Well, I can only say that I am born.

But Qiao Yu thought it was good, at least he had an extra hour in the afternoon to clear his mind.

Just like that, at two o'clock in the afternoon, Qiao Yu rushed into Tian Yanzhen's office carrying a bag containing a thick stack of manuscripts that he had reorganized at noon.

It's good. The tutor is very punctual. He came two minutes early, but the two professors were already drinking tea in the office.

"Director Tian, ​​hello, Professor Zhang, hello!"

Although he was very excited, Qiao Yu still maintained basic courtesy.

"Here, sit down. Should we continue discussing yesterday's issues or..."

Zhang Yuantang, who had already rested, decided to have some exchanges with Qiao Yu this afternoon.

Although he was very tired from talking yesterday, after taking enough rest, Zhang Yuantang felt that he was in a good state today.

This is what Tian Yanzhen is happy to see.

To put it bluntly, just as Qiao Yu thought, inviting Professor Zhang to give this lecture was just to give Qiao Yu a small start.

This was also something I had said hello to in advance.

No matter whether Qiao Yu can finally solve a series of problems with prime numbers as he and Mr. Yuan expected, at least Qiao Yu is definitely the person who is currently most promising to make achievements in this direction.

As Qiao Yu's mentor, he will naturally not be stingy about continuing to invest in this direction.

Anyway, there is a fund every year to invite professors of sufficient importance to give lectures at the Mathematics Research Center.

As for who to invite, that is a matter of opinion. Publicly concerned and cutting-edge research directions are naturally one of the choices.

Qiao Yu has this ability and hopes to solve a series of prime number problems that are of great concern to the mathematical community, so this is not even considered favoritism.

At most it's just a little biased.

"Thank you, Professor Zhang. But you inspired me a lot yesterday. After I went back last night, I did some small work based on some of the ideas you gave me.

How about you take a look at the ideas I summarized last night, and then give me some advice to see if there are any immature aspects of my idea?"

Qiao Yu said politely.

Zhang Yuantang was stunned. He thought about the last question Qiao Yu asked yesterday about constructing modal space all night.

Even after having dinner with Tian Yanzhen, he read two papers and combined his research on prime numbers over the years to give Qiao Yu some suggestions.

As a result, this kid didn't play according to the routine...

"Oh? Let me take a look first." Zhang Yuantang nodded.

Qiao Yu immediately opened the bag, took out a thick stack of manuscripts, and then cut it into two parts.

One copy was handed to Professor Zhang Yuantang, and the other was handed to Director Tian.

At this time, Lao Xue's foresight was shown.

Tell him that there should be a printer in the study, which would be much more convenient. Apparently Lao Xue was right.

Printing two copies will prevent Director Tian from getting bored when Professor Zhang reads his manuscript. Qiao Yu has always been very careful in this regard.

Zhang Yuantang took the manuscript from Qiao Yu and subconsciously read the title: "Axiomatic system of generalized modal number theory on multiple transcendental spaces?"

"Yes, it's actually the modal space that we didn't finish discussing last night. But after I got back, I felt that using modal space to describe it was not quite accurate.

Because this system is not only modal space, but also modal numbers, modal mapping, etc., these concepts can only be constructed through the interaction of these concepts."

Qiao Yu nodded and replied.

Zhang Yuantang and Tian Yanzhen looked at each other, and then they both focused on Qiao Yu's manuscript.

After briefly browsing the introduction given by Qiao Yu, the focus was on the following arguments.

Then the first sentence made Zhang Yuantang a little confused.

Good guys, let’s customize a brand new mathematical structure Multitranscendental TS(λ,Ω).

λ represents the dimension, and Ω represents the set of all possible infinite boundaries.

Zhang Yuantang frowned and subconsciously raised his head to take a look at Qiao Yu, but found that the boy had already run to the bookcase behind Tian Yanzhen's desk.

Like planning to pick up a book to read while they look at this structure?

Okay, this can probably be regarded as being easy to learn, right?

Zhang Yuantang withdrew his gaze, this time completely focusing on the framework given by Qiao Yu.

One night, trying to build an axiomatic framework? To be honest, Zhang Yuantang is not optimistic about it.

He even wondered if Qiao Yu was enjoying himself. It is true that mathematicians have sufficient freedom, but this freedom is based on a strict logical reasoning process.

A complete axiom system requires not only rigorous logic but also applicability and stability.

Rigorous logic ensures the internal consistency and credibility of mathematics; applicability is related to the practical value of the system; stability means that there will be no self-contradiction in the expansion.

Rigorous logic is a must, while applicability and stability require a good balance.

In short, building a new axiom system is definitely a very challenging task.

Coming up with such a grand title in one night, and being able to feel the complexity just by looking at its structure, was enough for Zhang Yuantang to examine Qiao Yu's ideas with the most critical eyes.

As for Tian Yanzhen...

Well, although he was mentally prepared for Qiao Yu's ability to create miracles, he still had a slight feeling that Qiao Yu was joking.

Of course only a few.

What's more, I hope that Qiao Yu really has a more mature idea, at least it won't be a joke.

But after looking inside, Tian Yanzhen realized that this kid was not bold enough to joke around with everyone.

There's something about this manuscript.

In particular, not only is the definition very clear, but it also lists many detailed examples...

Tian Yanzhen even doubted whether Qiao Yu had prepared it in advance.

As for Qiao Yu, he had found a book that interested him, pulled it out, sat on the sofa next to Zhang Yuantang and started reading silently.

The two professors couldn't just sit around while they read his manuscript, right? Playing with their mobile phones at this time seemed to show disrespect for the professors, so they could only read.

Then the office became completely quiet. Only the occasional sound of turning the pages of a book was left.

In this way, the office was quiet for a full hour. Qiao Yu became bored while flipping through books, and even took out his mobile phone to chat with Qiao Xi who was still on the high-speed train.

Zhang Yuantang finally raised his head.

Qiao Yu had finished reading the manuscript, and his mind was a little confused. He didn't know how to evaluate it for a while.

He somewhat suspected that Qiao Yu was a lunatic, but he also sensed the mathematical prospects if this axiom system could really be built, because it was so flexible!

Under the axiom system that Qiao Yu plans to construct, it can be said that any number is a set, and any operation can cover all directions and unify mathematics in a sense.

It's very abstract, but incredibly flexible! Its practical significance is even greater than the Langlands Program.

Give the simplest example: 1+1=?

Any child who has attended kindergarten can clearly answer this math question.

But if under this 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}.

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

If the modal parameters are brought in, it can also be transformed into: N_α,β(1)⊕α,βN_α,β(1)=N_α,β(2+δα,β)

Once in the periodic modal space, we can also draw the conclusion that N_α,β(1)⊕α,βN_α,β(1)=N_α,β(0).

Because this means that 1+1 will return to the modal value of "zero", forming a closed structure in the modal space.

etc……

So if we must give a general solution to 1+1 in this axiom system, it is: N(1+1)={N_α,β(1)⊕α,βN_α,β(1)∣(α,β)∈ All modal spaces}

For ordinary people to look at it, it is obvious that this is making a simple problem complicated.

But for a mathematician, especially a mathematician who studies number theory, I just feel that this is too flexible!

Different expressions directly represent different hierarchical structures and the meanings that mathematicians want to give them.

This means that in future papers, there is no need to customize a bunch of mathematical symbols with special meanings, and all mathematical structures can be integrated.

You must know that in traditional number theory research, many times in order to express a specific phenomenon or problem, the author has to customize a set of symbols or definitions for a specific structure, which not only increases the difficulty of understanding, but also is not conducive to general promotion.

There is no way, this is how traditional mathematical analysis works. There is also a nice name called custom framework.

But if Qiao Yu can really build this framework, it will mean that a highly flexible and unified mathematical language has been defined for number theory and even future algebraic geometry research.

You don’t need to redesign a set of symbols for a certain problem, you just need to choose the appropriate expression from this large framework!

It doesn't even matter whether this thing can solve the twin prime conjecture, because if this framework is really built and popularized, it will be equivalent to having something similar to a programming language for future mathematical research.

Tian Yanzhen, who was standing next to him, had obviously realized this. He looked up at Qiao Yu with a somewhat scrutinizing look, and a hint of confusion.

"Can you tell me the purpose of designing this axiom system?" Zhang Yuantang asked the first question after being silent for a long time.

"Isn't this what you said? When we study prime numbers, we start by classifying numbers. I am classifying all numbers. Don't you think this is very convenient for the subsequent study of prime numbers?
To be continued...