Enter the Immortal Cultivation

Facing Feng Luoyi's questioning, Wang Qi understood that this was an invisible test.

It’s not impossible to push everything to inspiration and intuition. But inspiration doesn't come without a trace. This kind of thinking activity is just something in the subconscious that accidentally shows special patterns.

And saying that one suspects that mathematics itself is incomplete and wants to start elsewhere means that one has deviated from the path of the master of calculation. What's more serious is that if someone comes to Godel's incompleteness theorem because of his own words, then Li Zong and his family will be dismissed directly.

At this time, Wang Qi had an idea and said: "Teacher, my original goal was not to prove completeness. This was just an unintentional result. What I actually want to do is another thing."

Feng Luoyi was surprised: "Such a rigorous theory is actually unintentional? What is your original intention?"

Wang Qi hesitated: "This is just an immature idea."

"Since you have already achieved results, it means that this path is feasible. Even if you don't get to the point you originally wanted to reach, you can still get a glimpse of a major avenue."

Wang Qi gritted his teeth and asked, "Teacher, do you think arithmetic is 'one arithmetic' or 'multiple arithmetic'?"

Feng Luoyi shook his head: "Different mathematicians have different opinions. There is no correct answer to this."

“When I entered Taoism, I was thinking about the increasing number of sub-disciplines of arithmetic. Is this the development process of an organism with a solid structure, which is gaining greater and greater coordination and unity with new developments, or is it the development process of an organism with a solid structure? Is that tendency toward progressive fragmentation inherent in the nature of arithmetic, in which the separate disciplines, not only their aims but also their methods and even their languages, are becoming more and more clearly separated? Is there one mathematics or are there several mathematics?”

Feng Luoyi nodded imperceptibly. Many mathematicians have thought about similar problems. Every disciple of Wan Dharma Sect can also express his or her own opinions. However, there are really not many people who can ask so many questions.

As long as a field raises a large number of questions, it is full of vitality. The lack of problems heralds the end or decline of independent development. This is what Master Ximen once said, and Feng Luoyi has always believed it.

He asked: "So, what do you think?"

"Of course, there is only one." Wang Qi showed a confident, or arrogant smile: "There can only be one."

"Give me a reason, otherwise your theory will make no sense."

Feng Luoyi calmly poured cold water on his disciple. Every year, some young cultivators come up with one wild idea after another with enthusiasm. But unfortunately, due to the lack of accumulation of the proposer himself. Most of these ideas are worthless. There are even some little guys who don’t even understand what they want to criticize, but they clamor to reshape the system of modern law.

Regarding Feng Luoyi’s question. Wang Qi could only express his speechlessness: "Teacher Feng, my idea is the same as Master Ximen's ideal of proving that arithmetic is complete, error-free, and judgeable. It is just a concept and an ideal. But if you want me to talk about my ideas, then I can do it. Say something."

Mathematics is not just a simple sum of various subjects. There are inextricably linked relationships between various fields of mathematics. In fact, as long as we follow the main idea of ​​abstraction, formalization and axiomatic methods. Through this approach, the similarities and differences of various structures as well as their levels of complexity are apparent.

The basis of structure is collections. The concept of a set is relatively simple. It only involves the simple relationship between sets, elements, and elements belonging to the set. It does not discuss the relationship between elements, but the various relationships between elements and elements and between elements and sub-sets, sub-sets and sub-sets. This is the structure. This structure can completely become the framework of mathematics and unify it.

What Wang Qi is saying now. In fact, it is one of the foundations of modern mathematics and the guiding program of the Bourbaki school.

The School of Bourbaki was a group of mathematicians who had a great influence on modern mathematics. Most of them were French mathematicians. Their activities began in the mid-1930s. They published some articles in mathematics magazines and compiled the multi-volume "Principles of Mathematics". They are one of the most important schools in the history of mathematics development.

In a sense, the Bourbaki school, like the Göttingen school, can be called a model of a mathematical school. The Göttingen School is a "bo". Its glory lasted for nearly two hundred years from Gauss to Weyl, and its fields covered almost the entire mathematics. Bourbaki is "deep", and it has almost perfectly completed the tasks assigned to it by its own era in creating new mathematics and promoting the development of mathematics as a whole.

Feng Luoyi listened for a moment. For the first time, a look of surprise appeared on his face: "This is a good idea."

How high is Xiaoyao's vision? Being able to get a good word from him is enough to make many Wan Dharma disciples feel that they will die without regrets.

Wang Qi didn't have any obvious mood swings. He knew very well that what Feng Luoyi praised was not himself, but the great school behind him. He continued: "It is my ideal to bring all mathematics into one subject, and my research ideas are also the same. I use a structural method to organize mathematics and gain a thorough understanding of mathematics. The completion rate is an unexpected gain for me."

"That's the principle." Feng Luoyi nodded and said nothing.

in this Q\u0026A. Wang Qi reversed cause and effect. In fact, the achievements of the Bourbaki school are to some extent based on Gödel. Wang Qi claims that Gödel's visit was based on Bourbaki's program, which is not logically unjustifiable. However, Feng Luoyi still had questions: "Then why don't you use a more intuitive and credible induction principle? Is the foundation of the transfinite method solid?"

"My level is not enough to allow me to complete it in a short time, but I at least hope to complete part of it so that I can prove my own path. So even though I know it is a detour, I have to see the results first."

Feng Luoyi was not very satisfied with Wang Qi's answer, but it was still within the acceptable range. He nodded and waved Wang Qi away.

On the other side, after watching Feng Luoyi's full broadcast, Xi Baiche fell into silence. Then he smiled bitterly: "What an incredible genius."

Ai Keman asked: "Master, these papers..."

"I didn't expect that I would have to rely on something that I don't fully agree with to respond to the enemy." Xi Baiche felt frustrated for a moment. But he soon regained his energy: "However, Wang Qi's ideas gave me some new ideas. His approach is actually very close to ours. What he can't accomplish, maybe we can accomplish it."

Feng Luoyi objected: "But our ultimate goal is to prove the stability of arithmetic itself."

"This is an idea that axiomizes arithmetic, which is very good." Xi Baiche pointed to Suan Jun's paper: "And we only set aside a month to do this. A month later, we will still follow our own pace Walk."

Independently asked another question: "This is Wang Qi's idea. If you do this, you will take away someone else's way."

"I will compensate him in all explicit or implicit ways." Xibeche said firmly.

………………

The calculation master didn't know that at the same time he made the decision to compensate, Wang Qi was lying in front of his desk, writing furiously while wailing: "It's over, it's over, I've done a big death, oh my god! Oh my god, my god!"

"Seek death?" Chen Youjia expressed curiosity about this word.

"It's similar to playing with water to show off your water skills and being drowned in the end is called death." Wang Qi was about to cry.

I just hope to be able to guide the results of the Bourbaki School and make the arithmetic in this world closer to that of my previous life... I can't do the work of the Bourbaki School, you bastard!

Analytical mathematics, probability theory, applied mathematics, computational mathematics, especially theoretical physics and dynamical system theory are the fields I want to pursue... These are all areas ignored by the Bourbaki school!

"Teacher Feng, Master Ximen, please solve this problem yourself! Don't let me solve it!"

This is what the young man prayed for. (To be continued ~^~)

PS: The second update from Alliance Leader Xie. This is not the first time that this meme of the Virtual Sun Rat and the Moon Palace Toad has appeared. If you are interested in the origin of this meme, you can search "The War between Frogs and Rats" on Baidu.