Numberphile's Coverage of Four Classic Unsolved Math Problems — E8 Intelligence Research

FINDING: Numberphile videos cover four major unsolved/classic problems — Hadwiger-Nelson (chromatic number of the plane), Collatz (3n+1), the 7825 counterexample (likely the Boolean Pythagorean triples problem), and Josephus (survivor permutation) — plus Veritasium on odd perfect numbers. No new mathematics is presented; these are expository. | MATH: Hadwiger-Nelson: χ(ℝ²) ∈ {5,6,7} (lower bound 5 from de Grey 2018, upper bound 7 from hexagonal tiling). Collatz: T(n)=n/2 if even, 3n+1 if odd; no cycle other than 4→2→1 proven. 7825: first n for which the Pythagorean triples property fails (SAT solver proof, Heule et al. 2016). Josephus: J(n,k) = (J(n−1,k)+k) mod n, J(1,k)=0. Odd perfect numbers: σ(N)=2N, N odd; none known, lower bound N>10^1500. | CONNECTION: Hadwiger-Nelson upper bound 7 arises from hexagonal tiling — a crystallographic lattice (hexagonal, 6-fold symmetry, root system A₂). The lower bound 5 uses a 1581-vertex unit-distance graph with 5-chromatic structure — related to Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com