is blue, then all three edges are red and we have a red triangle, namely, ABC. Ramsey's paper The utter simplicity of this argument, which so powerfully produces a very interesting conclusion, is what makes the theorem appealing. In 1930, in a paper entitled 'On a Problem of Formal Logic,' Frank P. Ramsey proved a very general theorem (now known as Ramsey's theorem) of which this theorem is a simple case. This theorem of Ramsey forms the foundation of the area known as Ramsey theory in combinatorics. Boundaries to the theorem The conclusion to the theorem does not hold if we replace the party of six people by a party of less than six. To show this, we give a coloring of K5 with red and blue that does not contain a triangle with all edges the same color. We draw K5 as a pentagon surrounding a star (a pentagram). We color the edges of the pentagon red and the edges of the star blue. Thus, 6 is the smallest number for which we can claim the conclusion of the theorem. In Ramsey theory, we write this fact as: References V. Krishnamurthy. Culture, Excitement and Relevance of Mathematics, Wiley Eastern, 1990. . External links Party Acquaintances at cut-the-knot (requires Java) Ramsey theory Theorems in discrete mathematics Articles containing proofs