Unsolved Math Problems from Numberphile and Veritasium — E8 Intelligence Research

FINDING: The search results surface five distinct unsolved/classic problems from Numberphile/Veritasium — Hadwiger-Nelson (chromatic number of the plane), Josephus problem, odd perfect numbers, Catalan's conjecture (now theorem), and Collatz conjecture — plus one irrelevant omnidirectional video quality paper. | MATH: Hadwiger-Nelson: χ(ℝ²) ∈ {5,6,7} (lower bound 5, upper bound 7; exact value unknown). Josephus: J(n,k) = (J(n−1,k)+k) mod n, J(1,k)=0. Odd perfect: σ(n) = 2n, n odd — none known; if exists, n > 10¹⁵⁰⁰. Catalan: xᵃ − yᵇ = 1 has only solution 3² − 2³ = 1 (proved by Mihăilescu). Collatz: T(n) = n/2 if even, 3n+1 if odd; conjecture all n → 1. | CONNECTION: Hadwiger-Nelson is a lattice/chromatic problem — the Moser spindle (7 vertices, 11 edges) and Golomb graph are unit-distance graphs; the lower bound 5 uses a 5-chromatic unit-distance graph. The hexagonal lattice (base-60-adjacent, 6-fold symmetry) gives the upper bound 7 via 7-coloring of the plane. Collatz's 3n+1 structur Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com