Ramsey theory
Graph theory and combinatorics
The study of the order that must appear in any sufficiently large structure, however that structure is arranged.
What is usually left out
Its slogan is that complete disorder is impossible. The results are typically existence statements with terrible bounds: R(5,5) is known only to lie between 43 and 46, and Erdős’s remark that humanity should sooner try to destroy an alien demanding R(6,6) than compute it is a fair summary of the difficulty.
Related terms
In the atlas
- Ramsey numbers — Combinatorics, open