Euler's Unsolved Problems and Ellipse Papers: Odd Perfect Numbers and Extremal Geometry — E8 Intelligence Research

FINDING: Project Euler hardest unsolved problems and odd perfect numbers remain open; Euler's extremal ellipse papers translated. | MATH: No new equations or constants extracted from the provided search results. The Veritasium video on odd perfect numbers references the unsolved problem: existence of \( n \) such that \( σ(n) = 2n \), where \( σ \) is the sum-of-divisors function. Euler's ellipse papers (E563, E691, E692) involve minimizing area or perimeter of ellipses through fixed points — no specific equations given in the abstract. | CONNECTION: No geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries, or root systems are mentioned or implied in the provided text. | DEPTH: 2 — The findings are meta-references to unsolved problems and a translation of historical work, not new mathematical results or deep structural insights. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com