Numberphile Videos on Classical Unsolved Problems, Not New Discoveries — E8 Intelligence Research

FINDING: The search results are a mixed bag — mostly Numberphile videos on classical unsolved problems (Hadwiger-Nelson, odd perfect numbers, Catalan's conjecture, the 7825 problem) plus one irrelevant arXiv paper on omnidirectional video quality. No single new mathematical discovery is presented; the content is expository. | MATH: Hadwiger-Nelson: chromatic number of the plane χ(ℝ²) — known bounds 5 ≤ χ ≤ 7 (lower bound raised from 4 to 5 by de Grey in 2018, using a 1581-vertex unit-distance graph; the "7825" video refers to a smaller 7825-vertex graph also proving χ≥5). Odd perfect numbers: if N is odd perfect, N = p^k m² with p ≡ k ≡ 1 (mod 4), and N > 10^1500 (current lower bound). Catalan's conjecture (Mihăilescu's theorem): x^a − y^b = 1 has only solution 3² − 2³ = 1. Josephus problem: J(n,k) recurrence J(1,k)=0, J(n,k) = (J(n−1,k)+k) mod n; closed form for k=2: J(n) = 2(n − 2^⌊log₂ n⌋) + 1. | CONNECTION: Hadwiger-Nelson is deeply tied to lattice structures — the hexagonal lattic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com