Into the Immortal Cultivation

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"New Progress in the Fundamentals of Arithmetic" is really a big and empty thesis topic. Papers such as "New Developments in the ** Field, New Achievements, and New Insights in the Application of New Technologies" are usually searched for, copied, and pasted in a rough and scrambled article with some of your own opinions-saying that the papers are somewhat reluctant. The major journals in the earth academia are not rare.

However, if you write with great power, it will be different.

Even if a true God of Learning writes a summary, it is a essay of the nature of a document, and that is also something that determines the development of the discipline and looks forward to the future. It has great guiding significance.

Shujun Pang Jialai is obviously such a character.

Huang Fulian said: "This is just the paper that came out. In addition to a special issue of" The Ten Thousand Laws Collection ", it contains all the clash records of Lianzong Lizong in recent decades, including yours!"

"Your article, this one, and the other one by the fortune teller are the first three!"

Wang Qi instantly foreseen the trouble that was about to follow: "Really ... I am directly in the middle of the storm!"

"The center of the hurricane is often calm and calm." Chen Youjia came over and said: "If you are not troubled, no one will trouble you."

Wang Qi shook his head and started reading this paper by Pang Jialai.

Huangfu Lian couldn't help but say: "Sister Brother, don't be angry, don't feel frustrated ... that's the difference in concept."

Chen Feng also came over and asked curiously: "What's going on? Shujun overthrew your last paper?"

"No, no, I think the proof process is still perfect and meticulous. It's impossible for the king to pick bones from the eggs."

The corner of Chen Youjia's mouth slightly raised: "But there is still a" hair egg "in the south, and there are bones in it."

Chen Feng ignored Chen Youjia's ridicule this time. He has already looked into it.

Shujun did not deny Wang Qi's "complete law". One is because Wang Qi ’s proof process is perfect, and second, more importantly, he feels that his precious talents should not be wasted on thinking about set theory and related issues.

For these tyrants, some things obviously do not need to think.

Mathematics is established, self-consistent, and complete. This is truth, not logical reasoning.

"I knew it, 'a logic trick full of creative geniuses' ... this is even more ruthless than direct denial."

Yes, in the eyes of Junjun, everything Wang Qi has done is just a useless trick.

The real mathematics should not include such "tricks".

Mathematics should not be based on logic. If arithmetic only evokes the law of logic, then normal thinking should be able to accept it; if it is based on the common law understood by everyone, it cannot be denied unless it is insane. But actually? Can everyone master math?

Obviously not. Not everyone can create mathematics; not everyone can use it flexibly after learning a certain theorem; not everyone can understand mathematical analysis thinking, even if it is explained repeatedly. And most people who can keep up with analytical thinking also find it difficult.

A real mathematician may not be able to beat a Chinese player on the chessboard, but a problem that can make this Chinese player overnight is not a big deal for a clever mathematician.

It can be seen that arithmetic is not simply a stack of computing power or a simple arrangement of concepts according to a deductive method. It is formed by the deductive method in a specific order, and the order is more important than the element itself. If someone has a certain sense of this sequence, or intuition, and can perceive the whole of reasoning with just one glance, then this person will not worry about forgetting one of the elements, because each element is placed in this array in a specific way It does not require people to remember it with memory.

This is the intuition of mathematics, the intuition that is elegant and immortal.

Using logic can only prove that using intuition can create.

For Shujun, this intuition can even cover physical problems. The physical laws we know and have mastered are not direct inductions of experience. They can only be created by intuition, guided by empirical facts.

In this paper, Shujun once again reiterated his point of view.

This elder first pointed out the biggest problem in the field of logic very maliciously—the unsolvable paradox of the alchemist. He sneered happily: "This thing is not only empty, but also contradictory."

Immediately afterwards, he pointed out the biggest problem with Wang Qi ’s complete law—first-order predicate logic could not accurately define any mathematical concept, it was too weak. Its appearance is instead a criticism of Lizong-their proof cannot yet prove the monster they made, the monster named "infinite" [infinite].

Anything that cannot be defined with a finite sentence is meaningless and should be removed.

"Huh, this is simply declaring war!" Wang Qi's tone is very uncomfortable: "This is just saying, 'I heard that your monkeys who learn to use stone tools are excited because of an interesting logic trick, so I come back and step on it. You, let you see the reality '. "

Chen Youjia hummed in Wang Qi's ear: "You have really been overdone recently."

Wang Qi found out that he was already surrounded by people. Chen Youjia and herself recently, the two have reached a point where they can breathe. Chen Youjia finished reading with herself. The punch on the periphery was the onlookers represented by Li Zhengguo with full armrests. Most of them have heard the name of Shujun. I want to see who was criticized by the name of Junjun. Outside, there are people asking "who is the monarch". Chen Feng simply stood far away, because he understood that he could not understand.

"I guess Junior Brother, you might need this very much, so I took it directly." Huangfu Lian shook his head and sighed: "Well, some guys at the outer gate of Shenjing have already exploded. Your paper has been continuously evaluated by the counter-counter. It ’s a bit irritating to them ... and maybe someone will trouble you recently, you better avoid it and then calm down and adjust your mindset. "

"Adjust mentality? Is it necessary?" Wang Qi felt very strange.

Huang Fulian pointed to Wang Qi's finger: "You ... are you shaking?"

Wang Qi noticed that his fingertips had been shaking since just now.

This guy won't be scared by the pressure from seniors, right?

People around me think so.

Only Chen Feng drank: "Are you crazy?"

Only he here can read other people's emotions, so only he found that there was no trace of fear in Wang Qi's heart, only warfare.

Suanjun Pang Jialai is expecting a closed, self-consistent mathematical system, so he very much rejects the concept of "infinity" ... or should he admire his intuition? This concept will eventually smash his beloved circle and bring the mathematics to life again. Did he feel it all intuitively from the beginning?

What a terrible intuition ... hahahahaha, but what about that?

"We must know, we must know." Wang Qi murmured, and then put away the paper, said: "Dongjia, I want to take a few days off, you look at the deduction for the latest wages?"

Chen Feng worried: "Don't mess up!"

It is not easy to find a scientific research dog that is so easy to use.

Wang Qi laughed and pushed out the door, preparing to go to Wanfamen station to pack things.

At this moment, Mo Zhen ran from a small mouth holding a stack of paper. He ran and shouted, "Brother, look at this ..."

"Already read it, but **** doesn't work."

Wang Qi waved his hand and strode forward.

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This chapter is a bit difficult to write, and it is mainly about Junjun's interpretation of logic and intuition. This part mainly draws on Henry Poincaré's speech and part of the ORZ of "Mathematical Enemy".

"Using logic, we prove that using intuition, we create" is Poincaré's famous quote, and Wang Qi's last chant "We must know, we will know" is Hilbert's belief. In the end, Wang Qi ’s evaluation was not a personal arrogance, but the mathematicians of the two schools were indeed intolerant. The mathematics in Poincaré's ideal is a closed, finite system. He did not allow the concept of "infinity" to enter mathematics-but in Wang Qi's time, unlimited research was part of mathematics. Although the logic involving infinity seems to be contrary to common sense.

Therefore, some people worry that Jun will prove Gödel's incompleteness theorem in front of Wang Qi-this is impossible. There is still hope for those in the count, but it is impossible to count. In his eyes, this problem is not a mathematical problem that can be used for thinking. The biggest loophole of set theory "Russell's Paradox" [sometimes called "Barber's Paradox") was created by Russell, a proponent of set theory, not Henry Poincaré. The latter is far superior to Russell in mathematics, but he does not bother to think about such problems at all.

Regarding the "monkey" stalk-according to the diaries and manuscripts discovered by Henry Poincaré after his death, he did treat people who do not understand math as monkeys. I think Russell is probably a senior monkey who has always mastered stone tools in his eyes?

Finally, "I have read it, but I don't know what to do", three-body terrier, cough.

In the end ... finding a recommendation ticket ... I'm so embarrassed to say it!

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