Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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
Related
- MERLIN SCIENCE — Numberphile Videos Survey Unsolved Problems Without New Mathematical D — E8 Intelligence Research
- Search Yields No Unsolved Putnam Problems, Only Solved Ones — E8 Intelligence Research
- Geometry vs Binary: Unsolved Mathematics — unsolved problems in computational geometry 2025 o — E8 Intelligence Research
- Surveying Competition Problems: Erdős–Straus as Most Accessible Unsolved Conjecture — E8 Intelligence Research
- Unsolved Math Problems and Competition Math Video Compilation — E8 Intelligence Research
BibTeX
@misc{caldin2026numberphile,
title = {{Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465123},
url = {https://zenodo.org/records/23465123},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Numberphile Videos Survey Unsolved Problems Without New Mathematical Discovery — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465123
UR - https://zenodo.org/records/23465123
AB - 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
ER -