"On New Advances in the Fundamentals of Arithmetic" is really a big and empty thesis topic. Papers such as "New Advances/Latest Achievements/Applications of New Technologies/New Insights" are usually shoddy articles that are written by looking up some information, copying and pasting, and adding some of their own opinions - the papers are a bit reluctant. It is not uncommon for major journals in the academic world of the earth to be published.

However, if it is written by a great power, it is different.

Even if a true scholar writes a review and a paper in the nature of literature, it is also something that determines the development of the discipline and looks forward to the future, which is of great guiding significance.

Pang Jialai, the soathman, is obviously such a character.

Huang Fu Lian said: "This is a paper that has just come out, except for a special issue of the "Ten Thousand Laws Anthology", which includes all the records of the confrontation between Lianzong and the Sect in the last few decades, including your paper!"

"Your one, this one, and the other one of the Lord, are the first three!"

Wang Qi instantly felt the trouble that was about to follow: "It's really ...... Now I'm right in the middle of the storm!"

"The center of a hurricane tends to be calm. Chen Youjia came over and said, "If you don't have a lot of trouble, no one will trouble you." ”

Wang Qi shook his head and began to read Pang Jialai's paper.

Huangfu Lian couldn't help but say, "Senior brother, don't be angry, and don't feel frustrated...... That's how that philosophy is different. ”

Chen Feng also leaned over and asked curiously, "What's the matter?"

"No, no, I think the proof process is still perfect and meticulous, and it is impossible for you to pick a bone out of the egg. ”

The corners of Chen Youjia's mouth rose slightly: "But there is still a 'hairy egg' in the south, and there are bones in it." ”

Chen Feng ignored Chen Youjia's ridicule this time. He's already seen it.

The Counting Jun did not deny Wang Qi's "law of completeness". First, because Wang's proof process was perfect, and second, more importantly, he felt that his precious talents should not be wasted thinking about set theory and related problems.

For these tyrants, there are things that obviously do not need to be thought about.

Arithmetic is valid, self-consistent, complete, and this is truth, not logical reasoning.

"I know, 'a logical trick full of genius and creativity'...... This is even more ruthless than a direct denial. ”

Yes, in the eyes of the counter, everything Wang Qi did was just a useless trick.

True arithmetic should not contain such "tricks".

Arithmetic should not be logic-based. If arithmetic evokes only the laws of logic, then the normal mind should be able to accept them, and if it is based on the usual laws that all know it, it cannot be denied unless it is insanity. But in reality, can everyone master arithmetic?

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

A true mathematician may not be able to beat a national player on the chessboard, but the arithmetic problems that can make this national player lose his head overnight are nothing to a clever arithmetic.

It can be seen that arithmetic is not simply a stacking of computing forces or a simple arrangement of concepts according to the deductive method. It is arranged in a specific order by deductively, and the order of arrangement is more important than the elements themselves. If one has some feeling, or intuition, of this order, and perceives the whole of reasoning at a glance, then that person will not worry about forgetting one of the elements, because each element is placed in this array in a particular way, without the need for one to memorize it.

This is the intuition of arithmetic, the intuition that is as elegant as a fairy.

The use of logic can only prove that the use of intuition can create zào.

For the arithmetic, this intuition can even overturn physical problems. The physical laws that we know and have mastered are not direct inductions of experience, but can only be guided by empirical facts and created through guò intuition.

And in this paper, Shuan Jun once again reiterated his opinion.

First of all, the elder maliciously pointed out the biggest problem in the field of logic - the insolvability of the alchemist's paradox. He happily mocked, "This thing is not just empty, it contradicts itself." ”

Immediately afterwards, he pointed out the biggest problem of Wang Qi's law of completeness - the first-order predicate logic cannot accurately define any arithmetic concept, it is too weak. Its appearance is instead an attack on the renunciation - their proof cannot prove the monster they have created, the monster called "Immeasurable" infinity.

Everything that cannot be defined in finite statements is meaningless and should be cut off.

"Tsk, this is basically a declaration of war!" Wang Qi said in a very unhappy tone: "This is basically saying, 'I heard that you monkeys who have learned to use stone tools are excited because of an interesting logical trick, so I will come back and step on you to let you see the reality clearly'." ”

Chen Youjia hummed softly in Wang Qi's ear: "You have indeed been too excited recently. ”

Only then did Wang Qi realize that he was already surrounded by a circle of people. Chen Youjia and himself are recently, and the two of them have reached the point where their breath can be heard. Chen Youjia watched it with himself. The punch on the periphery was the onlookers represented by Li Zhengguo, who fully armrested his hand. Most of them have heard of the name of Shujun. I want to see what kind of characters are being named and criticized by the counter. There are still people on the periphery asking "who is the counter". Tatsukaze simply stood in the distance, because he knew he couldn't read.

"I guess you might need this, so I just took it. Huangfu Lian shook his head and sighed: "That, some guys from the outer gate of Shenjing have already exploded." It's a bit irritating for them that your paper has been evaluated in a row that is completely opposite to that of the Counter...... Also, someone may be looking for trouble with you recently, so you'd better avoid it and then be alone and adjust your mentality. ”

"Is it necessary to adjust your mentality?" Wang Qi thought it was strange.

Huangfu Lian pointed at Wang Qi's finger: "You...... You're trembling, huh?"

Wang Qi noticed that the tips of his fingers had been trembling since just now.

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

That's what people around me think.

Only Chen Feng drank: "Are you crazy?"

Only he can read other people's feelings here, so he is the only one who finds that Wang Qi has no trace of fear in his heart, only a fighting spirit.

The arithmetic monarch Pang Jialai expects a closed, self-consistent mathematical system, so he is very reluctant to "infinite" and other concepts...... Or should we admire his intuition? This concept will eventually break through the circle he loves and give arithmetic a rebirth. Did he feel this qiē intuitively from the beginning?

What a terrible instinct...... Hahaha, but so what?

"We must know, and we will know. Wang Qi muttered, then put away the paper and said, "Boss, I'm going to take a few days off, and you can deduct the latest salary, right?"

Chen Feng said worriedly: "Don't mess around!"

It's not easy to find such a good research dog, and he hasn't used it enough?

Wang Qi laughed, pushed the door and walked out, ready to go to the Wanfa Gate station to pack up his things.

At this moment, Mo Zhenzhen ran over from a small mouth with a stack of papers. He ran and shouted, "Senior brother, look at this ......"

"I've read it, but I don't understand it. ”

Wang Qi waved his hand and strode forward.

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This chapter is a bit laborious, mainly because of the explanation of logic and intuition. This part mainly borrows from Henri Poincaré's speech and part of the oRz of "Mathematical Enmity", and also asks the great god to correct it

"Using logic, we prove, using intuition, we create zào" is Poincaré's famous saying, and Wang Qi's final chant "We must know, we will know" is Hilbert's belief. In the end, Wang Qi's evaluation is not personal arrogance, but the two schools of mathematicians are indeed incompatible. Poincaré's ideal of mathematics was a closed, finite system. He did not allow the concept of "infinity" to enter mathematics - but in Wang Qi's time, the study of infinity was part of mathematics. Although the logic of infinity seems to be contrary to common sense.

Therefore, some people worry that the arithmetic king will prove Gödel's incompleteness theorem before Wang Qi - this is an impossible thing. There is still hope for the people of the Lord's faction, but it is impossible to count the king. In his eyes, this question is not a mathematical problem that can be used to think about it at all. The biggest loophole in set theory, Russell's paradox, is called the "barber's paradox" in the vernacular, and it was coined by Russell, a proponent of set theory, not Henri Poincaré. The latter was far more mathematically superior to Russell, but he did not bother to think about such problems at all.

Joke about "monkeys" -- According to the diaries and manuscripts found after Henri Poincaré's death, he did treat people who did not know mathematics as monkeys. I think Russell is probably a high-level monkey who has mastered stone tools in his eyes, right?

Finally, "I have read, bullshit doesn't work", three-body terrier, cough cough.

The Last ...... Ask for a referral ticket...... I'm so embarrassed to say it!