Exploring Immortality Cultivation-Chapter 905 - 234: The Twilight of Genius

The proof of incompleteness and undecidability is actually quite simple, unlike many significant mathematical proofs—such as the proof of the twin prime conjecture.

Many of the Wanfa Sect disciples participating in this training camp have long since undergone multiple worldview transformations, and a slight doubt about the completeness, consistency, and decidability of mathematics has already been planted in their hearts.

Now, the obstacles preventing them from delving further are not only their long-held subjective experiences but also the interpretations rooted in classics.

Those "classics" were mostly written by the Masters of Calculation.

Feng Luoyi, a contemporary representative of the Genting Sect alongside the Master of Calculation, dealt the final blow to "completeness," causing the knowledge barriers in everyone's minds to begin shattering.

The proof of undecidability was also taught to them together.

Feng Luoyi finally said to everyone: "Currently, we have only disclosed the first stage of the thesis, 'A Discussion on Formal Undecidable Statements and Related Systems in Volume One Arithmetic Chapter of <All Laws Mathematical Collection>.' People only know about the loss of completeness. Some cultivators are not even aware of this yet.

Soon, we will also publish the second stage of the thesis 'On Computable Numbers and Their Application in Decision Theorems.' This will bring about an even greater impact.

Now, you need to utilize the results of your training over these past few months and gently inform the Wanfa Sect disciples you know that completeness and decidability are now historical. This is your current task."

"Go!"

In just a short moment, many cultivators in the training camp scattered like stars and clouds. Only a few, like Chen Youjia, were walking slowly out.

Chen Youjia was still hesitating, repeatedly thinking in her heart: "Should I send that person a message to ask… This has the greatest impact on the Li Sect. He is a Great Grandmaster in the field of Number Theory, leaning towards the Li Sect… Yet, he is also the current Sect Leader of the Wanfa Sect? Surely, he already knows… and doesn't need my concern..."

"Hey!" Suddenly, someone tapped her on the shoulder… Hmm, according to her Spiritual Sense, it was a Spiritual Body.

Chen Youjia turned around and saw Wang Qi's smiling face.

"As expected, it's you." Chen Youjia took a deep breath: "This whole situation is your doing, isn't it? Even though Mr. Feng didn't directly mention the author's name, I know, it's you…"

Wang Qi pulled Chen Youjia to a quiet corner, laughing as he said, "Of course, who else but a genius like me could make such a breakthrough?"

Chen Youjia wanted to mock him as she used to, but for some reason, she couldn't bring herself to say it.

A single thesis by Wang Qi required the Immortal Alliance to spend half a year preparing to accept.

If he isn't a genius, who dares to claim they are?

Chen Youjia pouted: "What made you think of visiting me?"

"My disruptive thesis wreaks too much havoc!" Wang Qi unscrupulously pinched Chen Youjia's cheek: "Wanted to see if you were hurt."

"Stop playing around." Chen Youjia swatted Wang Qi's hand away: "You know, I'm an Arithmetician leaning towards applications. Aside from some spite, I don't view the dispute between the Li Sect and the Linked Sect very seriously, nor do I care about that 'foundation'. Moreover… the story of 'Silver-Winged Assassin' was also your doing, right?"

Wang Qi immediately put on a moved expression: "I didn't expect us to be so in sync! Come, give me a hug!"

Chen Youjia, while being hugged, scoffed: "Stop it, I just have a good memory—speaking of which, you told me this story a long time ago, so why worry that I couldn't handle this?"

"I have confidence in you, but I still wanted to check!" Wang Qi retreated two steps: "Oh, I have some matters 'over there', I have to leave now!"

Watching Wang Qi disappear, Chen Youjia blinked and then sent a Spirit Message to her father: "How are you?"

Just four simple words.

Chen Youjia didn't expect a reply. But unexpectedly, her calculator immediately returned a prompt: "Safe."

................................................................................................

A slight smile crossed Wang Qi's lips. He used Divine Separation to meet Chen Youjia. That projection of "Wang Qi" was both his Divine Separation and kept in sync with him through the Ten Thousand Immortals Illusion Realm.

"Daoist Fellow, have you thought of something?" asked Master Turing, sitting across from Wang Qi.

Wang Qi shook his head: "No, no, just recalled some other matters. I'm still focused on this 'Heavenly Transformation Formula' idea..."

"The limit of the Heavenly Transformation Formula..." Master Turing sensed a hint of heaviness: "In the past, we said that 'Heaven-Changing Form' meant the Heavenly Transformation Formula and believed it could calculate everything... Can my truly all-encompassing algorithm, despite self-contradictions, still provide insights into the ultimate transformation? Really unexpected."

Since yesterday, the two had been discussing continuously. Wang Qi had not memorized many theses from his past life, so every proof process was independently derived by him. Engaging with this genius in dialogue brought him substantial benefit as well.

Additionally, Wang Qi found that although Master Turing was straightforward and a bit rigid in speech, he was fundamentally very approachable. Occasionally during breaks, Wang Qi would consult Master Turing about Cultivation issues.

Elder Ji, being the progenitor of calculators, also highly appreciated Wang Qi's Dataized Cultivation Method. This founder of calculators provided Wang Qi with new understandings of Cultivation.

The more they talked, the more they found common ground.

At that moment, they received a message from Feng Luoyi. Then, the scene before them changed, and they found themselves in front of Feng Luoyi.

Feng Luoyi, looking dim, said: "Wang Qi, seven days from now, I will arrange for you to give a public lecture, through the Ten Thousand Immortals Illusion Realm, to explain this incomplete doctrine to the entire Wanfa Sect. Anyone in all of Shenzhou can freely choose to listen or not. Prepare well."

After saying this, he looked downcast: "Ultimately, I must part ways with old friends."

He wasn't born of the Genting Sect, but he is also a representative figure of Genting. He has now made up his mind to fully support Wang Qi, promoting undecidability and incompleteness. To the people of the Genting Sect, this is a stab in the back to the Master of Calculation.

This is undoubtedly a betrayal.

Master Turing comforted, "Brother Yue Han, don't take it to heart. Ximen Master is extraordinarily magnanimous. Daoist Fellow He Wai'er is his direct disciple. He leaned towards Li Sect later, yet Master of Calculation did not sever ties with him, let alone you? You are on the right side now."

Wang Qi then asked, "Teacher, how is it on Ximen Master's side?"

"Other daoist fellows from the Genting Sect are tending to it." Feng Luoyi sighed, "I hope they can get through this calamity."

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In Genting, the fragrance lingered. However, even the highest quality incense could not cover up the strong scent of gunpowder here.

"It's too absurd!" a disciple from the Genting Sect cursed under his breath.

They dared not raise their voices, even using mana to concentrate the sound around them, fearing they would disturb their mentor.

No one knew whether the Master of Calculation had seen the paper, "On the Formally Undecidable Propositions in the Arithmetic Chapter of Volume One of

and Related Systems". Now they were discussing how to stabilize their teacher.

"How about this..." a cultivator from the Genting Sect sniffled, as if he had been crying, "we tell the teacher that we still have decidability..."

"No!" Fairy Ruoche exclaimed softly in alarm. Decidability will also be refuted in a few days! Using this to console will only lead to trouble!

Then Ai Kemeng took out a few more pages: "This is the part that hasn't been made public yet."

"What is this... 'On the Computable Numbers and Their Application in Decision Theory'..." The cultivator from Genting who read the paper was struck as if hit by a powerful divine skill, rendered speechless.

—Is even decidability over?

—Are there some... propositions that we simply cannot determine the truth or falsehood of?

This is too terrifying...

Many high-order cultivators shivered.

At this moment, the inner chamber door of the Geting's Study was pushed open. The Master of Calculation walked out with a perplexed expression.

"Why are you all gathered here?"

"Teacher..." "Master!" "Teacher!" "Mentor!" Everyone exclaimed together, and finally, Fairy Ruoche stepped forward, inquiring, "Teacher, the second question of the 'Twenty-Three Questions' has already been answered..."

"I know that." The Master of Calculation blinked. At that moment, he seemed like an old man suffering from memory decline, his face filled with confusion: "I just read the paper... I would know about any paper regarding the 'Twenty-Three Questions' first."

Everyone held their breath.

He Wai'er stepped forward, concerned, "Teacher, are you... are you okay now?"

"I'm fine." The Master of Calculation replied, and then he repeated, as if to emphasize, "I'm fine. Although I didn't expect... didn't expect the result to come in this form, but... the second question being solved is cause for celebration."

There was no trace of joy on his face.

"Teacher..." Madern rushed forward, "if you're feeling uncomfortable... you can talk about it." 𝘧𝓇ℯ𝑒𝓌𝑒𝑏𝓃𝘰𝘷𝘦𝘭.𝒸ℴ𝓂

"No time for that." The Master of Calculation finally smiled, "No time to complain to the heavens. Don't we have work to do?"

Everyone was puzzled.

The Master of Calculation gathered everyone here to prove completeness, decidability, and consistency. Now, consistency has been proven, but decidability and completeness have been refuted. What does Xi Baiche want to do?

"I am wondering... perhaps there are some issues with their approach. Of course, incompleteness itself may not be a problem, but can't it really be circumvented? After all, as a mathematical proof, Wang Qi's incompleteness is really too weak..."

The Master of Calculation became more spirited as he spoke. For a moment, the aura of the master of the entire Mathematics Sect returned to Xi Baiche.

However, He Wai'er felt a cold shiver in his heart.

—Is this confidence and new perspective real?

—Or is it just self-deception and self-consolation?

The hearts of Fairy Ruoche, Ai Kemeng, Madern, and other Carefree Practitioners were filled with desolation.

They felt that they were witnessing the twilight of a generation of talents, a generation of heroes.

Although in terms of age, the teacher was still young. The years he has lived compared to the lifespan he still has are very short. But, the Dao of the Master of Calculation, Xi Baiche, is already dead.

—In this turmoil, almost no one from the Wanfa Sect could seize the opportunity to rise to the top.