A Survey of Mathematics' Unsolved Frontiers: From Collatz to the Millennium Problems — E8 Intelligence Research

Abstract

FINDING: A cluster of popular expositions on unsolved problems (Collatz, Millennium Prize problems, oldest open problems) — no new mathematics, but a survey of the field's frontier. MATH: Key problems referenced: Collatz conjecture (T(n)=n/2 if even, 3n+1 if odd; no cycle other than 4→2→1 proven); Riemann hypothesis (ζ(s)=0 ⇒ Re(s)=1/2); P vs NP; Navier–Stokes existence/smoothness; Yang–Mills mass gap; Birch–Swinnerton-Dyer (L(E,1)=0 ⇔ rank>0); Hodge conjecture. No new constants or ratios derived. CONNECTION: None directly stated. However, Collatz's 3n+1 structure relates to modular arithmetic (mod 2), and the Riemann zeta's critical line Re(s)=1/2 is a symmetry axis — but no explicit golden ratio, base-60, or crystallographic link in the videos' summaries. The "oldest unsolved problem" (likely perfect numbers / Euclid–Euler) touches on Mersenne primes (2^p−1) and even perfect numbers (2^{p−1}(2^p−1)), which have a lattice-like divisibility structure but no direct 0.618/1.618 ratio Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com