Enter the Immortal Cultivation

It is precisely because of his advanced mathematical knowledge that Wang Qi knows the significance of this mathematical paper better than anyone else.

In mathematical discussions, those who can give a specific object or a calculation method for a specific object are often called constructive. Constructive mathematics is an important field of modern mathematical research, and its fundamental feature is the emphasis on constructibility. The so-called constructibility refers to the ability to give a specific object or a calculation method for a specific object.

The difference between constructive mathematics and classical mathematics is that constructive mathematics believes that "existence is constructed". In order to achieve constructivity, mathematicians must reinterpret existential quantifiers and other logical connectives and quantifiers in order to explain the meaning of the proof of propositions containing these logical expressions from the perspective of construction.

The computational theory based on constructivity has very powerful advantages. It is very reliable, unlike set theory and logical mathematics, which have unstable foundations. But on the other hand, it is too stable, so it appears very closed. This theory excludes logical proof, real infinity, and countless practical and known methods. In short, it cuts off all unreliable and imperfect things to form a limited "perfection".

This method with too much "destructive power" is exactly what the Master of Calculation rejects. More importantly, it is precisely because this idea restricts too many methods that mathematicians are restricted in dealing with problems, and it has no practical use. Therefore, this concept is widely criticized.

And Master of Calculation solved this problem.

Master of Calculation made a new breakthrough in constructive algorithms. He strongly ignored the achievements made by Xi Boche in this field, only retaining its constructive part and eliminating all non-constructive parts. Such a new algorithm is extremely simple, and due to its constructive characteristics, it has strong feasibility. The potential infinite characteristics are also more suitable for practical applications in the field of computational science.

For a long time, Li Zong despised Lian Zong because of the role of mathematical logic in promoting arithmetic, but this time, Lian Zong's mathematical theory surpassed Li Zong in practicality!

"This... this is not scientific?" Wang Qi sighed.

On Earth, constructive mathematics was not introduced until the 1960s. At this stage, all mathematicians' three views have been devastated again and again by great gods such as Gödel, Turing, and Church, and countless wrong paths have been rejected; then the Bourbaki school, Grothendieck and countless other mathematicians have found many new paths. At that time. Recursion theory and modern mathematical logic have become basic content. It can be said that the mathematics of this era is very different from the mathematics of the early twentieth century. In such soil, constructive computational theory can take root and sprout.

But in this world, in this Shenzhou, Gödel was absent from this historical event, the "golden diagonal" was broken, and the old Turing did not play his due light. Since no one doubts that there is a contradiction between semantics and grammar, that is, the defects of human language itself, the master of calculation is still banging against the south wall of completeness.

In this case. Such mathematics should not be possible!

However, if you think about it carefully, it doesn't seem impossible. After all, in the history of the Earth, Henri Poincaré died too early, missing the great development of mathematics, and allowing Brouwer to lead intuitionism into the dead end of his personal philosophical quirks, and he did not witness the day when mathematics derived computer science and changed the times. But Master Poincaré has been alive!

His accumulation is far beyond his Earth counterpart.

"Master Poincaré's paper was proposed by Earth scientists fifty years after Henri Poincaré's death. It seems that the history of the Earth cannot be used to determine the upper limit of Shenzhou Xiaoyao in the future. Relying on his sense of mathematics, he has skipped countless wrong paths. Opening up this new path... Master Poincaré is indeed one of the strongest geniuses in the history of Shenzhou! Very strong! If I hadn't studied the mathematical theory of the 21st century, I wouldn't even be able to think of comparing with him." Wang Qi secretly admired, while carefully looking at Feng Luoyi's face.

This time, our Ge Ting is afraid of pills!

In the illusion of all immortals, no small action can be hidden from Feng Luoyi. Feng Luoyi sensed Wang Qi's expression and smiled bitterly: "How is it?"

"Very strong, I don't know how to describe it. But this paper can be used as a signpost to guide the development of Shenzhou mathematics, especially the development of applied mathematics."

"It is very strong both in theory and application. We thought that with your first-order complete law, we could be one step ahead in mathematical logic. Unexpectedly, we overestimated ourselves and underestimated the Lord of Calculation." Feng Luoyi shook his head: "It is worthy of being a peerless strongman who once overwhelmed the entire Wanfamen with one person."

He is the younger Xiaoyao of Wanfamen. When he embarked on the path of cultivation, it was the time when Xi Boche rose and the two generations of strongmen of Wanfamen handed over. And the time when he became a free and easy person was around the establishment of the Immortal Alliance. The Lord of Calculation left Shenzhou to guard elsewhere not long after. Therefore, Feng Luoyi did not have the opportunity to face the tyrant directly.

"Do you think too highly of yourself?" Wang Qi pretended to be confused, "Is there something wrong with the proof of completeness?"

Before Gödel, no one doubted that there was a contradiction between semantics and grammar. Some concepts cannot be defined by human language, and some problems cannot be understood by existing logic. It should be possible to figure it out with your toes. It is almost impossible for the master to get the result he dreamed of.

But, this is how science develops. The master of calculations hits the wall there, and it is impossible to prove universal and extensive completeness. However, in this process, they will inevitably verify some dead ends and put forward some theories that are obtained by accident. These results will become the basis for the future development of mathematics. If possible, Wang Qi even hopes to guide the many free and easy people of the Goting School to the path of the Earth Bourbaki School, so that countless free and easy people can transform Shenzhou mathematics and make it closer to the Earth mathematics that Wang Qi is more familiar with and more advanced.

Feng Luoyi sighed: "Master Xi is complaining. He seems to have vaguely seen the destination, but there is always an invisible wall blocking him, making him feel like he is spinning in place..."

Suddenly, Feng Luoyi changed his face and looked at Wang Qi straight: "Wang Qi, Master Xi asked me to ask you a question, you have to answer me honestly."

Wang Qi didn't understand, and secretly wondered which important question it was.

Feng Luoyi asked, "You have already perfectly proved the completeness of first-order logic within a limited framework. Why did you suddenly violate the framework of finitism and use the method of transfiniteness to do the next step of research?"

Wang Qi was speechless: "This... it was just a flash of inspiration..."

"Did you foresee this dilemma at the beginning? Or did you hide some discovery?" (To be continued ~^~)