This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
In 1928, a young English mathematician and philosopher named Frank Ramsey was not trying to found a branch of combinatorics. He was trying to settle a question in formal logic, the decision problem for a fragment of first-order logic, and along the way he proved a lemma so useful on its own that it eventually outgrew the paper that contained it. The result now called Ramsey's theorem says, in its simplest form, that if the connections between enough objects are each colored one of two colors, some large fully one-colored group of connections is guaranteed to exist, no matter how the coloring is chosen. Color every pair of people at a large enough party as mutual acquaintances or mutual strangers, and Ramsey's theorem guarantees a group of a certain size who all know each other, or a group of a certain size who are all strangers, however the party's friendships happen to fall. The theorem generalizes far beyond parties and pairs, to larger groups, more colors and more abstract objects than people, but the party version is the one that made the result famous outside mathematics. Ramsey died in 1930 at twenty-six, having never seen his lemma become a field. Ramsey theory, the branch of combinatorics built on generalizing it, asks how large a structure has to be before some specified kind of order becomes unavoidable inside it, and the honest, almost paradoxical answer his theorem gives is that past a certain size, complete disorder is not a possibility at all. The exact size where order becomes unavoidable, the Ramsey number for a given case, is itself often extremely hard to compute; some small Ramsey numbers are still not known exactly, only bounded, decades after the theorem that guarantees their existence.