Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research

FINDING: The search results are a mixed bag of Numberphile videos on unsolved problems (Hadwiger-Nelson, odd perfect numbers, Josephus problem, hat problems, zero) plus one irrelevant arXiv paper on omnidirectional video quality. No single new mathematical discovery is presented; rather, these are pedagogical expositions of known open problems. The only concrete mathematical content is the *existence* of these problems and their known partial results. MATH: - **Hadwiger-Nelson problem**: The chromatic number of the plane, χ(ℝ²). Known bounds: 5 ≤ χ ≤ 7 (as of 2018; the lower bound was raised from 4 to 5 by de Grey using a 1581-vertex unit-distance graph). No exact value. - **Odd perfect numbers**: If N is odd and perfect, then N = p^α · m² where p ≡ α ≡ 1 (mod 4) (Euler form). No such N known; lower bound N > 10^1500 (current). - **Josephus problem**: For n people, step k, the survivor J(n,k) satisfies J(1,k)=1; J(n,k) = (J(n-1,k)+k-1) mod n + 1. Closed form for k=2: J(n,2) = 2l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com