Exploring Immortality Cultivation-Chapter 320 - 74: The Broken Golden Diagonal [Plus Five More - s]

"Do I really have such a high level of ability?"

The thought had scarcely formed before Wang Qi thoroughly squashed it.

He was well aware of his limitations in his previous life.

This was a truly world-class accomplishment. By Earth's standards, it was more than sufficient to be published in the world's leading mathematical journal, "Mathematical Annals," and whether it could secure a Fields Medal was uncertain, but it was certainly enough to support a mathematician for a lifetime.

"How long did I take, one day?"

Wang Qi found the idea ridiculous.

"Impossible..."

From the exploration of the arithmetic system's subsystem to the proof of Gödel's Completeness Theorem.

"Ahaha... That's right, this life's computational ability is several times better than my last, with quicker thinking, so I wrote faster."

Wang Qi chuckled dryly, making excuses for himself.

A person's cognitive abilities are limited by the speed of the brain, much like the speed at which programs run is limited by hardware. Enhancing computational abilities was akin to adding intelligence points.

But Wang Qi was also aware that thinking speed wasn't everything. Improving hardware could boost performance, but such improvement was limited. A Windows system installed on a supercomputer thousands of times more powerful than an ordinary computer could only be at most twice as fast, not a thousand times faster. There was a limit to what Windows could do; it couldn't utilize such immense computing power.

That is to say, Wang Qi himself was capable of utilizing his own computational abilities.

"Have I really become stronger?"

"I really have become stronger!"

After triple checking, Wang Qi finally confirmed that his abilities had indeed surpassed those of his past life.

By a lot.

"Having a smart head really makes a difference." Wang Qi patted his forehead.

Decades of accumulation from his past life, combined with the cultivation and diligent studies of this life, the result was far from a simple sum of one plus one.

"Wuhuhuhu..." Wang Qi suppressed an impulse to burst into hysterical laughter, his shoulders shaking. But in the end, he could not help but laugh out loud!

Zhen Chan finally spoke, "What on earth did you accomplish?"

"It's just a pity I'm still in the Qi Cultivation Stage," Wang Qi said with a tone of regret. "If I had written this during the Golden Core Stage, maybe I could've reached the Primordial Spirit directly."

However, though his tone suggested a lack of satisfaction, there was not a hint of regret on his face.

This truly counted as a thesis he had completed!

This was the Gödel Completeness Theorem!

In the most foundational part of the field of mathematics, he had nibbled it away piece by piece. And the fact that he could use it to achieve a breakthrough indicated that he had truly comprehended it thoroughly!

"I was worried before, thinking what if I kept throwing out mental theories and didn't understand them deeply enough—what would I do if someone questioned them."

"Now it seems that even if I forget all those theories from Earth, I can still make a name for myself!"

Wang Qi took several deep breaths, forcing himself to calm down. Then, he looked at the thesis again.

Gödel's Completeness Theorem!

From the data in the paper repository, it appeared that Shenzhou's version of Hilbert's Program or similar academic projects was in full swing; arithmeticians were most enthusiastic at the current time.

And this paper of his took a step forward from the research contents of those Great Mathematicians; every arithmetician focusing on this domain would not overlook this paper.

In other words, not only did this paper have exceptionally high prestige, but it was exactly in a hot field.

Prestige, citations, additional rewards, and such were all within reach!

Wang Qi estimated that after this paper was published, over half of the top-notch arithmeticians from the Wanfa Sect would be paying attention to him; at the very least, they would know that someone like him existed.

It was unlikely that he could immediately return to the Wanfa Sect and make Chen Jingyun kneel and sing "Conquest," but his treatment would probably improve significantly—at least, he would enjoy some covert benefits.

"However…" Wang Qi stroked his chin, "In Shenzhou, many concepts of mathematical logic do not yet have a consensus regarding their extension and intension, and I'm relatively inclined towards Earth's definitions. Also, I need to check my proof strategies again. It wouldn't be good if I used something that doesn't exist in Shenzhou yet."

"It would be best to polish it once more, preferably using the common thought processes and methods of Shenzhou's arithmeticians."

Having thought this through, Wang Qi opened the door and called out, "Boss, I'd like to request some Merit on credit, and it would be great if I could get an advance on next month's salary. I have urgent use for it."

Perplexed, Chen Feng took out a calculator terminal for the transfer, "It's not out of the question, but I need to know the amount so I can write it off as an emergency expense."

Wang Qi took out his own calculator and glanced at the paper repository again: "There are Elder Feng's papers—about seven from Feng, the manual player from the Sovereign State, then papers from Master of Calculation, Ximen Master, no less than five, and several from Master of Calculation Disciples—plus two monographs..."

"Eighty. You'll owe me a month and a half of labor."

"Deal."

After the transaction was completed, Wang Qi went back inside, leaving everyone in the yard looking at each other in confusion.

Huangfu Lian couldn't help but ask, "Junior Brother Chen, why did he call you Boss just now?" fɾēewebnσveℓ.com

Pretending to be calm, Chen Feng said, "Oh, I'm thinking about collaborating with him, to bring him into my Empirical Department."

Inside, however, he was already engulfed in a maelstrom of shock. That kid, what on earth did he prove! And, did I just make a huge profit this time?

Others, who knew of Chen Feng's status as True Disciple through Huangfu Lian, were now envious that Wang Qi was going to collaborate with him.

Joining the Empirical Department meant substantial benefits.

Li Yue couldn't hide her irritation, "Junior Brother Chen, aren't you offering him too high of a salary? Are you sure you're not making a mistake?"

"You can rest assured on that point." With his mind made up to keep Wang Qi, Chen Feng took out a request form from his pocket and handed it to Liu Yunxiang, "Junior Master Liu, please review this application."

After returning to his bedroom, Wang Qi redeemed seventeen or eighteen papers for study. He didn't read every paper in full but began with the abstracts, then jumped straight to the conclusions. After going through all the conclusions, Wang Qi picked a few papers for close reading.

After quickly finishing a few, Wang Qi finally gained a rough understanding of Shenzhou's Set Theory.

Mathematician Georg Cantor had a very famous logical argument called the diagonal method—a special kind of reductio ad absurdum. The names Georg Cantor, Kurt Godel, and Alan Turing lined up in a sequence, running through all of mathematical logic and termed the "Golden Diagonal."

Yet in Shenzhou, history took a curious detour.

Godel had not been born, and the Golden Diagonal was broken in the middle.

Sect Master Kang of the Wanfa Sect had once dominated Shenzhou, while Elder Ji Turing forever held sway over Fusang, but Godel mysteriously did not appear, and his achievements had not been replicated by anyone else.

Shenzhou's mathematicians, unable to use the crystallized line of thought extending from Godel, chose different methods to construct their own logic. Some arithmeticians devoted themselves to building a system larger and stronger than Pishi's Axioms, bypassing this pitfall. Many more arithmeticians, under the guidance of Xi Baiche, strived towards an ideal System of Modern Law that was aspired to yet unattainable.

"So that's how it is. It seems that the paper's revisions won't be so straightforward, huh."

After pondering for a while, Wang Qi opened the door and shouted, "Boss, let's discuss anything you need now. I'm going to be busy polishing the paper for the next few days!"