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Chapter 145 If you can complete it, your contribution will be greater than Newton!
On the Internet, a crosstalk star made a line popular.

"You don't understand dad's happiness at all."

In fact, the essence of the meaning is a replica of the emperor using a golden hoe to hoe the ground, but it is expressed in more sarcastic language.

It is difficult for poor people to understand the happiness of rich people, just as it is difficult for ordinary people to understand the happiness of highly intelligent people.

But from time to time, this world will produce some extremely talented people who will humiliate the IQ of ordinary geniuses over and over again.

It was as if in that era when technology was still very backward, people racked their brains to figure out how Einstein came to the conclusion that the speed of light was constant, and his conclusion about the relativity of time and space.

After all, the core idea of ​​the special theory of relativity of this physics giant directly challenged Newton's intuitive understanding and empirical common sense of classical mechanics.

How can time expand if it is eternal and unchanging?

How can the speed of light be constant? It is even introduced into the mass-energy equation?

What is most speechless is that mass can be converted into energy?

You have to know that in classical physics at that time, mass and energy were regarded as completely different physical quantities. They were conserved and could not be converted into each other. This is common sense!

But the fact is that a series of experiments later gradually proved Einstein's point of view.

Especially after human scientists discovered nuclear fission and nuclear fusion, research on atomic nuclei found that Einstein knew so much!

When a boy and a fat man demonstrated their enormous power, the mass-energy equation became an unquestionable basic formula in physics.

In a sense, Qiao Yu also wanted to do something like this. But mathematics is different from physics, and Qiao Yu's ideas are freer.

In order to save time when asking Professor Zhang for advice tomorrow, Qiao Yu fell into an excited creative state.

He needs to give Professor Zhang some examples.

For example, the number 1.

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

It is denoted as N_α,β(1). And because it has some unique properties under this fixed axiom system.

For example, the automorphism of the modal unit number.

Expressed as a formula:
This means that even though the modal space is changing, the modal unit number always appears as the unit element in any mode.

That is to say, no matter how the modality changes, the modal unit number always has the concept of 1, but may exist in different forms.

At the same time, due to the change of mode, different modal dependencies need to be shown in different modal spaces.

For example, in the complex domain:
In essence, the concept of the automorphic representation space of the Langlands program has been introduced here, or in other words, the automorphic representation space has been structured accordingly.

Similarly, if we want to continue to operate on the number 1, we can also use the concept of modal convolution. In Qiao Yu's construction, modal convolution Gm is an extremely important operation.

The modal unit number appears as a neutral element of the modal convolution in the convolution. For any modal number N_α, β(n):
In addition, for better operation later, the modal unit number must be self-referential.

A simple 1, in this framework, can be a complex phase modal unit number, an exponential recursive unit number, or a unit number represented in multiple dimensions.

With these definitions, we can transform some concepts in classical number theory.

For example, in classical number theory, the formula for an arithmetic sequence is: a_n=a_1+(n1)d.

When this formula is extended to the modal space, so that the tolerance and term values ​​of the sequence can depend on the changes of the modal parameters (α, β), the modal arithmetic sequence should be recorded as:

The purpose of doing this is actually very simple.

Since existing tools cannot solve a series of problems related to prime numbers, we can simply elevate number theory problems to the dimension of modal space.

This allowed Qiao Yu to use a series of tools he defined under this axiomatic system to solve those outstanding number theory problems.

Qiao Yu thinks this can be called the modalized Langlands program.

To be honest, this feeling of creation is very refreshing. It is like really building a brand new digital universe, and it even makes Qiao Yu addicted to it.

Of course, although this feels great, there is still a lot of work to be done to establish corresponding connections between these tools and operations and classical number theory.

But Qiao Yu didn't need to think so much for now. He just needed to construct this multi-level structure containing different modal spaces.

Then tomorrow he will discuss this with Professor Zhang who made this suggestion to him. The specific improvement will be a huge project.

By the time Qiao Yu felt sleepy, it was already three o'clock in the morning.

Generally speaking, Qiao Yu actually lives a very regular life and goes to bed at 11 o'clock.

He can even go to bed without even glancing at his phone.

There were only a few moments like this when I was so passionate about mathematics that I forgot about sleepiness because of my high concentration and stayed up until the early morning.

But it didn't matter, because when he felt sleepy, he really couldn't hold on for another second.

As for washing and brushing one's teeth, these things have become a luxury at this time.

He stood up and staggered into the bedroom, then lay down on the bed. In less than thirty seconds he was snoring softly.

This way you can often sleep very soundly.

……

For a child who decided to shoulder the burden of supporting his family in fifth grade, Qiao Yu was very clear about one thing: this is a world full of competition.

There is no such thing as a free lunch. If you want something, you have to fight for it.

To achieve this you need to do the right thing at the right time according to your goals.

For example, if he wants to become a star-level professional game player, he has to spend a lot of time practicing the game every day, trying to figure out the advantages and disadvantages of each skill of each game character, constantly honing his skills, mastering various tactics, and building tacit understanding with his teammates...

But now if he wants to become a mathematician, he must devote time and energy to study and research, and obtain results that people can recognize.

In Qiao Yu's opinion, this is fair. Just like what he once said to Zhou Shuang, if there is no reward for hard work, then you should withdraw in time.

If one can get fairly satisfactory rewards for his efforts and can get along well with the people around him, then it is enough to show that he is not only suitable for this job, but also can achieve a win-win situation with those who cooperate in doing this job.

There is no doubt that Qiao Yu now feels that he is indeed suitable to be a future mathematician. The path chosen by the good man for him is quite good and suitable for him.

Then he must seize the opportunity to make some achievements, meet everyone's expectations and achieve himself.

So even if he went to bed at three in the morning, Qiao Yu would still get out of bed at seven-thirty the next day in high spirits to continue his research.

Even though Professor Zhang Yuantang’s lecture today doesn’t start until 10 o’clock.

But if he did do more preparation in the early stages, it would mean that the question-and-answer session that Director Tian helped him get would be more efficient.

In other words, he can squeeze more out of the teachers he hired to teach him experience and knowledge.

This is nothing to feel guilty about.

After all, being able to invite a professor to give such an academic lecture is not something that can be achieved simply by relying on face; it still requires money.

Qiao Yu felt that he was simply trying to make Director Tian spend his money more cost-effectively.

……

The two-hour lecture was packed, but Qiao Yu felt that he did not gain much from it.

Because the content presented in public lectures is actually similar to the ideas expressed in the paper.

Qiao Yu could also understand this.

After all, professors also have to save their reputation. In public, they would be hesitant to discuss content that is too radical or unsure.

For example, many people like to use the word "obviously" in mathematical proofs. Even some professors often use this word on the blackboard when teaching.

So much so that these two words are often taken for granted.

It's okay in private, but if a big shot uses these two words during a lecture, and someone obviously raises doubts about this when asking questions, two situations may arise.

The first is that the big guys just give a few lines of explanation and proof. That is really obvious, which makes the person asking the question look like a fool.

The second type is that the big guy picks up his pen to prove why it is obvious, but finds that it is not so obvious and he cannot prove it for a while, which makes the person giving the lecture on the stage look like a fool.

This situation is not only embarrassing at the time, but also shameful if it gets out.

Therefore, when giving a lecture, the big guys will definitely avoid saying things that have not been carefully thought out or that they are not necessarily sure of.

Even if there are, they will be placed in the final outlook section.

But it is different when discussing privately, as it will not hurt the professors’ reputation, and they will be bolder. Some new ideas can be discussed without any scruples.

So compared to the public lecture, Qiao Yu was more looking forward to the private exchanges in the afternoon.

This is what Tian Yanzhen promised him yesterday.

However, what surprised Qiao Yu was that after the morning lecture, Director Tian did not invite him to have lunch together.

I just told him to go to his office at 2pm sharp and Professor Zhang would be there.

Well, I can only say that we are strangers.

But Qiao Yu thought it was not bad. At least he had at least one more hour in the afternoon to sort out his thoughts.

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 was pretty good. The tutor was very punctual. He arrived two minutes early, but the two professors were already drinking tea in the office.

"Director Tian, ​​ok. Professor Zhang, ok!"

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

"Come on, take a seat. Should we continue discussing yesterday's issue or..."

Zhang Yuantang, who had already had a good rest, decided to have a good communication with Qiao Yu this afternoon.

Although he was very tired from chatting yesterday, after getting enough rest, Zhang Yuantang felt that he was in a very good condition today.

This is also what Tian Yanzhen is happy to see.

To put it bluntly, just as Qiao Yu thought, inviting Professor Zhang to give this lecture was to give Qiao Yu special training.

This was also informed in advance.

Regardless of whether Qiao Yu can eventually solve a series of problems about prime numbers as he and Mr. Yuan hoped, at least Qiao Yu is definitely the person who has the greatest hope of making achievements in this direction.

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

Anyway, there is a sum of money every year to invite professors of sufficient importance to give lectures at the Center for Mathematical Research.

As for who to invite, that is a matter of opinion. Research directions that are of public interest and cutting-edge are also a natural choice.

Qiao Yu has the ability and has the hope of solving a series of prime number problems that are of great concern to the mathematical community, so this cannot even be considered as favoritism.

At most, it's just a little bit biased.

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

How about you take a look at the ideas I summarized last night and give me some advice to see if there is anything immature about my ideas?"

Qiao Yu said politely.

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

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

As a result, this guy didn't play by the rules...

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

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

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

This is when Lao Xue’s foresight was revealed.

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

Printing two copies will prevent Director Tian from feeling 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 out the title: "Axiom system of generalized modal number theory on multiple transcendental spaces?"

“Yes, actually it’s the modal space that we didn’t finish discussing last night. But after going back, I felt that using modal space to describe it is not quite accurate.

Because this system is not only about modal space, but also about modal numbers and modal mappings, etc. These concepts interact with each other to build this system. "

Qiao Yu nodded and replied.

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

After briefly browsing the introduction given by Qiao Yu, the focus was placed on the subsequent argument.

The first sentence that followed made Zhang Yuantang a little confused.

Wow, right from the start, we customized a completely new mathematical structure, Multitranscendental Spaces, or MTS (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 they were planning on picking up a book to read while they were looking at this structure?

Well, this can probably be considered as being studious, right?
Zhang Yuantang withdrew his gaze and this time focused completely on the framework given by Qiao Yu.

Trying to build an axiomatic framework in one night? To be honest, Zhang Yuantang was not optimistic.

He even suspected that Qiao Yu was just being self-indulgent. It is true that mathematicians have sufficient freedom, but this freedom is based on a strict logical reasoning process.

A complete axiomatic system requires not only logical rigor 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; and stability means that there will be no contradictions during expansion.

Logical rigor is a must, but a balance needs to be struck between applicability and stability.

In short, building a brand new axiomatic system is definitely an extremely challenging task.

Coming up with such a grand title in one night and feeling its complexity just by looking at its structure were enough to make Zhang Yuantang 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 also felt a little bit that Qiao Yu was kidding.

Of course only a little.

I still hope that Qiao Yu really has more mature ideas, or at least not a joke.

But after watching it carefully, Tian Yanzhen realized that this kid was not brave enough to joke 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 suspected whether Qiao Yu had prepared in advance.

As for Qiao Yu, he had already found a book that interested him, so he took it out, sat on the sofa next to Zhang Yuantang, and began to read silently.

He couldn't just sit there while the two professors were reading his manuscript, could he? Playing with his phone at this time seemed disrespectful to the professors, so he could only read.

The office fell completely silent, except for the occasional sound of turning pages. In this way, the office remained silent for a full hour. Qiao Yu got bored of flipping through the book, so he took out his phone and chatted 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, so he didn't know how to evaluate it for a moment.

He was a little suspicious that Qiao Yu was a lunatic, but he also realized the mathematical prospects if this axiomatic system could really be built, because it was so flexible!
Under the axiomatic system that Qiao Yu intends 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.

Very abstract, but incredibly flexible! Its practical significance is even greater than that of the Langlands Program.

Let’s take the simplest example: 1+1=?
Any child who has attended kindergarten can clearly give the answer to this math problem.

But if under 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}.

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 conclude 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.

and many more……

So if we must give 1+1 a general solution in this axiom system, it is: N(1+1)={N_α, β(1)⊕α, βN_α, β(1)∣(α, β)∈all modal spaces}
To ordinary people, it is obvious that this is complicating a simple issue.

But for a mathematician, especially a mathematician who studies number theory, this just feels 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 will be no need to customize a bunch of mathematical symbols and give them special meanings, and all mathematical structures will be integrated.

It should be noted that in traditional number theory research, in order to express a specific phenomenon or problem, the author often 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 universal promotion.

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

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

You don't need to redesign a set of symbols for a specific problem, just choose the appropriate expression from this big framework!

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

Apparently Tian Yanzhen next to him had also realized this. He looked up at Qiao Yu with a scrutinizing and a hint of confusion.

"Can you tell me the purpose of designing this axiomatic system?" Zhang Yuantang asked the first question after a long silence.

"Isn't that what you said? When we study prime numbers, we should start by classifying them. I am classifying all the numbers. Don't you think this will make it easier for us to study prime numbers?
So the ultimate goal is of course to study prime numbers. Well, don't think this is a bit complicated, but I have thought about it. Under this framework, both symmetry invariance analysis can be much more convenient.

In particular, think about it, if I can create this system, then the twin prime conjecture will become the modal distance relationship between prime number pairs in different modal spaces, right?
Can't we build a bridge between number theory and geometry? Then when I do conjecture research, I can also incorporate those geometric tools.

Use geometric tools to analyze number theory problems, symmetry, invariance, periodicity, curvature...

Just think about it, if we can use tools such as geometry, topology, differential geometry, etc. directly when doing number theory analysis, wouldn’t the perspective of analyzing number theory problems be broadened immediately? "

Qiao Yu said excitedly and quite proudly.

Of course, Qiao Yu also had selfish motives in designing this axiomatic system.

Qiao Xi will follow his master to study geometry in the future. He has already made up his mind to do research in number theory. So how can the two of them work together?

Of course, a unified framework is needed.

By breaking down a complex number theory problem into many geometric problems for analysis, he could easily include his mother in his research team.

No one could criticize the results, as his framework allowed geometric solutions to number theory problems.

Just thinking about it makes me feel that this is a very interesting thing. Qiao Xi will become his most attentive assistant in future number theory research.

Obviously, for Qiao Yu, climbing a mountain alone is not as fun as climbing it with someone else. Not to mention that it would be more fulfilling.

After saying this, Qiao Yu looked at Tian Yanzhen and Zhang Yuantang looking at each other in confusion.

I couldn't help but ask suspiciously: "Well, is what I said wrong? Or is there something wrong with the design of my system? That's why you are not optimistic about it?"

Zhang Yuantang took a deep breath and said, "Based on the simple definition and the examples you gave, I can't see any problems at the moment, but..."

Qiao Yu quickly answered, "Excuse me, Professor Zhang, I have to interrupt you. It is true that the examples I have given are a bit simple, mainly due to time constraints. I haven't had time to add more things.

But I actually have a lot of ideas. And I have thought that this framework can fully incorporate group theory, graph theory and other theories.

For example, if we want to define a modal group, it can also contain all possible modal mappings, and the group operation is defined as the composition of the mappings.

In fact, this can also make the relationship between modal mappings more intuitive. Well, how should I put it... Yes, it is just like the role of classical symmetry groups in geometric transformations.

In graph theory, we can think of any modal space as a node, and the edges of the node directly represent the modal mapping. Think about it, can the relationship between modal spaces be represented by the connection of the graph?
In this way, we can directly visualize the transformation relationship of the modal space, so that the relationship between the same mode can be understood through the connection path of the graph..."

Qiao Yu became more and more excited as he spoke, and some ideas that were not yet fully mature popped up in his mind like mushrooms after a rain.

Yes, after the introduction of graph theory tools, the relationship between modal numbers is no longer just an abstract symbolic operation, but the interaction between nodes and edges in the graph structure.

If graph theory is combined with group theory, the complex relationship of the modal group can be simplified into multiple relatively independent components by analyzing the connected components of the modal space graph.

Qiao Yu didn't even notice that he had stood up unconsciously, as if he was giving an exciting speech.

Until the end he gave a summary: "Wow! Really, I suddenly feel like I am a genius. How did I come up with such a powerful axiom system?!"

After saying this, Qiao Yu, who had been gesticulating, seemed to realize that this was Director Tian's office. Looking at the two professors with strange expressions opposite him, Qiao Yu smiled awkwardly.

He raised his hand and scratched the back of his head, then sat back in his seat obediently.

"That..." Qiao Yu felt that he had finished speaking, and then looked at Zhang Yuantang, waiting for the professor to continue.

He still needs some advice.

After all, this framework is just a prototype, and there is still a lot of work to be done if we really want to establish this axiomatic system.

After all, this is definitely a huge systematic project! There is a lot of proof work to be done.

Even every integration of a theory requires a lot of proof work.

Definition of spatial property modal number, basic axioms of modal mapping, modal operation rules and systems, geometric distance in modal space, topological characteristics...

These basic axioms are only what needs to be proved in the first stage and only represent the rationality of this framework.

In order to make everyone accept it and recognize its practicality, there will be a second stage, a third stage, and so on, constantly expanding the entire theorem system.

However, before Zhang Yuantang could speak, Tian Yanzhen, who had been silent all this time, suddenly spoke up: "That's right, Qiao Yu, you are really a genius!

"Huh... Qiao Yu, if you can successfully build this axiomatic system, then your contribution to the development of modern mathematics will be no less than Isaac Newton's contribution to the development of world science!"

That’s right, Tian Yanzhen was talking about science, not just mathematics.

But in fact, Qiao Yu’s focus was not on what the tutor said, but on Tian Yanzhen’s expression at the moment.

Qiao Yu believed that his mentor didn't mind showing some true feelings in front of him.

But he had been at Yanbei University for half a year and had met Tian Yanzhen many times. Director Tian had shown undisguised joy and appreciation for his progress...

But to be honest, he had never seen his mentor show such excitement so far...

Even when meeting with Professor Yuan across the table, or when his paper was published in Ann.Math, Director Tian's emotions were actually expressed very subtly or just right.

But today was obviously different. He could see from Tian Yanzhen's expression the excitement that he wanted to suppress but couldn't suppress well enough.

It felt like he had already proved the Riemann hypothesis. Yes, Qiao Yu felt that even if he really proved the twin prime conjecture, it probably wouldn't excite Director Tian to this extent.

Later, Qiao Yu also felt that Zhang Yuantang's attitude was actually a bit strange.

The reactions of these two people also made Qiao Yu realize that he might have underestimated the axiomatic system or new mathematical framework he was planning to build.

At this time, Zhang Yuantang also let out a long breath and said seriously: "Yes, I also agree with Academician Tian's opinion. But Qiao Yu, this is definitely not a job you can accomplish alone.

In other words, this is not a job that you can complete by yourself in a short period of time, such as ten or twenty years. Of course, this does not mean that I am questioning your ability.

Because this work involves a huge amount of proof. You should be responsible for building the big framework, and leave the detailed proof work to other people in the team. "

After saying that, Zhang Yuantang glanced at Tian Yanzhen.

This sentence is actually very pertinent, but everyone has selfish motives. If possible, he hopes to bring a group of people to join this work.

But coincidentally, Qiao Yu’s mentor is Tian Yanzhen, and he has also heard about the relationship between Qiao Yu and Yuan Zhengxin.

In other words, if Yanbei and Huaqing work together on this framework, they will be able to form a team to supplement the framework.

After all, if Qiao Yu can really build the big framework, the detailed proof process can be handled by forming an excellent team of doctoral students who are related to the project.

Qiao Yu or the person in charge of the research team only needs to give the final review.

Zhang Yuantang believed that after knowing the topic of this team, no mathematics practitioner who understood its significance would be able to resist such temptation.

Even if it was just to enter the list of thanks, he couldn't say such words.

Although Qiao Yu has only given a possibility at present, this possibility now seems likely to succeed.

Because even if Qiao Yu only gave the simplest part of the idea, the logic is very rigorous. And it works as long as you put yourself in the picture and think about it.

"So my idea is of great value, right?" Qiao Yu asked after taking in everything.

Although this is nonsense, Qiao Yu just wanted to ask this.

Tian Yanzhen pursed his lips and ignored him. He had already made his evaluation and didn't want to answer such a boring question.

It has been said that his contribution to the scientific community is comparable to that of Newton, so how can it be more valuable?
Should we add Einstein into the mix?
Zhang Yuantang, however, asked back indifferently: "Qiao Yu, how many papers have you read?"

Qiao Yu thought for a moment and replied, "So far, there are more than 30 articles."

After that, Qiao Yu added: "Although I haven't read many of them, they are all papers that are worth reading, such as your two heavyweight papers, Professor Zhang."

Although Zhang Yuantang was indeed pleased with Qiao Yu's roundabout flattery, he just smiled and said, "You will probably understand after you have read hundreds of papers of varying quality."

After saying that, he looked directly at Tian Yanzhen next to him.

Tian Yanzhen, who had been thinking for a long time, met Zhang Yuantang's gaze and said, "Why don't I ask Mr. Yuan to come over and talk about it. This idea really needs to be treated seriously. Let's see how to set up the project."

Qiao Yu opened his mouth but said nothing.

Although it was he who proposed the idea, it seemed that Director Tian never thought of asking for his opinion.

Zhang Yuantang was just stunned for a moment, then nodded.

So Tian Yanzhen took out his cell phone.

"Mr. Yuan, are you busy?"

"Qiao Yu has some very interesting ideas again, and they have already taken shape. If you have time now, I hope you can come and listen to his ideas."

"Yes, Professor Zhang Yuantang is also here."

"Okay, I'll wait for you."

After a few words, Tian Yanzhen hung up the phone, then looked at Qiao Yu and said, "Mr. Yuan will be here in about fifteen minutes. Qiao Yu, go downstairs and wait, and I will pick Mr. Yuan up later."

After saying that, Tian Yanzhen picked up Qiao Yu's manuscript again and started reading it from the beginning.

"Okay, Director Tian." Qiao Yu agreed and walked out of the office. It was obvious that he didn't want him to talk nonsense here for the time being.

Zhang Yuantang also glanced at Qiao Yu, said nothing more, and also picked up the manuscript.

This attitude shows that Director Tian will fully support him in building this framework, which also means that Qiao Xi can start doing research while learning.

Since Mr. Yuan has been called over, there is no reason for outsiders to benefit from their own projects, and with the old man around, he will definitely not suffer any loss.

……

Yuan Zhengxin is in a good mood today.

Specifically, he should have been in a good mood since the day before yesterday. Qiao Xi took the initiative to ask if he could come before school started, which really surprised the old man.

Both mother and son are studious, which is great.

If you have talent and are willing to learn, age is not a problem. Although it is difficult to achieve success in mathematics late in life, it is not impossible, not to mention that there is Qiao Yu to help you in the future.

In short, Yuan Zhengxin is still very optimistic about Qiao Xi's future development.

Originally, he planned to wait for Qiao Xi to come to Huaqing today, make arrangements for his female students, and then invite Qiao Yu to have dinner in the evening.

Unexpectedly, Tian Yanzhen called him again. Although the words were understated, Yuan Zhengxin could hear that the tone of his former student was very serious.

Well, what new tricks has Qiao Yu come up with?
After deciding to come and take a look, he called the driver who was sent to pick up Qiao Xi and asked him to take Qiao Xi directly to the Yanbei Mathematical Research Center.

After all, Qiao Xi was almost there at this time. If Tian Yanzhen specifically called Zhang Yuantang over, it would definitely not be possible to talk things out quickly.

Soon, the car arrived at the Yanbei Mathematical Research Center. Before getting off the car, I saw Qiao Yu standing at the door of the research center.

As soon as the car stopped, Qiao Yu hurried over, opened the door attentively, and then directly supported the old man's arm.

"I'm not so old that I can't walk." Yuan Zhengxin said with a smile.

"I know, but Grandpa, my teacher specifically asked me to come down to pick you up, so I have to do something, right?"

"You are the most naughty. By the way, what terrible thing did you do that your teacher called me over specially?"

"Not calling, but asking! Well, I just made a universal axiomatic framework, but the teacher said that if I can really perfect this axiomatic system, my contribution to modern mathematics will be greater than Newton's contribution to the development of world science."

Qiao Yu did not hesitate to use Tian Yanzhen's words to praise himself again.

This sentence made Yuan Zhengxin pause for a moment. He turned his head to look at the well-behaved boy beside him and asked seriously, "Did Tian Yan really say that?"

Qiao Yu nodded proudly and said, "Yes, it's the original words. I didn't change a single word."

"A universal mathematical axiomatic framework has made a greater contribution than Newton? You have proved all the correspondences of the Langlands Program?" The old man was a little surprised.

Qiao Yu shook his head, not knowing how to explain for a moment, so he simply said, "Well... I have the manuscript, you will know when you go up and read it."

"Walk faster." Yuan Zhengxin quickened his pace.

……

"Mr. Yuan."

"Mr. Yuan."

"Well, Professor Zhang, long time no see. Well, let's stop talking nonsense. Where is the manuscript? Let me take a look." Yuan Zhengxin greeted Zhang Yuantang casually, then turned to Tian Yanzhen and said.

Tian Yanzhen handed over the manuscript in his hand.

Yuan Zhengxin took the manuscript, found a seat and sat down, then pointed at Qiao Yu: "Come here and sit next to me. I will ask questions at any time."

"Okay." Qiao Yu nodded and sat down obediently.

After Qiao Yu sat down next to him, Mr. Yuan began to read Qiao Yu's manuscript seriously.

Zhang Yuantang shook his head when he saw this scene. It seemed that those rumors were not exaggerated at all. This faction was really closely integrated.

For a moment, Zhang Yuantang felt a little sad and thought too far ahead.

The day this axiomatic system came out, China's status in the mathematical community was likely to be infinitely elevated.

Well, are the Tsinghua and Peking University schools going to dominate the world?
　11 words completed in days! Finally finished, brothers! Pudding is really a good author who keeps his word! !

　　
　
(End of this chapter)