Enter the Immortal Cultivation

"On the New Progress in the Foundations of Mathematics" is really a big and empty paper title. Papers like "New Progress in ** Field/Latest Achievements/Application of New Technologies/New Insights" are usually crudely made articles that are made by looking up some information, copying and pasting, and adding some personal opinions - it's a bit of a stretch to call them papers. It's not rare to publish them in major journals in the academic world on Earth.

However, if a great man writes it, it's different.

Even if a true academic god writes a review or a paper of a documentary nature, it is something that determines the development of the discipline and looks forward to the future, which is of great guiding significance.

Pang Jialai, the Master of Mathematics, is obviously such a person.

Huangfu Lian said: "This is a paper that just came out. In addition to a special issue, "Selected Works of All Laws" includes all the records of the confrontations between the Lian Zong and the Li Zong in the past few decades, including your paper!"

"Your paper, this paper, and the other paper by the master of calculation are the first three!"

Wang Qi instantly felt the trouble that was about to come: "Really... Now I am directly in the center of the storm!"

"The center of a hurricane is often calm." Chen Youjia walked over and said: "If you don't meddle in other people's business, no one will bother you."

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

Huangfu Lian couldn't help but say: "Junior brother, don't be angry, and don't feel frustrated... That's how different the concepts are."

Chen Feng also came over and asked curiously: "What's the matter? Did Suanjun overturn your last paper?"

"No, no, I think the proof process is still perfect and meticulous. Suanjun can't find bones in eggs."

Chen Youjia's mouth corners slightly raised: "But there is a thing called 'hairy eggs' in the south, and each one has bones."

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

Suanjun did not deny Wang Qi's "Complete Law". First, because Wang Qi's proof process is perfect, 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 don't need to be thought about.

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

"That's what I knew. 'Logical tricks full of genius and creativity'... This is even more cruel than direct denial."

Yes, in the eyes of the Calculator, everything Wang Qi did was just useless tricks.

Real mathematics should not include such "tricks".

Mathematics should not be based on logic. If mathematics only evokes the laws of logic, then normal thinking should be able to accept it; if it is based on the usual laws that everyone knows, it cannot be denied unless it is mentally disturbed. But what about the reality? Can everyone master mathematics?

Obviously not. Not everyone can create mathematics; not everyone can flexibly apply a theorem proof after learning it; not everyone can understand mathematical analytical 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 national player on the chessboard, but a math problem that can make this national player white-haired overnight is nothing to a brilliant mathematician.

It can be seen from this that mathematics is not simply formed by stacking calculation power or simply arranging concepts according to deduction. It is arranged in a specific order by deduction, and the order of arrangement 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 mathematics, the intuition of ethereal fairy.

Using logic, you can only prove, using intuition, you can create.

For Suanjun, 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 through intuition guided by empirical facts.

In this paper, Suanjun reiterated his point of view.

The elder first maliciously pointed out the biggest problem in the field of logic - the unsolvable alchemist paradox. He was happy to sneer: "This thing is not only empty, but also self-contradictory."

Then, he pointed out the biggest problem of Wang Qi's complete law - first-order predicate logic cannot accurately define any mathematical concept, it is too weak. Its appearance is, on the contrary, an attack on Li Zong—their proof cannot prove the monster they created, the monster called "Infinite".

Anything that cannot be defined by finite sentences 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 are excited because of an interesting logic trick, so I came back to step on you and let you see the reality clearly'."

Chen Youjia snorted in Wang Qi's ear: "You are indeed too excited recently."

Wang Qi then realized that there was already a circle of people around him. Chen Youjia was closest to him, and the two of them were so close that they could hear each other's breathing. Chen Youjia finished watching with him. The crowd outside was represented by the crowd represented by Li Zhengguo. Most of them had heard of the name of Suanjun. They wanted to see who was criticized by Suanjun. There were also people outside asking "Who is Suanjun". Chen Feng simply stood far away because he knew he couldn't understand.

"I guess you might need this, so I just took it." Huangfu Lian shook his head and sighed: "Well, some guys in the outer gate of Shenjing have exploded. Your thesis has received completely opposite evaluations from Suanjun and Suanzhu, which is a bit stimulating for them... and someone might cause trouble for you recently, you'd better avoid it and be alone to calm down and adjust your mentality."

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

Huangfu Lian pointed at Wang Qi's finger: "You... are obviously shaking?"

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

Will this guy be frightened by the pressure from the senior master?

People around him all thought so.

Only Chen Feng shouted: "Are you crazy?"

He was the only one who could read other people's emotions, so he was the only one who discovered that Wang Qi had no fear in his heart, only the will to fight.

Mathematician Pang Jialai expected a closed, self-consistent mathematical system, so he was very opposed to concepts such as "infinity"...or should we admire his intuition? This concept will eventually break the circle he loves and let mathematics be reborn from the ashes. Did he feel all this by intuition from the beginning?

What a terrible intuition...hahahahaha, but so what?

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

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

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

Wang Qi laughed, pushed the door open, and prepared to go to the Wanfamen station to pack up his things.

Just then, Mo Zhenzhen ran over from the small entrance holding a stack of papers. He ran and shouted, "Brother, look at this..."

"I've read it, it's bullshit."

Wang Qi waved his hand and strode forward.

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This chapter was a bit difficult to write, mainly because of Suanjun's explanation of logic and intuition. This part mainly draws on the speech of Henri Poincaré and some parts of "Mathematical Enmity" ORZ, please correct me

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

So some people are worried that Suanjun will prove Gödel's incompleteness theorem before Wang Qi-this is impossible. There is still hope for the people of Suanzhu's school, but Suanjun is impossible. In his eyes, this problem is not a mathematical problem that can be used for thinking. The biggest loophole in set theory, "Russell's paradox" [more colloquial name is "barber's paradox\