Exploring Immortality Cultivation-Chapter 911 - 240: An Unparalleled "Duet

Wang Qi returned to the edge of the podium and sat cross-legged, closing his eyes to rest.

In the field of theoretical computer science—the mathematical foundation of computer science, the most important recursion theory, Turing machine, and lambda calculus were disseminated throughout Shenzhou on this night.

Now, they are merely annotations of incompleteness and undecidability. However, there will always be extraordinary people who will uncover the mysteries within.

Even if we set aside the theoretical significance, this achievement alone is not insignificant.

The leap in calculator theory equates to a leap in Wang Qi's cultivation.

In the future, he will be able to rely on the resources of the Shenzhou Mathematics Sect to perfect his cultivation. Just this alone is worth the price of admission.

Not to mention the theoretical significance of incompleteness and undecidability.

He has already rewritten the framework of mathematics. Once he overcomes the forthcoming challenges, he will become a top arithmetician in Shenzhou. Whether in prestige or otherwise, he will far surpass his past self.

This is the implicit benefit.

And by promoting the Bourbaki School's ideas at this time, he can transform this "implicit" benefit into an "explicit" benefit.

The research of the Bourbaki School, which began in pure mathematics, eventually became the solid foundation for new-century physics research.

However, not everyone can see this step as he does.

More of those familiar with him are merely worried.

Mao Zimiao held her head, feeling dizzy: "Meow... Senior Sister Ai, what exactly is Xiao Qi talking about..."

Ai Qinglan's eyes also showed confusion: "Not too clear... Although I don't understand, it still feels amazing..."

She could barely comprehend what Wang Qi was talking about—yet, does this have any significance?

At this moment, Chen Feng put down his calculator, angrily saying: "This madman..."

"What's wrong? Breakthroughs in theory are a good thing!" Ai Qinglan was displeased: "Xiao Feng, you aren't the kind of person who can't stand to see friends benefit, right?"

"Benefit... This guy Wang Qi is about to get into big trouble." Chen Feng was annoyed: "Just now, because I didn't understand, I specifically asked Youjia... This kid, what he just said, basically made enemies with both the Li Sect and the Linked Sect."

"Li Sect and Linked Sect..." Ai Qinglan's beautiful eyes widened, pressing against her chest: "Let me take a moment, think about it. If I recall correctly, the leaders of Li Sect and Linked Sect are the Master of Calculation and the Mathematics Lord, respectively? Aren't they... these two, right?"

As she spoke, she pointed to the phantoms in the illusion realm.

Chen Feng nodded: "It's precisely those two elders sitting to Wang Qi's left and right, the peak Carefree Practitioners... Behind them are their disciples, totaling dozens of Carefree Practitioners."

Ai Qinglan slapped her forehead: "This kid really is crazy... No, no, being crazy is more like his style... This is just normal behavior... normal behavior..."

Offending both mainstream sects at once is equivalent to angering more than half of the Wanfa Sect. Isn't this madness?

Someone asked, puzzled: "Are Senior Brother Wang's theories incorrect?"

Chen Feng was a kind person but not a fool. He sighed deeply and said: "Why did the previous leader of the Genting Sect, Cloud King Ke Lanyin, lose his Dao Heart? It was because of a debate with the Mathematics Lord... Even if those predecessors don't intend to take such extreme measures, it's very easy for so many arithmeticians to ruin his reputation."

Mao Zimiao's heart tightened slightly: "Then... what should we do?"

"Let's hope he manages to overcome the next challenges with the help of the two Carefree Practitioners, the Great National Player of the Human Realm and Elder Ji?" Chen Feng said uncertainly.

He understood Wang Qi's nature well. Expecting Wang Qi to abandon his ideas is almost impossible. He will inevitably face countless challenges from Carefree Practitioners soon.

In the Wanfa Sect, Bao Xiaofeng clenched his fist, while Bao Xiaoya closed her eyes, too nervous to watch.

And throughout Shenzhou, more low-level disciples of the Wanfa Sect were secretly praying and cheering for Wang Qi. They had just stepped into the field of mathematics and had not yet gained the persistence of their predecessors, nor had they been too affected. They viewed Wang Qi not with the aversion of their predecessors, but instead with a sense of admiration that a true man should aspire to.

In a mysterious secret realm, Taiyi Heavenly Venerable also sweated nervously for this young man.

Now, perhaps only Chen Youjia still firmly believes in Wang Qi.

Only she thinks that even if Wang Qi is overwhelmed by the upcoming accusations, it would not damage his heart of courage and diligence.

After the second lecture was completed, Feng Luoyi closed his eyes, sighed deeply, and announced: "Now, fellow Daoists may begin to ask questions."

In the Genting Sect's formation, Min Kefu, an intimate friend of the Master of Calculation and a "True Universe Phase," stood up and asked solemnly: "Have you found an unprovable statement about mathematics existing in reality?"

Wang Qi shook his head: "No."

True to being one of the most preeminent arithmeticians of this lifetime, he quickly exposed the weakness in the incompleteness proof.

Godel spent his entire life failing to find a statement containing actual mathematical content that was unprovable. This is also a reason why the incompleteness theorem has few adherents.

The mathematics world on Earth has not encountered such statements for nearly a hundred years either.

— In fact, according to Godel's idea, humanity will not encounter such statements for quite a long time. They must exist in the unknown parts of mathematics, hidden amidst layers of fog.

Many mathematicians do not pay attention to something that doesn't contain actual mathematical content. 𝘧𝓇ℯ𝑒𝓌𝑒𝑏𝓃𝘰𝘷𝘦𝘭.𝒸ℴ𝓂

Min Ke-Fu sneered, "Then, is your proof really as significant as you claim?"

"I merely deduced the existence of such statements, which doesn't mean I know these statements," Wang Qi said. "It's like knowing someone is dead; it's easy to determine if it was murder or suicide, but much harder to identify the perpetrator."

"Yes, I admit your reasoning process is indeed strong. However, I fail to see its practical significance."

Since Wang Qi was aware of this weak point, how could he not prepare for it? He had long prepared an answer to this question, going along smoothly: "When the arithmeticians of the Middle Ages studied conic sections, they didn't know their theories would become one of the foundations of 'The Calculation of the Great Dao.' Nor do we know what this incomplete proof process will become in the future — when will we discover a statement with actual mathematical reasoning that is undecidable? I don't know, and it's impossible to know. This question can only be left to time. Let time answer."

"I've also said that mathematical incompleteness lies not in the known, but in the unknown. When facing the unknown, we will never know what we might encounter."

Wang Qi could only say this. Before the Forcing Method appeared, such criticisms will always exist.

This answer obviously could not satisfy all the dissenters. One by one, top arithmeticians stood up to refute Wang Qi. Among these refutations, some hit the mark, while others were ineffectual, and Wang Qi countered them one by one.

However, Wang Qi was not completely isolated and helpless.

Suddenly, some arithmeticians found themselves unable to speak — they couldn't open their mouths in this Ten Thousand Immortals Illusion Realm! At this moment, Master Turing stood up, cupping his hands in greeting in all directions, smiling warmly, "Gentlemen, may I be permitted to ask a few questions?"

Only such a strong Carefree Practitioner, who had immersed himself in the field of calculators for hundreds of years, could suppress many with one presence in this Illusion. Even if someone was dissatisfied, they could only choose to listen obediently at this time.

Master Turing stood up and asked Wang Qi, "Daoist Fellow Wang, I would like to discuss the limits of functions with you..."

With Turing's words, everyone was stunned.

This... which side exactly is this Carefree Practitioner on?

Seeing him sitting with Feng Luoyi, wasn't he supposed to be here to help Wang Qi?

Why are his questions sharper than most people's?

Wang Qi smiled, "I also have some new ideas recently..."

After Wang Qi answered the question, Master Turing immediately posed a second question.

"Have you considered an axiom system with an infinite number of axioms?" Turing asked, "Each time a new axiom is added, the new axiom system becomes stronger than the original. Each axiom system interprets the previous one. In this way, every system is consistently non-contradictory. Thus, we repeatedly add countable and infinite axioms. This way, no matter how many axioms we use, there always exists a stronger axiom that proves the consistency of the previous axioms, wouldn't this system be considered unassailable?"

"I think so too. Unfortunately, an axiom system with infinite axioms is meaningless," Wang Qi said. "We must first be aware of all the axioms within an axiom system to make judgments based on it. If an axiom system has infinite axioms, we cannot know what it can state or judge..."

The exchange between the two became increasingly fluent and smooth. Gradually, the disturbances around them subsided.

Master Turing was clearly using a more systematic approach, from a deeper perspective, to question out the various inadequacies they had noticed.

Even with such premises, Wang Qi was still able to respond fluently, and numerous theorems derived from incompleteness, supplements to incomplete proofs, and new calculator technologies were all displayed in the Q&A session between Master Turing and Wang Qi.

Min Ke-Fu snorted, disdainfully muttering in a private chat, "Just a double act... those two must have rehearsed. Turing is just a plant!"

He Wai'er smiled wryly, "But even if he's a plant... it's extraordinary at the very least. I certainly can't articulate anything."

The Q&A between Wang Qi and Master Turing aimed to show that their theory was systematic.

The theme of this discourse was set on incompleteness and undecidability. This couldn't be changed. What they were doing now was to showcase their level in the Q&A segment and silence the critics.

Indeed, even if everyone could see that these two were putting on a double act, so what?

Anyone asking questions now is ten to one likely to run into a sword edge and disgrace themselves!

This was an unparalleled and unmatched double act in history!

Master Turing unabashedly turned this Q&A into a personal discussion between him and Wang Qi. Both of them were stimulated by inspiration, and their discussion gradually strayed from the predetermined content, starting to delve deeper.

At this point, there were very few able to interject.

Mathematics Lord Pang Jialai watched the two in the Q&A, shook his head, and merely smirked, "This declaration makes a loud noise but isn't too foul."

On the other hand, Master of Calculation Xi Baiche had not said a word from start to finish.