A Structural Taxonomy of Unsolved Mathematical Problems — E8 Intelligence Research

FINDING: The corpus is a curated list of popular expositions on unsolved problems (Collatz, Millennium Problems, Riemann Hypothesis, etc.), not a single new mathematical result. The key meta-insight is the *structural taxonomy* of these problems: most reduce to questions about **iterative dynamics on integer lattices**, **analytic continuation of zeta-type functions**, and **constraints on Diophantine approximations**. MATH: - Collatz: \( T(n) = \begin{cases} n/2 & n \equiv 0 \pmod{2} \ 3n+1 & n \equiv 1 \pmod{2} \end{cases} \) — open question: does \(\forall n, \exists k: T^k(n)=1\)? - Riemann Hypothesis: \(\zeta(s)=0 \implies \Re(s)=\frac{1}{2}\) — critical line symmetry. - Millennium Problems: P vs NP, Navier–Stokes existence/smoothness, Yang–Mills mass gap, Birch–Swinnerton-Dyer, Hodge conjecture, Poincaré conjecture (solved). - Constants implied: \(\zeta(2)=\pi^2/6\), \(e^{\pi\sqrt{163}}\) (near-integer), and the golden ratio \(\varphi = \frac{1+\sqrt{5}}{2} \approx 1.61 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com