Exploring Immortality Cultivation-Chapter 392 - 144 Bourbaki School [Fifth Update]
Facing Teacher Feng's questioning, Wang Qi understood that this was an invisible test.
It was not impossible to attribute everything to inspiration or intuition. However, inspiration was not without traces. This kind of mental activity was just an occasional manifestation of special patterns in the subconscious.
To express his suspicion that mathematics itself was incomplete and to seek answers elsewhere meant deviating from the path of the Master of Calculation. More seriously, if someone concluded Godel's Incompleteness Theorem based on his words, then the Li Sect could directly be finished.
At that moment, Wang Qi had a flash of inspiration and said, "Teacher, my initial goal was not actually to prove completeness; that was simply an unintended result. What I actually wanted to do was something else."
Teacher Feng was surprised and asked, "Such a rigorous theory was an unintended result? What was your original intention?"
Wang Qi was somewhat evasive, "It's just an immature idea."
"If you've already achieved results, that means this path is feasible. Even if it doesn't lead to the goal you originally wanted to reach, it can still reveal a major path."
Wang Qi, biting the bullet, asked, "Teacher, what do you think about mathematics—is it 'one mathematics' or 'multiple mathematics'?"
Teacher Feng shook his head, "Different mathematicians have different opinions; there's no correct answer."
"When I entered the path, I wondered whether the growing sub-disciplines of mathematics represented an organically structured entity undergoing development, increasingly gaining more coordination and unity with new developments, or if the gradually fragmenting tendency it exhibited was inherent to the nature of mathematics? Independent disciplines, not only in their objectives but also in their methods and even their languages, are increasingly becoming distinct. Do we now have one mathematics or several mathematics?"
Teacher Feng nodded imperceptibly. Many mathematicians had thought about a similar question, and every disciple of Wanfa Sect could mention their own view. However, not many could raise as many questions as he did.
As long as a domain could pose lots of questions, it was brimming with vitality; a lack of questions, on the other hand, presaged the cessation or decline of independent development. This was something Ximen Master once said, and Teacher Feng deeply agreed with it.
He then asked, "So, what do you think?"
"Of course, there is only one," Wang Qi revealed a confident, or perhaps arrogant, smile. "And there can only be one."
"Give reasons, otherwise your theory means nothing."
Teacher Feng calmly threw cold water on his disciple. Every year, some young cultivators came up with enthusiastic but far-fetched ideas. Unfortunately, because the proposers lacked depth, most of these ideas were worthless. Some even clamored to reshape the Modern system without understanding what they were criticizing.
Facing Teacher Feng's questioning, Wang Qi could only indicate his speechlessness, "Teacher Feng, my idea, like Ximen Master's proof that mathematics was complete, without error, and decidable, is just an ideal. But if you want me to discuss the idea, then I can elaborate a little."
Mathematics is not merely the sum of various disciplines; the fields within mathematics are intricately interconnected. In fact, if one just follows the thought process of the Master of Calculation and employs methods of abstraction, formalization, and axiomatization, the similarities and differences of various structures and their complexities become apparent.
The foundation of structures is sets. The concept of a set is relatively simple, involving only sets, elements, and the relationship of elements belonging to sets. It doesn't discuss the relationships between elements, but the relationships between elements and their subsets, and between subsets themselves, form the structure. This structure can entirely become the framework of mathematics, unifying it.
What Wang Qi was now talking about was in fact one of the foundations of modern mathematics, guided by the Bourbaki School.
The Bourbaki School comprised a group of mathematicians with a profound impact on modern mathematics, a majority being French mathematicians. Their activities began in the mid-1930s; they published some articles in mathematical journals and wrote the multi-volume "Principles of Mathematics," one of the most important schools in the history of mathematics development.
In a sense, the Bourbaki School and the Göttingen School were like paradigms of mathematical schools. The Göttingen School was "broad," its brilliance stretching from Gauss to Weil for nearly two hundred years, covering nearly the entire domain of mathematics. Bourbaki, however, was "deep," having nearly perfectly fulfilled its era's task of creating new mathematics and advancing the entire development of mathematics.
Feng Luoyi listened for a moment before a look of surprise appeared on his face for the first time. "That's a good idea."
How lofty must one's vision be to earn his praise? A single commendatory word from him was enough to let many disciples of the Wanfa Sect die without regrets.
Wang Qi didn't show much emotional fluctuation. He was well aware that Feng Luoyi's praise was not aimed at him personally but rather at the great academic school he represented. He continued, "My ideal is to consolidate all Mathematics into a single system, and my research approach also follows this, systematizing Mathematics using a structural method, and thoroughly mastering it. The completeness ratio, to me, is an unexpected gain."
"That is the principle." Feng Luoyi nodded, saying nothing further.
In this Q&A session, Wang Qi had reversed cause and effect. In fact, the achievements of the Bourbaki School were largely built on Godel's foundations, but Wang Qi claimed that Godel's arrival was derived from the program of Bourbaki, which was logically arguable. However, Feng Luoyi still had doubts, "Then why don't you use a more intuitive and credible principle of induction? Is the foundation of the Transfinite Method solid?"
"I am not yet skilled enough to complete it in a short time, but I at least hope to finish a part of it to prove my path. So even though I know it's a detour, I still want to see the results."
Feng Luoyi was not very satisfied with Wang Qi's answer, but it was still within an acceptable range. He nodded his head and dismissed Wang Qi.
On the other side, after viewing the entire broadcast of Feng Luoyi's discussions, Xi Baiche fell into silence. Then he gave a bitter smile. "Truly an extraordinary genius."
Ai Kemeng asked, "So, Master, these papers…"
"I can't believe I actually have to rely on something I don't fully agree with to contend with challenges," Xi Baiche felt defeated for a moment. However, he soon reinvigorated his spirits, "But Wang Qi's ideas have given me some fresh thoughts. His approach is actually quite close to ours; what he can't finish, maybe we can complete."
Feng Luoyi raised an objection, "But our ultimate goal is to prove the solidity of Mathematics itself."
"This is a good idea to axiomatize Mathematics," Xi Baiche pointed to the Mathematics Lord's papers, "and we're only setting aside one month to work on this. After a month, we'll still proceed at our own pace."
Independently raising another issue, "This is Wang Qi's idea. By doing this, we're essentially taking his route."
"I will compensate him in all manifest or latent ways," Xi Baiche stated firmly.
......
The Master of Calculation didn't know that he was making this compensation commitment while Wang Qi was lying on his desk, frantically writing, all the while lamenting, "It's all over, I've totally screwed up, fuck! Fuck fuck!"
"Screwed up?" Chen Youjia was curious about the term. fгee𝑤ebɳoveɭ.cøm
"It's like showing off the Water Element and then drowning in water." Wang Qi almost cried.
I just wanted to lead to the results of the Bourbaki School, making the Mathematics of this world closer to my previous life... I can't handle the works of the Bourbaki School, damn it!
Analytical Mathematics, Probability Theory, Applied Mathematics, Computational Mathematics, especially areas related to Theoretical Physics and Dynamical Systems Theory, these are all the domains I wish to work in... And these are all domains that the Bourbaki School overlooks!
"Teacher Feng, Ximen Master, please handle this issue yourselves! Don't make me solve it!"
This was how the young man pleaded. (To be continued. If you like this work, please visit qidian.com to recommend and vote monthly. Your support is my greatest motivation. Mobile users, please read at m.qidian.com.)
