NOVPUB"On the New Advances in the Foundations of Mathematics," such a grand yet hollow title for a paper. Publications like "**New Advances in the Field/Latest Achievements/New Applications of Technology/New Insights" generally consist of gathered information, cut and paste material with some of one's own opinions poorly cobbled together into an article—it's a bit of a stretch to even call them papers. Major journals on Earth don't fancy publishing such.
However, when written by a Great Power, that changes everything.
A true Mathematics Lord, even when writing a review or literature survey, contributes significantly to the discipline's development and provides a far-reaching vision of the future, offering profound guidance.
Pang Jialai was certainly such a figure.
Huangfu Lian said, "This is a newly published paper. 'All Laws Selection' devoted an entire special issue, including your paper, and recorded all the confrontations of the Zongli Sect over the past few decades!"
"Your paper, this one, and another by the Master of Calculation are the first three papers!"
Instantly, Wang Qi had a premonition of the impending trouble: "Really now… I'm directly in the eye of the storm, aren't I?"
"The eye of a hurricane is often calm," Chen Youjia walked over and said. "If you don't meddle too much, no one will trouble you."
Wang Qi shook his head and began reading the paper by Pang Jialai.
Huangfu Lian couldn't help saying, "Junior Brother, please don't get angry or feel down… It's just a different philosophy."
Chen Feng joined in, curiously asking, "What's the matter? Did the Mathematics Lord refute your last paper?"
"No, not at all, I think the proof process was absolutely flawless and meticulous. The Mathematics Lord couldn't pick bones out of an egg."
Chen Youjia's mouth turned up slightly: "But down south, there's something called a 'hairy egg,' every one of them is full of bones."
This time, Chen Feng ignored Chen Youjia's teasing. He was deeply engrossed in the paper.
The Mathematics Lord did not invalidate Wang Qi's "Completeness Law." First, because Wang Qi's proof was impeccable; secondly, and more importantly, he felt it was wasteful to spend his precious intelligence on considering Set Theory and related issues.
To these tyrants, certain things clearly require no thought.
Mathematics is established, coherent, complete—this is the truth, not logic reasoning.
"I knew it, 'logical trickery filled with genius creativity'... That's even more ruthless than outright denial."
Indeed, in the eyes of the Mathematics Lord, everything Wang Qi did was nothing more than useless tricks.
Real Mathematics should not include such "tricks."
Mathematics should not be based on logic alone. If Mathematics merely evoked logical laws, then normal thinking should be able to accept it; if it were based on common rules understood by everyone, it would be undeniable unless one were mentally deranged. But is that the case? Can everyone master Mathematics?
Clearly not. Not everyone can create Mathematics; not everyone can apply a proven theorem flexibly after learning it; not everyone can grasp the thinking behind Mathematical Analysis, despite repeated explanations. And most of those who can keep up with analytic thinking still find it difficult.
A true Mathematician may not be able to defeat a Go master on the board, but a math problem that could make the master turn white-haired overnight is nothing remarkable to a skilled Arithmetician.
Accordingly, Mathematics is not a simple stacking of computational power or arranging concepts in a deductive fashion. It is an arrangement of deduction in a particular sequence, where the sequence is more important than the elements themselves. If someone has a certain feeling for this sequence, or call it Intuition, they only need a glance to grasp the entirety of the reasoning. Then such a person will not worry about forgetting an element because each element is specifically placed within this array, and it doesn't require one's memory to hold on to it firmly.
This is the Intuition of Mathematics, an ethereal, almost celestial intuition.
Using logic, one can only prove; using Intuition, one can create.
For the Mathematics Lord, this kind of Intuition could even encompass physical problems. The physical laws we know and understand are not the direct induction of experience, they can only guide experience and create through Intuition.
And in this paper, the Mathematics Lord reaffirmed his views.
The elder first maliciously pointed out the biggest problem in the logical domain—the unsolvable Alchemist's Paradox. He ridiculed with glee: "Not only is it vacuous, but it contradicts itself too."
Immediately afterward, he pointed out the biggest problem with Wang Qi's Completeness Law—first-order predicate logic could not precisely define any mathematical concept, as it was too weak. Its emergence was instead a strike against the Zongli Sect—their proofs still couldn't prove the monster they had created, that so-called "Infinite" monster.
Anything that cannot be defined with finite sentences, is meaningless and should be cut out.
"Ts, this is practically a declaration of war!" Wang Qi said with great dissatisfaction, "It's basically saying, 'I heard you bunch of monkeys who learned to use stone tools got excited over a funny logical trick, so I'm back to step on you and show you the reality.'"
Chen Youjia hummed softly beside Wang Qi's ear, "You've indeed been overly excited lately."
Only then did Wang Qi realize that a circle of people had formed around him. Chen Youjia was the closest, and the two were so near that they could hear each other breathe. Chen Youjia was the one who had finished reading along with him. On the outer ring were, with Li Zhengguo as their representative, the onlookers. Most of them had heard of the Mathematics Lord and wanted to see who was the person that had been criticized by the Mathematics Lord. Meanwhile, on the outskirts, people were asking, "Who is the Mathematics Lord?" Chen Feng simply stood farther away, for he knew he didn't understand.
"I guess you might really need this, so I brought it directly over," Huangfu Lian shook his head with a sigh, "That, some of the Outer Disciples of Divine Capital have already been thrown into chaos. Your paper receiving completely opposite evaluations from the Mathematics Lord and the Master of Calculation is somewhat stimulating for them... and someone might look for trouble with you lately, so it would be best for you to avoid it for a while and be alone, to adjust your mentality."
"Adjust my mentality? Is it necessary?" Wang Qi found it quite strange.
Huangfu Lian pointed at Wang Qi's hand, "You... your hand is clearly trembling, isn't it?" 𝙣𝒐𝙫𝙥𝙪𝙗.𝙘𝙤𝙢
It was then that Wang Qi noticed his fingertips had been trembling since a moment ago.
Could this guy be scared by the pressure from a senior expert?
That's what the surrounding people thought.
Only Chen Feng shouted, "Have you gone mad?"
Only he could read others' emotions, so only he realized, not a trace of fear in Wang Qi's heart, only a fighting spirit.
Mathematics Lord Pang Jialai was expecting a closed, self-consistent mathematical system, hence he was very averse to concepts such as "Infinite"... or should one admire his intuition? This concept, in the end, was still going to break through his beloved circle, allowing mathematics to be reborn from the ashes. Did he feel all this from the very beginning through intuition?
Such terrifying intuition... Hahaha, but what of it?
"We must know, we will know," Wang Qi murmured, then packed up his paper and said, "Boss, I'd like to take a few days off, and you can deduct from my recent wages, okay?"
Chen Feng said anxiously, "Don't be rash!"
Finding such a good research 'dog' was not easy, and he wasn't done making use of him.
Wang Qi laughed heartily, pushed the door open, and prepared to go to the Wanfa Sect's residence to pack up his things.
At that moment, Mo Zhenzhen came running over with a stack of papers, shouting as he ran, "Senior Brother, look at this..."
"Already read it, it's all nonsense."
Wang Qi waved his hand dismissively and strode forward.
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This chapter was a bit difficult to write, mainly the part about the Mathematics Lord's exposition on logic and intuition. This part mainly draws on Henry Poincaré's speeches and parts of "Mathematical Encounter Records" ORZ, and I ask the experts to correct me.
"To apply logic is to prove, to apply intuition is to create" is a famous saying of Poincaré, while the last phrase Wang Qi recites, "We must know, we will know," is Hilbert's belief. Wang Qi's final comment is not personal arrogance, but rather a true reflection of the incompatibility between two factions of mathematicians. In Poincaré's ideal, mathematics is a closed, finite system. He does not allow concepts like "Infinite" to enter mathematics—but in Wang Qi's era, the study of infinity is part of mathematics, even though logic involving infinity seems to be in violation of common sense.
Thus, some people are worried that the Mathematics Lord might prove Godel's Incompleteness Theorem before Wang Qi—that is an impossibility. There might be hope for people from the Master of Calculation's camp, but it's impossible for the Mathematics Lord. In his eyes, this issue is simply not a mathematical problem that can be pondered upon. The biggest flaw in Set Theory, "Russell's Paradox" [more colloquial term is "Barber Paradox"], was discovered by Russell, a supporter of Set Theory, not by Henry Poincaré. The mathematical capabilities of the latter far exceed Russell's, yet he did not deign to consider such issues.
Regarding the 'monkey' joke—according to diaries and manuscripts discovered after Henry Poincaré's death, he indeed regarded those who did not understand mathematics as monkeys. Perhaps, in his view, Russell was just a high-level monkey that had mastered stone tools?
Lastly, "Already read it, it's all nonsense," is a Three-Body problem joke, cough cough.
And lastly lastly... may I ask for a recommendation vote... I'm really embarrassed to ask!
