Unsolved Math Problems: A Survey of Known Bounds and Open Questions — E8 Intelligence Research

FINDING: The search results are a mixed bag of Numberphile/Veritasium videos on classic unsolved problems (Hadwiger–Nelson, odd perfect numbers, Josephus, zero, Catalan) plus one unrelated arXiv paper on omnidirectional video quality assessment. No single new mathematical discovery is presented; the core value is the *existence* of these open problems and their known partial results. | MATH: - Hadwiger–Nelson: chromatic number of the plane χ(ℝ²) — known bounds: 5 ≤ χ ≤ 7 (lower bound improved from 4 to 5 by de Grey in 2018; upper bound from 7 via hexagonal tiling). No exact value. - Odd perfect numbers: If N is odd perfect, then N > 10¹⁵⁰⁰, N has at least 101 prime factors (with multiplicity), and N ≡ 1 mod 12 or N ≡ 9 mod 36 (Euler form: N = q^α · m², q ≡ 1 mod 4). No existence proof. - Josephus problem: J(n,k) = (J(n−1,k)+k) mod n, with closed form J(n,2) = 2·(n − 2^⌊log₂ n⌋) + 1. - Catalan's conjecture (now Mihăilescu's theorem): x^a − y^b = 1 has only solution 3² − 2³ = 1. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com