Mathematics · Combinatorics & Discrete Mathematics
A topic within Combinatorics & Discrete Mathematics, itself one of 11 topics in that field and part of Mathematics.
No prior grounding assumed.
Happy Ending Problem
Ron Graham (Numberphile) · 2014
Explains the Happy Ending problem — that enough points in general position always contain a convex quadrilateral — as Ramsey theory in miniature, and…
Primary sources and full treatments.
On a Problem of Formal Logic
Frank P. Ramsey · 1930
Proves that any sufficiently large structure must contain a highly ordered substructure, showing total disorder is itself impossible past a certain…
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Ron Graham (Numberphile)
Explains the Happy Ending problem — that enough points in general position always contain a convex quadrilateral — as Ramsey theory in miniature, and traces the bound's link to Graham's number.
link checked 17 Sept 2026Frank P. Ramsey
Proves that any sufficiently large structure must contain a highly ordered substructure, showing total disorder is itself impossible past a certain size.
link checked 17 Sept 2026Paul Erdos & George Szekeres
Gives a new proof of Ramsey's theorem via the pigeonhole principle and uses it to show that enough points in general position always contain a convex polygon of any given size.
link checked 17 Sept 2026