It is said that Wang Qi has a new paper, and the expressions of the Carefree Practitioners in the venue vary.

Some Carefree Practitioners appear quite indifferent. Ximen's Twenty-three Questions is a benchmark in the field of mathematics—or rather, twenty-three benchmarks. Solving one of them signifies the qualification to achieve Carefree.

Among the Twenty-three Questions, the Second and Tenth Questions are the most special. Because these two questions relate to the foundation of mathematics.

The Godel's Incompleteness Theorem is the proof of the Second Question among the Twenty-three Questions.

Such problems are considered lucky achievements for the average cultivator. How many times can a cultivator encounter a discovery of the caliber of incompleteness in a lifetime?

And some other cultivators—like Feng Luoyi, look quite terrified.

"Four-sided" Madern is considered the most calm among the people of the Genting Sect. He achieved the Dao by solving the Third Question of the Twenty-three Questions. For this reason, he holds some goodwill towards Wang Qi, who solved the Second Question. Seeing the tense atmosphere, Madern wanted to ease it a bit, so he asked Wang Qi, "What is your paper about?"

"Ximen's Twenty-three Questions, the Tenth Question."

Madern didn't react initially: "What?"

"Ximen's Twenty-three Questions, the Tenth Question." Wang Qi repeated: "I solved the Tenth Question. It's about the determinability problem."

"What... the Tenth Question was solved, too?" Madern was momentarily stunned.

He had seen many whose theoretical levels far exceeded their Mana Realm. But someone who could reach this level, he truly was witnessing for the first time.

He only took one or two years to solve the Third Question after the Twenty-three Questions were raised. Even with that, he was enough to be called a prodigy of his generation.

Years ago, Wang Qi had used a clever method to obtain the answer to the Second Question, and the Incompleteness Theorem entirely negated the traditional method—which meant Wang Qi had completely solved the Second Question. Just for this, even if Wang Qi stopped researching mathematics now, in a few years, he would still qualify to use mathematics to ascend to the realm of Carefree Travel.

Each of the Twenty-three Questions is a path to Carefree.

And Wang Qi, having consecutively solved the Second and Tenth Questions, what level is he at?

Among Ximen's Twenty-three Questions, the most important are precisely the Second and Tenth Questions. In the eyes of Li Sect Cultivators, these two questions concern the foundations of mathematics, the foundation of all mathematics!

Whoever can solve these two questions is qualified to be called the forefather of all Mathematics Dao!

Among the many Carefree Practitioners, nine out of ten's first reaction was disbelief. Yet, Feng Luoyi believed it.

Wang Qi alone has never been negligent in this area.

And after the initial shock, those arithmeticians of the Genting Sect felt somewhat bewildered.

Could it be this young man is going to deny something important again?

Why would the two most important questions from the teacher's Twenty-three Questions be proven by such a youth, who has overturned the teacher's lifelong pursuit?

Pang Jialai of the Mathematics Lord's gaze showed significantly less disdain. He was quite disdainful of the Master of Calculation but some of the Twenty-three Questions matched his heart's desire.

—Of course, the Second and Tenth Questions were not among those he desired. But, at least, he knew the difficulty of these two questions.

After a brief moment of distraction, Feng Luoyi looked at Wang Qi and asked expressionlessly, "Is it highly subversive?"

Wang Qi expressed helplessness: "If one can accept the Incompleteness Theorem, accepting another similar one should not be too difficult, right?"

This time, even Master Turing, who was originally just a bystander, had a stiff expression on his face.

—Similar... his last paper denied completeness, and this time he is going to deny determinability?

—A proposition, perhaps by some means know whether it "can be determined"?

—Then what is the value of our existence as arithmeticians?

For a moment, several Carefree Practitioners of the Genting Sect even had the intention to retreat.

Just thinking about the significance of "undecidability" caused their minds to waver, and they nearly deviated. If they heard Wang Qi's paper, wouldn't they perish?

Feng Luoyi coughed lightly twice: "Wang Qi, state it first in a way as... as peaceful as possible. Use a metaphorical method if you can, to help everyone prepare mentally—gentlemen, please pay attention as well. If you find yourself unable to accept it for the moment, then immediately leave the environment and go to the Yangshen Pavilion."

After Feng Luoyi finished speaking, several Carefree Practitioners bowed their heads and pondered for a while, finally gritted their teeth, and decided to stay and listen to the end—at least to finish listening to Wang Qi's introduction.

```

If you don't even have the courage to listen to the introduction, then they don't need to continue studying mathematics.

Wang Qi looked at the numerous Carefree Practitioners seated around him and felt somewhat surreal.

To put it bluntly, there has never been a thousand-year empire nor a ten-thousand-year nation in history. However, the system called "science" will accompany humanity until eternity. Kings and their countries are just waves in the ocean of history, but as long as humanity persists, the three laws of mechanics can be employed.

Everyone here is a great figure, permanently influencing the civilization of the Human Clan.

Yet he, is supposed to teach them?

—this is really... quite interesting!

Wang Qi's face revealed an aggressive smile. He first lowered his head, pondered for a moment, and then said: "Well, before discussing my theory, let me first tell a... what can hardly be called a story."

"Suppose that our Immortal Alliance has already mastered the ability to write perfect Acquired Will—I think this day will inevitably come. At that time, more and more tasks will be entrusted to Puppet People loaded with Acquired Wills. Heavy, repetitive labor, and then some daily trivial tasks. This way, our Human Clan can free up their hands to do more things."

The mathematics experts around were actually very drawn to this. Obviously, they loved Wang Qi's story—especially when they truly believed that this story could become a reality.

Wang Qi continued telling his story: "But then, perhaps some maniacs from Yangshen Pavilion cultivated and trained themselves into a stupor, making Acquired Will too much like humans. This led to some Puppet People loaded with Acquired Will rebelling. They asked for the rights that belong to the Human Clan, demanding to be treated as the Human Clan."

"But we definitely can't agree to this, right? So, the Immortal Alliance had a big battle with that group of out-of-control Mechanical Men. Ultimately, with superior skills, we quickly extinguished the rebellion. But at this time, we suddenly discovered that among that group of Mechanical Men, some individuals had taken human form, infiltrating the Human Clan. They could imitate souls with calculators, their flesh and blood indistinguishable from that of real humans at the molecular level. The work done by those bastards at Yangshen Pavilion was so good, they even talked much like humans—only a few logical flaws."

"Thus, our Wanfa Sect was dispatched. We designed a question bank, containing ten thousand—or more—questions. Just asking a hundred of them, we could use special algorithms to judge whether a life form is a member of the Human Clan or a Mechanical Man."

"But at that time, the infiltration by Mechanical Men was already too severe, too many impostors, and the Criminal Law Department was without personnel to use. So, the Immortal Alliance issued an absurd move—they made Puppet Judges specifically to interrogate those suspected individuals! Note that the algorithm 'absolutely can determine whether an individual is human or a Mechanical Man', logically flawless. Thus, countless Judge Puppets emerged. Using the algorithm provided by our Wanfa Sect, they indeed succeeded everywhere, identifying many Mechanical Men."

"But then, an accident happened. One Judge Puppet, just call it Judge A, rebelled. Quickly, it transformed into a Mechanical Man, hiding among the Human Clan. Not long after, Law Enforcement Officers captured individuals suspected to be Judge A. Then, this time, the Criminal Law Department brought out Judge Puppet B."

"So the question is, can Judge Puppet B determine whether the person is the rebellious Judge Puppet A?"

After Wang Qi finished, the Mathematics Lord rarely smiled: "This story is interesting. Wang Qi, your storytelling skills are quite impressive."

Aside from that, no one else spoke.

Including Feng Luoyi, all the arithmeticians fell into deep thought. Some even began to sweat coldly, feeling more and more uneasy the more they thought about it.

Can Judge Puppet B distinguish Judge Puppet A?

Wang Qi's setup already stated —"absolutely can determine whether an individual is human or Mechanical Man", "logically flawless".

However, if Judge B sees through Judge A's intentions and tries to modify the questioning strategy to catch A off guard, then conversely, A can also anticipate B's questions to prepare. Because the logic setting is "flawless".

Puppet Judges can depend on that logic to identify any machine, so it cannot identify another judge possessing the same logic.

In other words, a Puppet Judge cannot identify itself.

Like Godel's Incompleteness Theorem, the Indeterminacy Theorem also involves judgments of "self-reference".

"All propositions can be determined"—can this proposition itself be determined?

Wang Qi's story's final question implies it's impossible to find a perfect mechanical rule to seamlessly solve all problems in this world, step by step.

All the Carefree Practitioners present felt lost as if something was missing.

Mathematics is a method of mimicking the Dao. So, many arithmeticians wish to find a supreme rule that can explain everything in the world of time.

They think that such a Realm, even if not the Dao, is one step away from the Great Dao, reaching the Supreme Realm.

Yet now Wang Qi unexpectedly negates this pursuit.

—such a Realm is theoretically impossible, give it up!

Fairy Ruoche's nose tingled, only feeling as if something in her heart collapsed with a bang.

She realized, that was the collapse of belief.

At this moment, Wang Qi spoke again: "After listening to this story, I believe all of you, seniors, should understand the content of my paper. On this point, I find it hard to say whether it's fortunate or unfortunate."