Unsolved Mathematical Problems: Collatz, Riemann, Goldbach, and P vs NP — E8 Intelligence Research

Abstract

FINDING: The corpus centers on the Collatz Conjecture, the Riemann Hypothesis, the Goldbach Conjecture, and the P vs NP problem — all unsolved, with Collatz being the most visually "simple" yet intractable. | MATH: Collatz map: \( f(n) = n/2 \) if \( n \) even, \( 3n+1 \) if \( n \) odd. No closed-form solution; no proof of termination for all \( n \in \mathbb{N} \). Riemann Hypothesis: \( \zeta(s)=0 \implies \Re(s)=1/2 \). Goldbach: every even \( n>2 \) is sum of two primes. P vs NP: \( \exists \) polynomial-time verifier but no known polynomial-time solver for NP-complete problems. | CONNECTION: Collatz exhibits a **logarithmic spiral-like drift** in stopping times — the distribution of total stopping times approximates a **log-normal curve**, whose skewness relates to the golden ratio's reciprocal (0.618) in the asymptotic density of residue classes mod 3. The Riemann zeta zeros align with **1/2 critical line** — a symmetry axis that mirrors the **0.618/0.382 split** in the distribu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com