Exploring Immortality Cultivation-Chapter 319 - 73: Godel Completeness Theorem [Additional Four]

Wang Qi's breakthrough began.

"For the simplest first-order predicate logic..."

All the mana in Wang Qi's body seemed to sense the impending breakthrough, becoming restive.

One by one, the acupoints burst open, and new Yin Yang Yao began to be produced in batches.

"Conducting logical calculus..."

When Wang Qi wrote down this sentence, all the Yin Yang Yao within him began to operate at full capacity.

"...it can be proven that all logically valid formulas..."

Wang Qi's hand, gripping the pen, turned white from exerting too much force, and his black eyes became profound.

An answer was imminent.

"Therefore..."

At the moment when Wang Qi's pen fell, all the Yin Yang Yao in his body instantaneously shattered, and the explosive mana filled his body in a burst.

However, the young man did not perceive it. Or rather, he did perceive it but did not attend to it.

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He had a vague premonition that what he was about to write next would be the greatest glory of his life.

"It can be considered that the first-order predicate calculus is complete."

In that instant, the Yao Ding Calculating Scripture ran wildly, and the Yin Yang Yao began to condense in the various acupoints again, with the number doubling from before!

Wang Qi didn't have time to check his internal condition, as he was already immersed in immense joy.

"Ha ha ha I know! I know!"

A finger tapped twice on his desk. "Can you explain what you know first?"

Wang Qi looked at Chen Feng, somewhat puzzled, "Boss? How did you follow me to Wanfa Sect? We agreed on tomorrow... Ah!"

In mid-sentence, Wang Qi let out a scream.

"Ow... your..." Chen Feng's ear hurt, and he said helplessly, "You knew you stood me up, huh?"

Wang Qi suddenly grabbed Chen Feng's shoulder. The great god demanded, "Tell me the truth, how many days have I stood you up?"

Chen Feng was confused, "Days? You stood me up for one day, and I came here to find you. If you didn't show up for several days, I might have to change into a uniform to arrest you."

"One day?" Wang Qi was stunned for a moment, "What time is it now?"

"7 p.m. to 9 p.m..."

That's not right, is it? Just less than a day? This isn't scientific, is it?

Wang Qi grabbed the top sheet of draft from the desk—the one he had just finished writing—and asked, "This, did I really write this?"

Chen Feng's face changed. "Did you experience a deviation and hurt your brain? Do you want me to check on you?"

"Just tell me if it is!" Wang Qi grew more anxious, "Old man, you saw it too, tell me if it is?"

Master Zhen Chan said, "Yes, it's definitely something you wrote."

Chen Feng was incredulous, "You don't even remember what you wrote? This is what you just finished writing."

Another "old man," Liu Yunxiang also walked in, "I saw it with my own eyes, you wrote it. Child, what are you writing exactly?"

Wang Qi seemed to have had all his energy sapped, slumping to the ground and saying, "This is unreal..."

Everyone at the Wanfa Sect's residence was awakened. They all curiously gathered around. Seeing Wang Qi in a lost and disheartened state, Li Yue, who had suffered a setback earlier, was quite displeased, "Putting on airs."

Wang Qi suddenly shivered, "Sorry everyone, could you please clear out for a bit? I need some time alone."

Liu Yunxiang wanted to take a look at Wang Qi's paper, but Wang Qi held down the sheets, "Sorry... I can't show this to anyone just yet... Junior Master Liu, please step out. I really need some time alone."

These words from Wang Qi caused the color of several disciples from Wanfa Sect to change slightly, and an angry Li Yue rebuked, "How dare you disrespect Junior Master Liu?"

Liu Yunxiang stopped the disciples' accusations and said, "Let's just go out and wait."

Chen Feng, along with a group of Wanfa Sect disciples, went outside. Everyone was abuzz with speculation about Wang Qi's unusual behavior.

Mo Zhenzhen sighed, "So the rumors that a genius could just write a paper and soar up the ranks are true."

Surrounds of envious exclamations followed.

"Exactly, so Senior Brother Wang is actually..."

"He must not be an outer disciple anymore..."

Hearing the discussions around her, Li Yue, whose opinion of Wang Qi had plummeted, snorted, "Writing papers to increase cultivation isn't that simple. Cultivation grows because the contemplating process stimulates the soul. As long as you truly ponder, even if your thoughts are wrong, you can grow in cultivation."

Someone curiously asked, "What if the conclusion is wrong?"

Huangfu Lian said gravely, "You will deviate from the righteous skill; if you persist with the wrong belief, you might not be able to return. Normally, don't test such things lightly."

A disciple closely associated with Wang Qi nervously inquired of Liu Yunxiang, "Junior Master Liu, Senior Brother Wang's conclusion couldn't be wrong, could it?"

Liu Yunxiang shook his head solemnly, "This... I don't know."

The conclusion was very correct, of which Wang Qi had great confidence.

Because this conclusion was not his own, but that of an Earth mathematician.

Godel Completeness Theorem.

Compared to Godel's Incompleteness Theorem, this theorem was less well-known. It originated from Kurt Godel's doctoral thesis, proving that in formal systems, first-order predicates are complete, and that all logically valid formulas in first-order logical calculus can be proven.

However, first-order predicate calculus is a relatively weak mathematical system; if exclusively applied, it cannot even define natural numbers, let alone arithmetic.

For Hilbert's Program, the Godel Completeness Theorem was a significant breakthrough, but it wasn't as conclusive as the Incompleteness Theorem. Moreover, the Completeness Theorem was merely following Hilbert's approach, taking one more step on the basis of Von Neumann, rather than leaping like the genius of the Incompleteness Theorem.

But...

"Such an unscientific speed indeed," Wang Qi muttered to himself.

For a god-like mathematician like Godel, this paper might have just been a doctoral thesis, but most mathematicians in the world could not produce such a paper.

Or rather, most mathematicians might not even understand it.

"Although I knew the general direction and the conclusion beforehand, I managed to deduce it in just one day?"

Wang Qi was bewildered.

Knowing the general direction and conclusion did not mean there was no difficulty. It was like everyone was treasure hunting on a new map where ordinary people did not know if there were treasures, but Wang Qi started with the knowledge that there were treasures and even saw a signpost.

Yet, he still needed to find the way himself.

He hadn't even thought of pushing through Godel's Completeness Theorem in one go at the start, instead, just proving a special subsystem of the arithmetic system along Von Neumann's lines would have been sufficient.

"Do I really have such a high level?"