.

This approach of first eliminating the fundamentals and then restoring it is quite strange even for mathematicians who have experienced abstract reasoning for a long time.

Mochii Shinichi’s system is precisely based on the feasibility of this kind of recovery.

If his system is correct and if his restoration is successful, it will bring about changes in the algebraic geometry branch of mathematics.

For example, the proof of the abc conjecture. For example, finally understanding the relationship between addition and multiplication.

Shinichi Mochii's status in the world of mathematics will jump to the same level as Wiles, who proved Fermat's Great Conjecture, and Perelman, who proved the Poincaré Conjecture.

but……

But now, not many mathematicians can understand his proof!

A brand-new theoretical system is not recognized by the mainstream mathematics community. As the founder of this system, Mochii Shinichi is certainly not enough to spread it through the ages.

As I get older, there are more and more doubts about the Teichmüller theory of the universe from the outside world.

Wangjing Shinichi finally couldn't stand it any longer.

With a strong sense of urgency, Mochii Shinichi gave up the idea of ​​being self-conscious and agreed to the invitation of the Clay Mathematics Institute to go out and hold this study class.

The purpose is simple...

The purpose is to allow more people to understand his theory and gradually be recognized by the mainstream mathematics community.

Strong blind optimism, coupled with confidence in his own strength, made Mochii Shinichi not feel that there were any loopholes in his theory.

The reason why it is not recognized by the mainstream mathematics community is that there are not many mathematicians who are proficient in this field.

…………

Inside the classroom.

The study class continues.

Wangjing Shinichi started from the most basic structure, p-advanced integers, and explained it from the beginning.

What is a p-adic integer?

The quickest and easiest definition for mathematicians is:

For prime p, the projection limit of (z/p^nz)n≥1.

This is indeed an easy-to-understand definition for mathematicians, but to ordinary people it is like an alien language.

However, p-adic integers are not that complicated after all.

Give the simplest chestnut~~

When p=7, the following numbers are all p-adic integers:

……00000000000000000042

……30211045064302335342

……12450124501245012450

(That’s right, the ellipsis is in front)

Each p-adic integer can be viewed as a string of numbers extending to infinity from the upper left to the left.

But they are not infinite, each of their numbers is different, and this way of writing is meaningful.

Next, here comes the key point!

On p-adic integers, addition and multiplication can be defined.

And the calculation method is the same as we are familiar with, starting from the low bit, and then slowly carrying through the calculation, like endless addition and multiplication.

Subtraction and division are also defined by this.

p-adic integers have the same four arithmetic operations as the integers we are familiar with.

Up to this point, Mochii Shinichi’s theory is still within the framework of the conventional mathematical system.

But next.

Mochii Shinichi made further extensions to p-adic integers.

Mochii Shinichi introduced the concept of ‘absolute value’.

According to this absolute value, we can regard all p-adic integers as a space, whose structure is given by this absolute value, which is the distance between two points.

But this is a weird space. Every triangle is an acute isosceles triangle, and if we take a sphere, every point in the sphere is the center of the sphere.

Because Mochii Shinichi found that the theory constructed from p-adic integers was still not enough to capture the number theory structure he wanted to study.

So use the concept of absolute value.

Wangjing Shinichi transformed p-adic integers into more universal p-adic numbers.

To construct the Teichmüller theory of the universe, it is necessary to use the tools of far-Abelian geometry and representation theory at the same time.

However, the two are incompatible and difficult to reconcile.

In order to make a compromise, Mochii Shinichi needed to split the basis of the theory, that is, the most basic operations, into addition and multiplication, and break them into more complex and abstract structures.

Then through the interaction and deformation of these structures, the desired properties are obtained, and finally it is proved that these structures can be restored to some kind of addition and multiplication.

Of course, as mentioned before, addition and multiplication in Mochii Shinichi's theory are completely different. They are not based on the same set of numbers like ordinary addition and multiplication, but they are completely different.

This is also the reason why it is so difficult for many mathematicians to understand Shinichi Kizuki's theory.

…………

Shinichi Mochii's interuniverse Teichmüller theory was developed based on p-adic numbers.

However, the status of p-adic numbers themselves in this theory is equivalent to the natural numbers in college entrance examination mathematics, which are only the most basic building blocks.

The discussion of p-adic numbers only occupies less than two pages of the 512-page paper.

However, just a basic theory such as p-adic numbers is enough to dissuade 90% of the mathematicians who come to read the paper.

As for those who had the patience to read the entire 512-page paper by Mochii Shinichi, there were even fewer of them.

Mochii Shinichi stood on the podium, spitting about how he had a flash of inspiration and regarded p-adic numbers as the cornerstone of his new theory.

And below the podium.

Gu Lu lowered his head and read Wangjing Shinichi's paper while his brain automatically filtered out the useless information in Wangjing Shinichi's words.

This was not the first time Gu Lu had read this paper.

Gu Lu first saw this paper when he was studying for his PhD at Princeton a few years ago.

At that time, Gu Lu bit the bullet and read more than a hundred pages, but he couldn't finish it and gave up helplessly.

For Gu Lu at that time, Mochizuki Shinichi's paper was still too abstract and empty.

It is obviously an article in the field of algebraic geometry.

What Gu Lu saw was the entire text and formulas, not even a geometric diagram.

It's simply anti-human!

At that time, Gu Lu's reasoning ability and spatial force attribute values ​​were very low, and he certainly could not cope with such a difficult paper.

But it's different now.

Gu Lu's current values ​​are at least twice as high as those at that time.

Facing this paper by Mochii Shinichi cannot be said to be easy.

But there is still no big problem in reading it.

Moreover, Gu Lu can now solve all the doubts that Gu Lu had when he read Wangjing Shinichi's paper a few years ago.

It was very foggy before.

Now Gu Lu saw a smooth road.

While Gu Lu was listening to Wangjing Shinichi's lecture, he re-read Wangjing Shinichi's paper.

In terms of theoretical construction, Gu Lu could not find any loopholes in this paper.

But……
Chapter completed!