Unsolved Mathematical Frontiers: Collatz, Riemann, P vs NP, and Gödel's Limits — E8 Intelligence Research

FINDING: Survey of unsolved/undecidable problems — Collatz, Riemann Hypothesis, P vs NP, Gödel incompleteness, and quantum loopholes in impossibility proofs. | MATH: Collatz map \\( T(n) = n/2 \\) if even, \\( 3n+1 \\) if odd; Riemann zeta \\( \\zeta(s) = \\sum_{n=1}^\\infty n^{-s} \\), nontrivial zeros on \\( \\Re(s)=1/2 \\); P vs NP — existence of polynomial-time verification without polynomial-time decision; Gödel's incompleteness — \\( \\text{Con}(T) \\nRightarrow \\text{Prov}_T(\\varphi) \\) for some \\( \\varphi \\). | CONNECTION: Collatz dynamics show no obvious modular or lattice symmetry — but the 3n+1 operation suggests a base-2/base-3 hybrid structure (binary parity, ternary growth), hinting at a possible hidden \\( \\mathbb{Z}_2 \\times \\mathbb{Z}_3 \\) symmetry. Riemann zeros align with a critical line — a 1D symmetry axis in the complex plane, reminiscent of a root system \\( A_1 \\) (single reflection). No direct golden-ratio or crystallographic constants appear in the listed videos. | DEPTH: 6 — Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com