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Kingdom of Math
Statistics, physics, astronomy, engineering... Mathematics finds applications in various scientific fields. Humans naturally believe themselves to be the sole darlings of these concise and lucid numbers. They devote themselves to expelling the Arcanists that symbolize disorder and chaos in number theory, all to preserve the harmony and unity of mathematics.
However, this remains merely a wish.
The realm of pure reason has never truly existed; perpetually hanging above it is the cloud of Gnosis.
Arcanum and rational systems; religious beliefs and scientific proof; the notion that "all things have numbers" and mathematics. They are all like two sides of a ruler, measuring everything in the world. The followers of Pythagoreanism have made significant contributions throughout history, and the theories of fundamental numbers have left an indelible mark on many.
However, the "Storm" swept unrelentingly throughout the world. Mathematics lost its once solid ground, leaving nothing but debris. Then, a pair of tender hands picked it up.
However, this remains merely a wish.
The realm of pure reason has never truly existed; perpetually hanging above it is the cloud of Gnosis.
Arcanum and rational systems; religious beliefs and scientific proof; the notion that "all things have numbers" and mathematics. They are all like two sides of a ruler, measuring everything in the world. The followers of Pythagoreanism have made significant contributions throughout history, and the theories of fundamental numbers have left an indelible mark on many.
However, the "Storm" swept unrelentingly throughout the world. Mathematics lost its once solid ground, leaving nothing but debris. Then, a pair of tender hands picked it up.
An Unfinished Demonstration
On the Supplementary Calculations of Soul Number 37
I hereby declare to approach this task with impartiality, to eliminate errors and omissions, and to treat each number with fairness, as I uphold the unique guidelines of a Corrector.
1: The smallest irregular prime number
Note: Based on the "Primitive Bernoulli Number" criterion, which is a rational number sequence closely related to number theory.
2: Repeating unit 111 (three consecutive 1s, where 3 is a prime number), 111 = 3 x 37
Note: She avoids the division between "finite" and "infinite."
3: Any number can be expressed as the sum of at most 37 fifth powers of 5
Note: She is special, possessing multiple possibilities.
4: A regular hexagon
Note: This corresponds to her influence and importance in the School of Apeiron.
...
37 is the third unique prime number in the decimal system and the third isolated prime number without a twin prime. It is the third Cuban prime, the fourth emirp, the fifth lucky prime ...
1: The smallest irregular prime number
Note: Based on the "Primitive Bernoulli Number" criterion, which is a rational number sequence closely related to number theory.
2: Repeating unit 111 (three consecutive 1s, where 3 is a prime number), 111 = 3 x 37
Note: She avoids the division between "finite" and "infinite."
3: Any number can be expressed as the sum of at most 37 fifth powers of 5
Note: She is special, possessing multiple possibilities.
4: A regular hexagon
Note: This corresponds to her influence and importance in the School of Apeiron.
...
37 is the third unique prime number in the decimal system and the third isolated prime number without a twin prime. It is the third Cuban prime, the fourth emirp, the fifth lucky prime ...
Geometric Problem
37: Oh! Another set of contradictions.
Pandora Wilson: Although I know very little about mathematics, I can sense the disappointment from your tone.
37: Free, selfish, untraceable—traits of irrational numbers. Fortunately, it adheres to coherence and maintains clear boundary criteria ...
Pandora Wilson: I hope this won't affect our conversation.
37: Of course not, addressing various math puzzles is precisely my job; I excel at it.
37: Now, please open up your quadratic surface.
Pandora Wilson: ...
Pandora Wilson: Ah—?
37: Fantastic! In Apeiron, we often engage with spheres and regular polyhedra... Opportunities to study special surfaces are quite rare.
37: Clearly, you don't belong to real quadratic surfaces, nor do you align with degenerate quadratic surfaces. But it's alright; I will find a place for you in the geometric classification of three-dimensional Euclidean space.
Pandora Wilson: ...Thank you.
Pandora Wilson: Although I know very little about mathematics, I can sense the disappointment from your tone.
37: Free, selfish, untraceable—traits of irrational numbers. Fortunately, it adheres to coherence and maintains clear boundary criteria ...
Pandora Wilson: I hope this won't affect our conversation.
37: Of course not, addressing various math puzzles is precisely my job; I excel at it.
37: Now, please open up your quadratic surface.
Pandora Wilson: ...
Pandora Wilson: Ah—?
37: Fantastic! In Apeiron, we often engage with spheres and regular polyhedra... Opportunities to study special surfaces are quite rare.
37: Clearly, you don't belong to real quadratic surfaces, nor do you align with degenerate quadratic surfaces. But it's alright; I will find a place for you in the geometric classification of three-dimensional Euclidean space.
Pandora Wilson: ...Thank you.