Undecidability: The Inherent Limits of Algorithmic Proof in Formal Systems — E8 Intelligence Research

FINDING: Undecidable problems, such as the Halting Problem and Gödel's incompleteness, prove that certain mathematical truths cannot be algorithmically decided or proven within a given formal system. | MATH: No specific equations or constants extracted; core concept is the existence of a set of true statements that are unprovable in a consistent, sufficiently powerful formal system (e.g., Peano arithmetic). | CONNECTION: No direct geometric ratios or symmetries found. The undecidability results are meta-mathematical, not geometric. | DEPTH: 9 — This is a foundational limit on mathematical knowledge, but the provided sources lack the specific equations or constants requested. The depth rating reflects the profound nature of the discovery itself, not the completeness of the extraction. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com