"On New Progress in the Fundamentals of Arithmetic", this is really a big but empty thesis title. "New progress/latest achievements/applications of new technologies/new insights in the field of **" This type of paper is usually a shoddy article that is made up of looking up some information, copying and pasting it and adding some of your own opinions - it is a bit reluctant to call it a paper. It is not rare to be published in major journals in the earth academic community.
But if it were written by a powerful being, it would be different.
Even if a true academic master writes a review or a paper of a documentary nature, it is something that determines the development of the subject and highly looks forward to the future, and is of great guiding significance.
Master of Calculation Pang Jialai is obviously such a character.
Huangfu Lian said, "This is a paper that just came out. In addition to a special issue, the "Selected Collection of Ten Thousand Methods" contains all the records of School of Separation School of Separation's battles in recent decades, including your paper!"
"The one you wrote, this one, and the other one written by me are the first three!"
Wang Qi instantly sensed the trouble that was about to follow. "It's really... now I'm directly in the center of the storm!"
"The center of a hurricane is usually calm." Chen Youjia came over and said, "If you are not troublesome, no one will cause trouble for you."
Wang Qi shook his head and started reading the paper by Pang Jialai.
Huangfu Lian couldn't help but said, "Junior brother, please don't be angry, and don't feel frustrated... That's why the concepts are different."
Chen Feng also came over and asked curiously, "What's going on? Did you overturn your last paper?"
"No, no. I think the proof process is very perfect and meticulous. It's impossible for you to pick out the bones from the eggs."
Chen Youjia raised the corner of his mouth slightly. "But there is a thing called 'hairy egg' over there in the south, and all of them have bones inside."
Chen Feng ignored Chen Youjia's teasing this time. He had already taken it in.
Suanjun did not deny the "completeness law" of Wang Qi. First, because the proof process of Wang Qi was perfect. Second, and more importantly, he felt that his precious talents should not be wasted on thinking about set theory and related issues.
For these tyrants, some things are obviously no-brainers.
Arithmetic is established, self-consistent, and complete. This is truth, not logical reasoning.
"I knew it, 'logical tricks full of genius and creativity'... This is even more cruel than direct denial."
Yes, in Suanjun's eyes, everything Wang Qi did was just useless tricks.
Real arithmetic should not involve such "tricks".
Arithmetic should not be based on logic. If arithmetic only evokes logic Principle, then normal thinking should be able to accept it; if it is based on the usual Principle that everyone understands, it cannot be denied unless it is insane. But in reality? Can everyone master arithmetic?
Obviously not. Not everyone can create mathematics; not everyone can flexibly use it after learning a certain theorem proof; not everyone can understand mathematical analytical thinking, even if they explain it 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 national player on the chessboard, but a calculation that can make this national player grow old overnight is nothing to Gaoming Mathematicians.
It can be seen that arithmetic is not formed by simply stacking calculation power or simply arranging concepts according to deduction. It is formed by deduction in a specific order, and the order is more important than the elements themselves. If someone has a certain feeling, or intuition, about this order, and can perceive the whole reasoning at a 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, and people do not need to remember it with memory.
This is the intuition of arithmetic, the intuition of being as elegant as a fairy.
Using logic can only prove, using intuition can create.
For Suanjun, this kind of intuition can even generalize physical problems. The physical laws we know and have mastered are not direct inductions of experience. They can only be created through intuition guided by empirical facts.
In this paper, Suanjun once again reiterated his point of view.
The elder first maliciously pointed out the biggest problem in the field of logic - the unsolvable problem of Alchemist's Paradox. He happily mocked. "This thing is not only empty, but also contradictory."
Then, he pointed out the biggest problem with Wang Qi's completeness law - first-order predicate logic cannot accurately define any mathematical concepts, it is too weak. Its appearance is an attack on School of Separation - their proof cannot prove the monster they created, the monster called "infinite" [infinite].
Anything that cannot be defined using finite statements is meaningless and should be removed.
"Tsk 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 learned to use stone tools got excited because of an interesting logic trick, so I came back to step on you and let you see the reality clearly'."
Chen Youjia hummed in Wang Qi's ear. "You've really been too excited lately."
Only then did Wang Qi realize that there was a circle of people around him. Chen Youjia was closest to him, and the two of them had leaned close to the point where they could hear their breathing. Chen Youjia had watched it with him. A punch from the outside was enough to provide an armrest. The crowd of onlookers represented by Li Zhengguo. Most of them have heard of Suanjun's name. They wanted to see who the person was named and criticized by Suanjun. Some people on the periphery were asking "Who is Suanjun?". Chen Feng simply stood far away because he knew that he could not understand.
"I guess junior brother, you may need this very much, so I just brought it over." Huangfu Lian shook his head and sighed, "Well, some guys in the outer gate of Shenjing have already made a fuss. Your papers have received completely opposite evaluations continuously, which is a bit exciting for them... and there may be people who will cause trouble for you recently. You'd better avoid it and calm down alone to adjust your mentality."
"Adjusting your mentality? Is it necessary?" Wang Qi found it strange.
Huangfu Lian pointed at Wang Qi's finger. "You... are obviously shaking?"
Wang Qi then noticed that the tips of his fingers had been trembling since just now.
Is this guy going to be frightened by the pressure from senior experts?
This is what the people around me think.
Only Chen Feng drank. "Are you crazy?"
He was the only one here who could read other people's emotions, so he was the only one who discovered that there was no fear in Wang Qi's heart, only the will to fight.
Master of Calculation Pang Jialai is looking forward to a closed, self-consistent mathematical system, so he very much rejects concepts such as "infinity"... Or should we admire his intuition? This concept will eventually break his favorite circle and make mathematics reborn. Did he feel all this intuitively from the beginning?
What a terrible intuition... Hahahahaha, but so what?
"We must know, we will definitely know." Wang Qi murmured, then put away the paper and said, "Boss, I need to take a few days off. Can you just watch and deduct the latest wages?"
Chen Feng said worriedly, "Don't mess around!"
It's not easy to find such a useful scientific research dog. Why hasn't he been used enough?
Wang Qi laughed loudly, pushed open the door and went out, preparing to go to the Myriad Dharma Sect's station to pack his things.
At this moment, Mo Zhenzhen ran over from the small opening holding a stack of paper. He ran while shouting, "Brother, look at this..."
"I've read it, it's bullshit."
Wang Qi waved his hand and strode forward.
This chapter was a bit difficult to write, mainly because of Jun's explanation of logic and intuition. This part mainly draws on Henry Poincaré's speech and part of the ORZ of "Mathematical Enemies". Please ask for corrections.
"Use logic, we prove, use intuition, we create" is Poincaré's famous saying, and the last chant of Wang Qi, "We must know, we will know" is Hilbert's belief. The final comment of Wang Qi is not a personal madness. It is delusional, but the two schools of mathematicians are indeed incompatible. Poincaré's ideal mathematics is a closed and limited system. He does not allow the concept of "infinity" to enter mathematics-but in Wang Qi's era, infinite research is part of mathematics. Although the logic involving infinity seems to be completely contrary to common sense.
So some people are worried that Mr. Suan will prove Gödel's Incompleteness Theorems in front of Wang Qi - this is impossible. People of the calculation group still have hope, but it is impossible for Mr. Suan. In his eyes, this problem is not a mathematical problem that can be used to think about. The biggest loophole in set theory is "Russell" The " Paradox" [called the "Barber Paradox" in some colloquial terms] was created by Russell, a supporter of set theory, not Henry Poincaré. The latter's mathematical level was far better than Russell, but he didn't bother to think about such problems at all.
Regarding the "monkey" joke - according to the diaries and manuscripts found after Henry Poincaré's death, he indeed regarded people who did not understand mathematics as monkeys. I think in his eyes, Russell was probably an advanced monkey who had always mastered stone tools, right?
Finally, "I've read it, it doesn't make any sense", Trisolaran Terrier, cough cough.
The last thing... please give me a recommendation vote... I'm so embarrassed to say it!
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