On the very night they received the journal, both Wang Qi and Chen Youjia received a message from the sender, Chebyshev of the Northern Country, Wanfa Sect. The content of the letter was simple—this legendary Carefree Practitioner wanted to meet the two young geniuses who had proposed a new Big Number Law to exchange ideas.
Chen Youjia's thoughts aside, Wang Qi was incredibly excited.
The Northern Country corresponded to Earth's historical Petersburg School, represented by figures like Chebyshev, Markov, and Lyapunov. Although in terms of fame and presence in the history of mathematics, it wasn't as renowned as the Paris School, Göttingen School, or Polish School of Europe, its influence on future generations was no less significant.
Chebyshev was the founder of Wanfa Sect's Northern Country Sect, a Great Cultivator who excelled in fields like number theory, functions, and integrals.
After responding, the two spent about a day preparing. It wasn't until the morning of the third day that they entered the Ten Thousand Immortals Illusion Realm together. Following the guide that came with the letter, they arrived at a place in the Illusion.
The scenery of the Northern Country was a vast expanse of ice and fluttering snow. In this silver realm, a semi-open hut steamed with warmth. Inside, two elderly men sat at a table, engaged in conversation. Wealthy people always liked to set their chat room illusions to locations they were most familiar with, and this ruler of the Northern Country was no exception.
The elder sitting on the main seat had white hair and beard but showed no signs of frailty; he was spirited and physically robust, his three-foot long beard meticulously groomed.
Hmm, he presented a stark contrast to the other elderly man beside him.
Wang Qi couldn't help exclaiming, "Teacher Feng? What are you doing here?"
Feng Luoyi's appearance wasn't so shabby either, but compared to Chebyshev's meticulousness, it was slightly lacking. It was hard to tell which of them was a Cultivator from the martial Northern Country.
With a smile, Feng Luoyi said, "Everything in the Ten Thousand Immortals Illusion Realm is under my management. It's normal for me to be here. Besides, this new thing you've come up with is very interesting; I also wanted to get involved—is that unwelcome?"
Chen Youjia tugged at Wang Qi and bowed his head, saying, "How could that be?"
For Chen Youjia, who aspired to apply mathematics, the strongest Arithmetician, Feng Luoyi, was quite simply an idol.
Chebyshev was much more amiable than expected. After hearing Wang Qi's spontaneous utterance of "Teacher Feng," he glanced at Feng Luoyi. Then, turning to the two juniors, he said with a smile, "You don't need to be concerned about this guy, nor do you need to be cautious around me. I just want to talk with you two about your ideas on probability theory."
Probability theory...
Wang Qi observed the elderly man, his eyes reflecting a complex expression. The mathematical law he and Chen Youjia had come up with, known on Earth as Chebyshev's Law of Large Numbers, facing this equivalent's presence gave him a peculiar feeling.
What surprised him even more was Chebyshev's latest published paper, "An Extension of Chen Wang's Law of Large Numbers."
That was clearly Markov's Law of Large Numbers.
According to Earth's history of mathematics, this was the representative achievement of Chebyshev's disciple, Markov, and a cornerstone of modern probability theory.
Although Wang Qi had always known that the research capacity and practical level of Shenzhou Carefree were superior to their equivalents on Earth, this was the first time he had been struck so directly.
—Well, thinking I could quietly finish up the Big Number Law all by myself was far too naive…
Shenzhou had overly disregarded the role of probability, deeming it merely an approximation of "absolute causality". With complete knowledge of all conditions, one could eliminate all uncertainties and derive inevitable outcomes—such was the creed in Shenzhou. Because the computational power of the Primordial Spirit far surpassed the human brain, many Cultivators simply used primitive statistical tools, and few renowned Arithmeticians ventured into the field of probability. Chebyshev had not previously entertained the idea of dabbling in probability.
As for Markov… he was similarly "missing". He had no presence in Shenzhou's history, and most of his mathematical achievements were developed by Cultivators from the Northern Country, represented by Chebyshev.
However, Chebyshev's Law of Large Numbers was extended to include Markov's Law of Large Numbers.
Yet, Wang Qi had ultimately underestimated the Carefree of this world. With sufficient accumulation, just a little bit of something could spark their inspiration.
This might not necessarily be good news for Wang Qi. He should no longer consider monopolizing the entire research chain in the future. He hadn't memorized many papers before transmigrating; only the results he was particularly familiar with in his previous life, which had significant academic status, remained in his memory. Such results, coveted by many Great Powers, would cause a rush once a breakthrough occurred.
But now, it seemed might also be an opportunity...
Chebyshev smiled and said, "I've seen your results; they are impressive studies. How did the two of you initially think of approaching it from this angle?"
Chen Youjia opened her mouth to speak, "This was an idea I had quite early on…"
Wang Qi's voice crisply interjected, cutting off Chen Youjia's words like a sharp blade, "Because this is the inevitable within the coincidental. The Law of Large Numbers is the backbone of the field of probability, and it is also the most practically significant issue in this field."
Chebyshev's eyebrows arched, "Oh? 'Most'? You're so sure about that? What's the reason?"
Wang Qi, at ease, expounded, "First, we need to think about one issue: What is the meaning of our Mathematics?"
What is the meaning of Mathematics?
Mathematics is a highly abstract, highly idealized fragile entity, not the same as the Material World. Events that do not occur perfectly according to probability, no truly uniform material, not even a standard straight line or a perfect circle exist.
What we can draw out in the Material World are only "approximations". Approximate straight lines, approximate circles.
Strictly speaking, the prerequisite conditions of all mathematical theorems are impossible to perfectly satisfy in the real world. Therefore, the conclusions asserted by mathematical theorems cannot be perfectly valid in the real world either.
This conclusion could be extended to all theories. The laws humans grasp are merely statistical averages of random events occurring, nothing more.
Then, what is the meaning of science, the meaning of mathematics?
Feng Luoyi nodded affirmatively, "I understand your point. The Law of Large Numbers is valid, approximation is meaningful. Our way is not the way, but it is close to the way. Perhaps the theory of the Immortal Alliance today and the way of today are akin to this relationship."
Within the occasional lies the necessary.
Chen Youjia looked at Wang Qi blankly. As she usually lacked expression, no one could discern what she was thinking.
"That bastard... I was the first to work on this! You only joined later! Why do you make it sound better than me?"
Chebyshev actually had a favorable impression of this young man, "You indeed have thoughtful ideas. It seems, we need more exchanges." (To be continued. If you work, you are welcome to vote on qidian.com. Your support is my greatest motivation. Mobile users, please visit m.qidian.com to read.)