Numberphile's Unsolved Math Problems: Chromatic Plane, Odd Perfect Numbers, and More — E8 Intelligence Research

Abstract

FINDING: Numberphile videos highlight several unsolved problems: Hadwiger-Nelson (chromatic number of the plane), Lollipop problem (graph theory), odd perfect numbers, Josephus problem, and the 7825 problem (Erdős–Graham conjecture). | MATH: Hadwiger-Nelson: chromatic number χ(ℝ²) ∈ {5,6,7} (lower bound 5 via de Grey, 2018). Odd perfect numbers: if N exists, N > 10¹⁵⁰⁰, ω(N) ≥ 101 (Nielsen, 2015). Josephus problem: recurrence J(n,k) = (J(n-1,k)+k) mod n, closed form for k=2: J(n) = 2(n - 2^⌊log₂ n⌋) + 1. 7825 problem: smallest n such that any coloring of {1,...,n} with 2 colors has a monochromatic solution to 1/x + 1/y = 1/z (Erdős–Graham: n=7825, proven by Croot, 2003). | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries appear. The Hadwiger-Nelson problem involves planar geometry and graph coloring, but no specific golden ratio or root system link. | DEPTH: 3 — These are well-known open problems with significant combinatoria Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com