Exploring Immortality Cultivation-Chapter 913 - 242: Yesterday and Today

"Although Master Turing has already used the metaphor of the 'Great Dao Artifact' to disprove the omnipotence of the 'Great Dao Sacred Sound,' today, I still wish to say—we can still believe that one day we will face the Great Dao directly and listen to its true sound."

"If anyone condemns us for being arrogant, if anyone orders us to fulfill our human obligations and abandon the pursuit of the Immortal Dao, if anyone asks why we stubbornly persist on this glacial permafrost where no one else but our fellow Daoists can survive, then we can stand tall and loudly respond—for our Dao to last forever!"

With an impassioned tone, Wang Qi concluded this lecture.

There was still no applause. However, many remained immersed in Wang Qi's earlier discourse.

If incompleteness and undecidability disrupted the existing system, then Wang Qi's speech was a reconstruction on the ruins of that disruption.

He proposed directions in which Shenzhou Mathematics might still break through within the dual constraints of "incompleteness" and "undecidability," and provided detailed ideas for pursuit.

After shattering the confidence of the Wanfa Sect, he then pointed out to the other cultivators of the sect which direction they should strive in next, and how Mathematics should develop.

Everyone can express their opinion on "development" based on their own insights. However, not everyone's views can gain widespread recognition. If one speaks without receiving acknowledgment, then it becomes a subject of ridicule.

The last person who did this and succeeded was Master Xi Baiche. The presence of the Ximen Twenty-three Questions turned the entire inclination of the Wanfa Sect. The wind of "always speaking of topology" within the sect, during the era of the Mathematics Lord's dominance, gradually diminished, as more cultivators began to believe that set theory constituted the foundation of mathematics. The Li Sect progressively turned the disadvantage brought by the Mathematics Lord into an advantage, triumphing over the Li Sect in the struggle.

A few seasoned cultivators instinctively wanted to rebuke Wang Qi and ask, "Why are you qualified?" or "Who do you think you are?". But before they could speak, they realized—no one else around had spoken up.

The domain Wang Qi addressed started from the fundamentals of mathematics and delved into every aspect of the field. And in this domain of mathematical reasoning, no one could rival him.

—The Mathematics Lord sincerely believed that the foundation of mathematics was beyond logic, unworthy of study. He had no desire to research this aspect, nor did he deign to study set theory. And the Master of Calculation… had just been toppled by this young man!

—Perhaps Feng Luoyi and Master Turing could compete with Wang Qi on this topic, but they certainly would not oppose him at this moment.

No one dared to respond!

And the various cultivators of the Geting Sect once again showed complex expressions mixed with resentment and gratitude.

Wang Qi, he was truly of the Li Sect. In this summation of the lecture, he indeed displayed some influence of the Geting Sect.

"The Master of Calculation's Geting Sect" was destined to end. The Geting House would most likely be handed over to He Wai'er, a mathematician of the Serial Sect. However, the efforts of the Geting Sect during the era led by the Master still continued in another form.

Even though this was not the way they had hoped.

And He Wai'er's perspective, differing slightly from his peers, questioned.

"From the perspective of the Li Sect, reorganizing the entire known domain and then proceeding from this 'discovered no problems' known domain… He clearly destroyed the Li Sect's confidence, yet still upheld the path of the Li Sect?"

The ideas of the Bourbaki School couldn't possibly be fully conveyed within a lecture lasting less than two hours. What Wang Qi truly presented was only a general direction. Thus, currently, only a very few mathematicians could discern the rigorous system within Wang Qi's directions.

—Unexpectedly, could it be that this guy is a steadfast believer in the Li Sect?

"In the past, we were groping in the dark for the truth. But now, we have learned, there is a cliff between this darkness. The finite is on this side, the infinite on the other. Henceforth, we must be cautious of the barrier between finite and infinite." Feng Luoyi's words marked the end of this lecture.

The first to leave were members of the Shaoli Sect led by the Mathematics Lord. Subsequently, figure after figure disappeared from the venue, and soon, in place of the throng of people, only a few remained.

Besides Wang Qi, Mana, and Master Turing, only Master Xi Baiche and a few core members of the Geting Sect stayed behind.

At this moment, the Master of Calculation, who had remained silent throughout, finally stood up.

Feng Luoyi unconsciously clenched his fists. He finally felt a hint of tension.

The current Master of Calculation, even if he suddenly died, it would not be surprising.

The loss of the Dao Heart signifies a change in thought. For high order cultivators whose thoughts and mana are already fully integrated, this indicates an obstruction in mana circulation.

This harbors the danger of death!

The Master of Calculation, even if he suddenly fell, it would not be surprising.

Wang Qi watched as this respectable elder took step after step towards him, swallowing a mouthful of saliva.

After approaching Wang Qi, the Master of Calculation raised his hand. This action itself seemed to have exhausted all his strength, making it exceedingly difficult.

Here is the Ten Thousand Immortals Illusion Realm, where movement of the "body" is sustained by consciousness. An inability to move the body indicates that one's inner thoughts cannot manifest in the Illusion Realm.

The Master of Calculation's consciousness had already begun to grow chaotic.

Suddenly, the elder's body trembled, and his actions became smooth again. He gently placed his hand on Wang Qi's shoulder and softly praised, "Well done… well done…"

An unexpected commendation.

"Teacher, how are you now?" Several disciples on the wall asked with concern.

Xi Baiche touched his chest and bitterly smiled, "Dao Heart... is probably lost. I truly cannot accept the principles of incompleteness and undecidability, yet I can't deny them either. There's a significant conflict between cognition and belief... the Dao Heart is no more."

"Teacher..." The members of the Geting Sect lowered their heads.

Even though they had mentally prepared for this day long ago, and even though they understood that this was the best outcome, they still felt immense sorrow when a prodigy and the leader of the Geting Sect truly lost his Dao Heart.

"It's no one's fault." Xi Baiche shook his head, "Perhaps it's my own dullness to blame."

Then, Xi Baiche turned to Wang Qi once more and said, "I must say, you did well, child."

Wang Qi's tone inevitably grew more somber, "Without the efforts of Senior Xi and everyone in the Geting Sect, I would not have achieved this accomplishment..."

Xi Baiche shook his head, "It's not just about your incompleteness and undecidability, but also your recent lecture—it's excellent."

On Earth, the Bourbaki School inherited part of Hilbert's ideals, formalizing the known calculations, and in this aspect, went the farthest,

and Master of Calculation Xi Baiche also saw this point.

"Originally, I thought that after this event, the Li Sect would be finished. However, since you are here, there's no need to worry about anything."

Feng Luoyi sighed deeply and asked, "Master Ximen, what plans do you have for the future?"

"I don't plan to give up on the path of formalization for now, at least not until the known parts are formalized. As for the rest..." the Master of Calculation smiled, "Yue Han, my Dao Heart is newly lost, and my strength is about ten percent of what it was. It's probably not enough to fight the West Sea Dragon King, but it should still suffice to suppress a region's monsters."

After dealing with all sorts of trivial matters caused by incompleteness, it was also time to settle scores with the Dragon Clan rebel, the Sea Demons, and the Ancient Method Practitioner.

On this planet, all threats needed to be eradicated in this battle!

"Very good." The Master of Calculation nodded, glanced at Wang Qi again, and smiled, "There is no need for guilt. My Dao Heart is shattered, but you had no malicious intent, unlike what the Mathematics Lord did back then."

After saying this, the Master of Calculation left.

The splendid illusion, faded in color, became black and white, as Yin and Yang alternated. Wang Qi, Feng Luoyi, and Master Turing stood facing each other.

"Eventually, it all has to end..."

Feng Luoyi shook his head and also disappeared.

"After all, there is no such thing as a feast that never ends." Master Turing showed a melancholic expression of lament for the passing of time, "How will mathematics develop in the future..."

"When it comes to the foundations of mathematical reasoning, there's just one last flash of brilliance left." Wang Qi also lamented, "The Mathematics Lord will regain power because in the future, capabilities in low-dimensional topology will become increasingly important..."

It must be acknowledged that even in mathematics, there is the phenomenon of "a generation of patches, a generation of divinity." In the past, the Heavenly Element Formation, Heavenly Transformation Formula, and curves were everything. In the era of the Mathematics Lord, the Li Sect prevailed, making geometry and topology mainstream. By the era of the Master of Calculation, set theory was at its peak. Even now, where Wang Qi draws a chasm between the finite and the infinite, set theory remains immense.

However, when I introduced the Forcing Method, set theory began to decline. Perhaps only the issue of "infinity" can still support this domain.

In the future, the development of mathematics will move into a realm difficult for predecessors to comprehend. The Langlands Program will span algebra, geometry, and group theory, triggering a new mathematical revolution.

Master Turing was curious, "You don't have much faith in the Geting Sect?"

"The Geting Sect does have some good things. However, the life span of 'formalization' is approaching its end count." Wang Qi pondered.

According to the thoughts of the Bourbaki School, formalization is just a tool for organizing the known parts of mathematics and is not something important. Once this step is completed, formalization will be thoroughly discarded.

Master Turing collected his thoughts and asked Wang Qi, "I've heard that Feng Luoyi also entrusted you with a secret task, asking you to take this opportunity to cultivate in seclusion for a while. During this time, rest assured and organize yourself."

Wang Qi nodded and exited the Ten Thousand Immortals Illusion Realm.

At this time, his communication logs were about to explode. Even with Jarvis managing it, it was still chaotic.

Wang Qi did not connect to any Spirit Messages. He simply sent a unified reply to everyone, informing them that he would be in seclusion for a while. Then, after some thought, he wrote separate letters to Su Junyu and Chen Youjia.

"The next potentially hot domains include Recursive Theory, which is still in its early stages and valuable since Calculator Theory always requires it. Then, if the approach leans towards the Li Sect, work on low-dimensional topology and algebraic topology; if it departs from the Li Sect, focus on abstract algebra..."

Su Junyu is his partner, and he can rely on him to work hard as his cultivation updates and evolves. Regarding Chen Youjia... does one need a reason?

After doing all this, Wang Qi exited the Ten Thousand Immortals Illusion Realm and said to Midao, "Alright, Senior Sister, let's go."

Now, it's time to head overseas and collect that debt.