Master of Calculation of the Genting Sect and the Mathematics Lord of the Li Sect clashed primarily over mathematical logic. This domain is the most fundantal part of mathematical reasoning. The understanding of this field by an Arithtician determines their overall grasp of mathematics.
Chen Feng's understanding of mathematics and that of Wang Qi could only be described as lantable, but he was aware of this point.
Wang Qi laughed, "Senior Feng also instructed the sa, following it isn't harmful."
Feng Luoyi and Xi Baiche both still believed Wang Qi had great talent in mathematical logic, and if he continued on this path of first-order logic, he would eventually reach the realm Xi Baiche envisioned.
However, Wang Qi knew that this path was not untraversable, yet the next step's result would only clash with Xi Baiche's expectation.
Godel's Incompleteness Theorem, the terrible theorem that destroyed the noble beauty of mathematics and dethroned it.
In Earth's history, Godel's Incompleteness Theorem proved Hilbert's second problem to be unsolvable, leading to the bankruptcy of Hilbert's Program. If it were released in Shenzhou, it might completely shake the prestige of the Genting Sect.
No matter how he put it, in others' eyes, he was already tagged as "Genting Sect," so when theorizing, it was still better to consider this aspect.
By the way, he also had to guard against others developing the incompleteness theorem along his line of thinking.
Though for a supre genius like Godel, moving from completeness to incompleteness only took one year, for ordinary mathematicians, the path Godel covered in one year was an absolute chasm.
Not to ntion that Godel himself reached the completeness theorem only through a sudden flash of spiritual insight.
The Li Sect Cultivators' understanding of mathematics was not completely in line with Godel's ideas, aning their philosophies and preferred thods also differed. It was not very likely that they would derive the incompleteness theorem from Wang Qi's papers; the greater threat now seed to be just the Mathematics Lord himself.
What really needed vigilance were "one's own people."
Wang Qi, familiar with subsequent history, knew that the promise of Hilbert's Program's outward journey wasn't in completeness or decidability, as those were explicitly debunked. Its only hope lay in the consistency of the arithtic system.
Godel's Incompleteness Theorem's second clause stated that for any mathematical system that includes an arithtic system, we cannot prove its consistency within that system. This was part of the answer to Hilbert's second problem.
Using Transfinite Induction not belonging in the arithtic system to prove the consistency of the arithtic system circumvented the iron wall outlined by the incompleteness theorem.
"So, the next step is to extract Transfinite Induction from Set Theory and then apply it to the interpretation of the arithtic system, steering the crux of the debate towards the consistency of the arithtic system."
This was Wang Qi's current plan.
Chen Feng frowned, "Do you realize what it ans to get involved in a debate between Mathematics Lord and Master of Calculation? Don't think just because you are in Divine Capital that you won't catch fire."
"I'll rely be throwing out a few papers, generally not responding directly to the challenges," Wang Qi said with a smile.
As long as he could guide the focus towards the consistency of the arithtic system, that would be sufficient.
And, organizing the arithtic system was a big project; he didn't have that much ti to complete it himself, and it was enough if he participated truly in just part of it.
Chen Feng looked at Wang Qi with puzzlent and asked, "You seem to have a deep obsession with this debate... am I mistaken?"
Wang Qi shook his head, "It's not a misconception."
I am truly eager to get involved in this debate.
In his previous life, when Wang Qi read the biography of Henri Poincaré, he felt a peculiar sense.
This man, born at the wrong ti.
While most mathematicians like to dabble in physics to show off their surplus intelligence, his era was when classical physics peaked, leaving him little to play with; by the ti Einstein sparked a new revolution, he was already old; he was in between generations with David Hilbert, and as his era aged, it was Hilbert's era rising step by step. By the ti Hilbert reached his peak, he had already stepped back from the front lines of mathematics.
Henri Poincaré never truly burned.
But in this world, he must face a once-in-a-lifeti genius in full splendor, Mathematics Lord Pang Jialai!
And on his side, Mathematics Lord Xi Baiche and world-class player Feng Luoyi! Mathematicians of the sa caliber!
Any capable mathematician would be thrilled by such a debate.
Moreover, Wang Qi himself had harbored a bit of a secret ambition.
"Perhaps I still can't match Godel at about fifty, at his peak… but I should have the level of a twenty-year-old Godel, shouldn't I?"
He wasn't participating for himself, but representing Godel, to partake in this grand event, impossible on Earth.
This thought alone was enough to make one's blood boil!
Initially, Wang Qi was terrified by his own crazy idea. But after calming down, his desire to partake in this debate only grew stronger.
This debate was like the Flower of the Soul for mathematicians, using all of their life and talent to bloom—a confirmation and ascension of life!
How could he miss it?
He must not miss it!
Even if just as a supporting role!
Perhaps detecting the passion burning beneath Wang Qi's calm deanor, Chen Feng clapped his hands and praised, "Interesting, that's more like it! Worthy of the partner I value—but speaking of which, are you still going to work on my stuff?"
Over the past few days, Chen Feng had sought Wang Qi a few tis, also hearing about the theories Wang Qi was working on. He vaguely understood the significance of Wang Qi's work and vaguely sensed his skill level. Now, he feared that Wang Qi might reconsider.
Wang Qi said, "Of course, why wouldn't I? Qi Cultivation Stage disciples cannot leave the Sect on their own; going out requires asking for leave, aning until the new arrangents from Wanfa Sect co down, I can't leave Divine Capital. And Divine Capital, your place has the best rit to earn, right?"
Chen Feng breathed a sigh of relief. However, he pressed on, "Are you planning to pay back the rit you owe now or work for for free?"
Wang Qi scratched his head, "Still go with what we agreed initially, right? Senior Feng said the benefits brought by my paper would only slowly show over the second month, the first month won't have much earnings, the second month just a bit more than the first. I'm still quite impoverished recently."
Chen Feng nodded, "Alright. So, what's your plan for the near future?"
"Naturally busy with the Foundation Establishnt. Once the Mathematics Lord returns and the debate begins, I reckon I won't have peace," Wang Qi sighed. "By the way, Boss, do you know anything about Artifact Refining? I skipped the Artifact Refining class at the Immortal Institute. Can I catch up?"
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