Exploring Immortality Cultivation

The proof process of Poisson's Law of Large Numbers was relatively uncomplicated. If written into an academic paper, one lengthy paper would suffice. However, Wang Qi suppressed the urge to finish it and only included some discursive content in the outline of the paper.

"After all, I need to leave room for that one-track mind to join in later," Wang Qi said.

However, unlike the Shenzhou academic culture, which focuses solely on the content of papers, the Earth academic community also places significant emphasis on the quantity of publications. Wang Qi still had some grasp of the technique of splitting one paper into two complete papers, where the conclusion of the first serves as the basis for the second.

After drafting a substantial amount, Wang Qi set this task aside, preparing to discuss it with Bao Xiaoya before finishing.

"Alright, what should I tackle next?"

Seeing Wang Qi deep in thought, Zhen Chan kindly suggested, "I seem to remember that in your Modern Cultivator research, the arithmetic problem of one plus one equals two is quite popular, isn't it? Isn't it called the Bright Pearl Calculation? Why don't you give it a try?"

"The Bright Pearl Calculation is in the domain of Number Theory, and it's not quite compatible with me—especially since thinking of this problem reminds me of Chen Jingyun, followed by the thought, 'I'm stuck in Divine Capital, and it's all that bastard's fault,'" Wang Qi said with a grimace. "Moreover, the Bright Pearl Calculation is not 'one plus one equals two,' it's 'a prime plus a prime equals an even number,' written as (1+1), not 1+1."

The Bright Pearl Calculation was known on Earth as the Goldbach Conjecture. Interestingly, this calculation was "unearthed" in Shenzhou, and was also related to the Bo Family. Bao Yage and Bao Yuehan of this generation had another brother who was not strong in mathematics but had a promising son, the fourth Carefree Practitioner of the Bo Family, Bo Ligou. Bo Ligou, like his brother Bao Li'er, loved to travel. One day, during his journeys, he accidentally uncovered an ancient Arithmetician Cultivator's cave dwelling. The inheritance, treasures, and elixirs within were not worth mentioning, but there was a pearl that was particularly interesting because it bore a calculation problem not famous in ancient times.

The question was, can every even number greater than two be expressed as the sum of two prime numbers?

At first glance, the problem seemed simple, and most people intuitively believed it to be true. However, proving it turned out to be immensely difficult.

Because it was inscribed on a pearl, everyone called it "the crown jewel of mathematical reasoning," the Bright Pearl Calculation.

[Note: In Earth's history, the Goldbach Conjecture was written in a letter by Goldbach himself, a letter that was sent to Euler. Euler was a student of Johann Bernoulli, had a close brotherly relationship with Daniel Bernoulli, and was also intimately acquainted with Nicolas Bernoulli. Goldbach was also pen pals and travel companions with Nicolas Bernoulli. These individuals were among the early researchers of the Goldbach Conjecture. However, since Goldbach was not a mathematician, leaving only a conjecture, this book has chosen a different way for him to exist.]

"I just don't get it..."

Wang Qi sighed, "You should think it through too; did Chen Jingyun have nothing better to do than research why one plus one equals two... Ah, that's not right, there seem to be mathematicians with genuine concerns about their prostate health..."

There were indeed mathematicians who studied why one plus one equals two.

The more self-evident something is, the harder it seems to explain. One plus one equals two is the most classic example. Everyone knows one plus one equals two, but how many can articulate why that is?

If one could say that the typical difficult problem is one that most mathematicians cannot understand, then this domain is where everyone understands, but pushing even a step further is stymied.

Undoubtedly, those who can explain the rationale behind "one plus one equals two" are the elite arithmeticians capable of blazing a trail in this most fundamental domain.

"It's just unfortunate that the Pinoar Axioms already exist in this world," Wang Qi shook his head, feeling it might be better not to touch this area. Apart from this subject's profundity, it was also not very popular; even bringing Bao Xiaoya into it wouldn't draw much attention. Not worth it. The Pianuo Axioms, as significant and equal in status to Euclid's Axioms, somehow lag behind in fame by more than just a few blocks.

At that moment, Wang Qi remembered another problem, "Speaking of which, this area's too basic, not knowing it doesn't affect much... Why do I remember it so vividly?"

Knowledge fades with disuse. Although the Pianuo Axioms are about why one plus one equals two, being ignorant of them doesn't impact the ability to calculate one plus one equals two.

Why do I remember it so well, that it comes to mind at the slightest mention?

Suddenly, an insight flashed in Wang Qi's mind.

"This... seems to have something to do with that major event."

Hilbert's Program, the largest and most renowned mathematical research of the 20th century.

At the beginning of the 20th century, paradoxes, especially Russell's Paradox, caused a major shock to the mathematical and logical communities of the time. It directly challenged the foundation of mathematics and logic, known for their rigor, and shook the standards of reliability of traditional mathematical concepts, propositions, and methodologies. In other words, the emergence of paradoxes related to the very foundation of all mathematics, leading to what was called the third Mathematical Crisis. The leading figure in the mathematical community, Hilbert, launched Hilbert's Program to address this crisis and to permanently solve all mathematical crises. The main goal of the project was to provide a secure theoretical foundation for all of mathematics. Its principal part involved proving completeness, compatibility, and decidability.

And yet, within this program, Godel unexpectedly proved incompleteness.

Turing completed the proof of decidability following Godel's ideas and, based on this breakthrough in mathematical logic, perfected computer theory.

Wang Qi leaped up and pulled out a "netbook" from his Storage Bag, a gift from Su Junyu, and began searching the Immortal Alliance's paper database.

"Keywords, proof theory... there it is! Then, natural numbers, arithmetic system..."

As Wang Qi added keywords, fewer and fewer papers appeared in the database search, until at last, he discovered what he was searching for.

"On the so-called Proof by Von Neumann," author, Feng Luoyi.

The paper was from five years ago.

The presence of Spiritual Energy in Shenzhou meant the "Technology Black Box" was significant, and the Technology Tree differed from Earth's. Comparably, calculators, the counterparts to computers, had been widely used for many years, and artificial intelligence was already on the agenda, yet mathematical logic, which underpins computer theory, lagged behind Earth's.

Wang Qi didn't hesitate to allocate the Merit points he had received from Beifeng today and exchanged them for the paper, skipping the process to read only the conclusion.

"In this subsystem, it is feasible to provide a rigorous proof of finiteness... This is a replica of Von Neumann 'On Hilbert's Proof Theory,'" Wang Qi closed his eyes and contemplated.

This cosmic System, lacking the existence of Godel, meant that mathematical logic took a path different from that of Earth...

Wang Qi exclaimed, "This is indeed a good path."