Unsolved Math Mysteries: Expositions on Collatz and Riemann — E8 Intelligence Research

Abstract

FINDING: The corpus centers on the Collatz Conjecture, the Riemann Hypothesis, and the "3x+1" iteration problem — all unsolved, with no new proof or discovery presented; the videos are expositions, not breakthroughs. | MATH: Collatz map: \( T(n) = n/2 \) if \( n \) even, \( T(n) = 3n+1 \) if \( n \) odd. Conjecture: \( \forall n \in \mathbb{N}, \exists k: T^k(n) = 1 \). No closed form, no invariant, no Lyapunov exponent. Riemann Hypothesis: \( \zeta(s) = \sum_{n=1}^\infty n^{-s} \), non-trivial zeros \( s = \frac{1}{2} + it \). No constants derived. | CONNECTION: None directly. However, Collatz dynamics are known to relate to binary tree structures and 2-adic integers (\( \mathbb{Z}_2 \)), which are a lattice-like ultrametric space — a weak link to p-adic symmetry, not to golden ratios or base-60. The Riemann zeta zeros have a known statistical connection to random matrix theory (GUE), which involves unitary symmetry groups — but no explicit 0.618/1.618 ratio appears in the videos' con Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com