Core Concepts
機械学習を使用して素数の公式を発見することは不可能である。
Abstract
Kolmogorov's theory of Algorithmic Probability explores the limits of Machine Learning within the framework of entropy and complexity.
Maximum Entropy methods are developed to derive fundamental theorems in Probabilistic Number Theory.
The Prime Coding Theorem establishes the impossibility of discovering a formula for primes using Machine Learning.
Fundamental Lemmas and Theorems for Algorithmic Probability are proven, including Kolmogorov's Invariance theorem and Levin’s Universal Distribution.
Gödel’s incompleteness theorem is discussed in relation to algorithmic probability.
Stats
Kolmogorov Complexity is not computable.
Almost all integers are algorithmically random.
Quotes
"God made the integers; all else is the work of man." - Leopold Kronecker