Exploring Immortality Cultivation-Chapter 327 - 81: Li Sect Versus Lian Sect, a Battle of Ideologies

After listening to Wang Qi's words, Feng Luoyi fell into deep thought. After a while, he asked seriously, "Wang Qi, answer me honestly—is it your opinion that 'the larger the logical system, the more apparent its incompleteness becomes'? Do you have any new ideas?"

Wang Qi instinctively wanted to nod but then caught himself, "No, no, no, I just had this vague idea while proving first-order completeness—that since only first-order completeness can currently be proven, it can be considered that anything beyond first order is incomplete."

It's better not to discuss Godel's Incompleteness Theorem before fully understanding it. Presenting something one doesn't completely understand is somewhat suicidal.

Feng Luoyi frowned, seemingly displeased with the answer, "And what exactly has led you to that conclusion? Intuition?"

Wang Qi's first reaction was to scoff, "Intuition? How could it be... No, no, no, it's not intuition. It's my own, um, not a conjecture, but rather, it can be considered one of my goals for the next phase, starting with completeness."

The guy in front of him doesn't seem to like the idea of intuition...

"You have a bad habit. How can you use something unproven as if it were an established conclusion?" Feng Luoyi's expression softened a bit, but he still reprimanded Wang Qi before asking, "One of them? What else is there?"

"I'm planning to work with Junior Sister Bao on the Big Number Law, and also, I've recently joined an Empirical Department, so I might get into some mathematical reasoning statistics and systems theory."

"The Big Number Law is a good topic, and statistics should have intersections with it, but the subject of systems theory is too broad," critiqued Feng Luoyi again.

"Isn't that because I lack direction outside the Sect? Like a cultivator with little difference from a Loose Cultivator, I lack resources, guidance, and a grand direction, so I can only study what I come across," Wang Qi playfully explained.

"You're the type to open a dye workshop the moment you get two colors," laughed Feng Luoyi. "Stop playing the poor card. The paper you submitted yesterday was very good. The exchange numbers and references won't be few. In a month or two, you'll be a rich man among the Qi Cultivation Stage disciples."

Bao Xiaoya cheered, "Great! Seeing the current treatment of my Senior Brother always makes me think I let him off too easily back then."

Feng Luoyi glanced again and said, "Additionally, Ximen Master has decided to nominate you—next January, for the Dao Artifact Award."

"Next year? So it's actually next year…" Wang Qi was only somewhat surprised about the time, rather indifferent to the Dao Artifact Award.

The Dao Artifact Award is roughly equivalent to Earth's "Fields Medal"—also known as "the Nobel Prize of the mathematics domain."

However, the Fields Medal restricts the age of its recipients, awarding only mathematicians under forty. The Dao Artifact Award does the same, specially rewarding young cultivators below the Primordial Spirit Stage. But forty is also about the age when a mathematician produces his best work, while a Golden Core Stage Cultivator is far from the peak of his brilliance; thus, the academic status of the Dao Artifact Award is slightly lower.

Securing a Fields Medal for Godel Completeness Theorem is within the realm of expected outcomes.

Feng Luoyi looked at Wang Qi, "You seem quite confident. But honestly, it might be difficult for you to win the Dao Artifact Award. There will be strong opposition within the Wanfa Sect."

Bao Xiaoya didn't understand, "Senior Brother is obviously very powerful, definitely the number one among his peers. My brother isn't even as strong as him."

"It's a factional conflict."

Bao Xiaoya was quite puzzled. Members of the Bo Family would never understand the fight for power and profit. While other families might scheme against each other to the point of wiping out entire clans for the position of Family Head, the Bo Family had long since treated the position of the head like a burden, a stumbling block, or dog poop, to be thrown around carelessly—Bao Yuehan had held a grudge his whole life against Bao Yage for getting smeared with dog poop in his face when they were younger.

"It's a conflict of the Great Dao and ideology," Feng Luoyi added, looking towards Bao Xiaoya, "Little girl, Wang Qi and I still have some matters to discuss, involving the affairs of the Wanfa Sect—do you have anything else?"

It was evident that the questions that followed were no longer suitable to discuss with her. Bao Xiaoya, although puzzled, still stood up to pay her respects, "If that's the case, I will take my leave now."

After Bao Xiaoya's figure had vanished, Feng Luoyi asked Wang Qi, "Do you know what the biggest ideological struggle within the Modern is?"

"It should be the debate between Mysterious Palace and Guiyi Alliance, right?" Wang Qi said, "Taiyi Heavenly Venerable and Quantum Venerable Master debated thrice at Yu'erwei Manor, and then the Wave Motion Lord posed the 'being born yet dying' problem to challenge the Mysterious Palace..."

Feng Luoyi shook her head, "Daoist of Uncertainty fell from grace for assisting the Demon Emperor, and the hearts of the people in the Mysterious Palace are already scattered. But conversely, Taiyi Heavenly Venerable has encountered a problem he cannot bypass, and his theory is also teetering on the edge of collapse. In short, this debate has already died down, and everyone is just waiting for the final result."

"If you're talking about being in full swing, inside the Wanfa Sect..." but no matter how hard he tried, Wang Qi could not remember any other debate that could be bigger than this series.

"You, kid, seem like you're from the Mysterious Palace or the Guiyi Alliance. During the Shape Comparison, Mysterious debates, I supported Mysterious, Ximen Master supported Shape Comparison, but Ximen Master and I share the same mathematical reasoning. Mathematics is the Great Dao that can transcend the logic of the natural flow of heaven and matter, understand?" Feng Luoyi said helplessly, "Do you know, the Ancient Mathematicians were divided into two Sects, one was Continuous Sect, and the other was Discrete Sect."

"The Continuous Sect believed that Heaven and Earth are one, everything is continuous. The Discrete Sect, on the other hand, believed that Heaven and Earth are discrete, like natural numbers, with nothing between one and two."

"The ideological struggle between the Continuous Sect and Discrete Sect has actually permeated the entire history of the Mathematical Dao, and today," Feng Luoyi pointed at herself, "I, Ximen Master, we are the representatives of modern Discrete Sect, and you can also call 'us' the Logicism. Of course, in the eyes of many, today's Discrete Sect is Geting."

Wang Qi's mouth hung open widely, as if his jaw had dislocated.

Wait a second, it seemed like he overlooked something...

The debate between Continuous and Discrete Sect on Earth's history was the "geometry and numbers" debate, which later developed into Newton and Leibniz's divergence on "geometric intuition and algebraic abstraction," followed by "Intuitionism, Structuralism, and Logicism"...

However, "Intuitionism and Structuralism" eventually failed to fight it out because, just as Structuralism and Logicism were becoming equals to Intuitionism, it was the era when Hilbert was in his prime, followed by Von Neumann joining the side of Logicism, while, unfortunately, Intuitionism did not have a grandmaster...

But the Earth's Intuitionism school merely "happened not to have" a grandmaster, not that it "never had" one. Henry Poincaré was born too early – not only missing the huge leap in physics he longed for but also missing out on a rival like Hilbert.

However, Cultivators in Shenzhou didn't have a lifespan issue...

Wang Qi's voice trembled as he asked, "Teacher Feng, could it be that Ximen Master plans to lead you in a confrontation against Sect Master Pang?"

Feng Luoyi was astonished, "Not 'us,' it's 'we.' Once your paper is published, anyone would consider you one of our side."

Wang Qi's vision darkened, and he nearly collapsed.

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1·Henry Poincaré's life was a lonely one. Top Mathematicians always liked to dabble in physics to show off their excess intelligence, but Poincaré happened to be in an era when old physics reached a deadlock, without a good entry point. By the time Einstein prompted a new wave of innovation, he was already too old to keep up with the calculations. Besides, he also missed out on a rival like Hilbert. What was the level of the second-best Mathematician in his era? Klein, called "God-like Klein," "the god standing above the clouds," [these nicknames are pretty stupid] Klein corresponded with Poincaré about Mathematics, and not long after, Klein suffered a mental breakdown from overthinking, and never recovered in his lifetime [Poincaré: I didn't even try hard, how could you fall?]

2·Be aware of trolls in the comment section, moderators and deputy moderators urgently needed [It's such a hassle for one person to manage highlighting posts, deleting posts, etc.~]

3·Asking for recommendation votes QAQ The ranking has been dropping TAT On my own