Exploring Immortality Cultivation

"At present, addressing the field of mathematics with a comprehensive view seems inherently fraught with insurmountable difficulties from the start,

because its subject matter is extensive, complex, and ever-changing. Just like all other fields of mathematics, the number of arithmeticians and related mathematical publications has grown enormously since the establishment of the Wanfa Sect—this is an ancient issue."

On the stage of the Thousand Mechanism Pavilion, Wang Qi spoke eloquently.

"As soon as the concept of mathematics sprouted, our predecessors had already raised this issue. Indeed, setting aside applied mathematics, there has always been a duality in the origins of geometry and arithmetic. Arithmetic initially was a branch of mathematics concerning discrete quantities, whereas geometry has always dealt with continuous quantities; these two aspects have led to opposing viewpoints since the discovery of irrational numbers. Moreover, it was precisely the discovery of irrational numbers that caused the initial attempts to unify this field of mathematics, specifically the arithmetization by the Ancient Separation Sect during the Middle Ages, to fail."

This was the true thought, the true program of the Bourbaki School, not merely a framework borrowed by the Master of Calculation Xi Baiche, but new structuralist mathematics.

The first to feel dizzy were the guests from other sects present at the venue. Their proficiency in mathematics was not very deep, and they were hardly aware of the dispute between the Zongli Sect and the set arithmetic route.

Xiang Qi looked at Wang Qi with an inexplicable expression. In her mind, Wang Qi was still the ignorant youngster from a year ago, who was at most somewhat impressive among the younger disciples, but now...

What in the world was he talking about...

"Has he become just like that bastard Junyu?"

However, the expressions of the arithmeticians from the Wanfa Sect gradually changed.

The arithmeticians from the Genting Sect had unanimously displayed a novel line of thought in their recent papers, providing a brand-new perspective for understanding mathematics. Until now, most brilliant mathematicians had grasped this new approach but lacked the capability to articulate it systemically.

Many were speculating that some great mathematician from the Genting Sect had written a programmatic paper or delivered an internal speech, proposing new guiding thoughts.

And were these words Wang Qi was now speaking... that legendary program? His speech was logically coherent and well-structured, definitely not some vague 'thought' or 'inspiration'! Where had he gotten this from?

What exactly was his relationship with the Genting Sect, and with the Master of Calculation Xi Baiche? Had he formally become a disciple of the Genting Sect?

The Grandmasters all looked uniformly toward Xi Baiche, standing in the center of the hall, hoping to perceive something from the face of the former sect leader.

But a more ingenious mathematician, such as the Mathematics Lord Pang Jialai, watched Wang Qi with puzzlement.

"This isn't Xi Baiche's path... No, this shares a 'skeleton' with recent papers from Genting, but its 'flesh and blood', its 'soul' is different from Xi Baiche's?"

"Is it impossible for Xi Baiche to suddenly abandon his own path and take this one? Is this a path that the kid has proposed using Xi Baiche's framework?"

"Or is it..."

Meanwhile, Xi Baiche and Feng Luoyi stood shoulder to shoulder. Feng Luoyi slightly shook his head: "He's still persisting on his own path."

"It's not necessarily wrong. Moreover, the path he's taking naturally leans towards ours, and it can complement the path we in Genting are currently following," Xi Baiche expressed nonchalantly. He wasn't particularly fond of the theory Wang Qi was expounding, but the Mathematics Lord would dislike it even more.

At that moment, Wang Qi began to discuss another topic—research methods in mathematics: "Past arithmeticians could only consider the special problems within their own narrow domains, but I think we also need to explore the commonalities between them, which is the unity of mathematics. Mathematics is not merely a simple sum of various subjects; there are intricate connections between different fields of mathematics, and not all problems hold the same value. The most valuable mathematics is that which is closely related to various fields, while more isolated problems are often of little significance."

The mathematician Diadoche of the Bourbaki School once classified mathematical problems into six categories, namely unsolvable problems, problems with no extensions, intrinsically meaningless problems that generate new methods during research, problems that generate general theories, problems from declining fields, and meaningless problems. Among these, the first and second types are isolated and have little connection to the overall field of mathematics; even if solved, they would hardly advance the development of mathematics as a whole, the third type, though isolated, generates new mathematical methods during the resolution process, which can be used to solve other problems.

The truly valuable problems that can propel the entire mathematical system are still the fourth and fifth types.

Hearing this, Feng Luoyi chuckled bitterly: "Additionally, this kid is somewhat narrow-minded, directly negating Chen Jingyun's path."

The Bright Pearl Calculation, the Goldbach Conjecture, is precisely a typical third-type problem; this isolated mathematical theory, even if proved, would not significantly promote number theory.

"Doesn't this still affirm the significance of the Chen Clan's sieving method?" Xi Baiche smiled lightly: "I've thought about these things, you have too, and even the esteemed elder Gao Si has mentioned something similar, and even Mr. Pang over there has had these thoughts. This kid just systematically articulated similar thoughts."

The quest of two generations of mathematicians from the Bourbaki School spanning half a century, if detailed, would take a year's time to complete. But if only a simple discourse is required, it's something that can be discussed briefly.

Soon, Wang Qi concluded: "… The word 'form' only in this context allows us to call the axiomatic approach, 'formalism.' It bestows unity to mathematics not through formal logic but through 'skeleton,' it is the negative entropy in the organic development process throughout its entirety, a conducive and prolific Seeking Dao Artifact. Perhaps since the emergence of 'group theory,' we ought to have accepted this—that in some domains, we are replacing computation with concepts."

In utter silence, Wang Qi stepped down from the stage. After a long while, Xi Baiche gently clapped, "Very impressive."

Following his lead, the cultivators in the hall offered sparse applause. But by now, no one was concerned about this.

Perhaps they had already vaguely sensed that the mathematics of Shenzhou was about to turn a new page. (To be continued. If you enjoy this work, we welcome you to vote for it on qidian.com, your support is my greatest motivation. Mobile users, please read at m.qidian.com.)