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  "body": "\n## Summary\n\nRamsey theory studies the statements that every large enough structure, divided into finitely many parts, has a part that contains a given regular substructure.\nIts founding result is [[Ramsey's theorem|00TQV3F5S4]] on monochromatic cliques in coloured complete graphs, with the [[Ramsey numbers|0K9QVPJYJF]] as its quantitative side.\nIn the integers it includes [[Schur's theorem|V6XJQXZ7E8]], [[van der Waerden's theorem|V96FRZ2ME1]] and [[Rado's theorem|BZSGRCTFH4]], and the abstract [[Hales–Jewett theorem|14SGZ5HA4Y]] contains many of these.\nDensity versions, such as [[Szemerédi's theorem|B23B0QEMN5]], link it to [[additive combinatorics|3NM362A2JG]] and ergodic theory.\n\n## Explanations\n\n### L1 human\n\nRamsey theory says that complete disorder is impossible.\nIf you colour the objects of a big enough structure with a few colours, some pattern always appears in a single colour.\nThe [[pigeonhole principle|0HGVCWQGY3]] is the simplest case: with $n$ colours and $n + 1$ objects, two objects get the same colour.\nA famous example: among any six people, there are three who all know each other or three who are all strangers to each other.\nThe hard questions are how big \"big enough\" must be, and these numbers are often unknown even for small cases.\n",
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