Numberphile's Unsolved Problems and a Video Quality Paper — E8 Intelligence Research

Abstract

FINDING: A collection of Numberphile videos on unsolved problems (Hadwiger-Nelson, odd perfect numbers, zero paradoxes, Catalan's conjecture, Josephus problem) plus an unrelated arXiv paper on omnidirectional video quality assessment. | MATH: No single equation extracted; key problems: (1) Hadwiger-Nelson — chromatic number of the plane, χ(ℝ²) ∈ {5,6,7} (recently narrowed to 5–7 via de Grey's 2025-unit-distance graph, but exact value open); (2) Odd perfect numbers — if N is odd perfect, N > 10^1500, N ≡ 1 mod 12 or N ≡ 9 mod 36, and N has at least 101 prime factors (with specific congruence constraints); (3) Zero division — undefined in fields; 0^0 is indeterminate in limits but often defined as 1 in combinatorics/binomial theorem; (4) Catalan's conjecture — only consecutive perfect powers are 8 and 9 (3²−2³=1), proven by Mihăilescu (2002); (5) Josephus problem — survivor position J(n,k) = (J(n−1,k)+k) mod n, with closed form J(n,2) = 2l+1 where n = 2^m + l. | CONNECTION: Weak direct l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com