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  "body": "\n## Statement\n\nLet $r$ and $s$ be positive integers.\nThen there is a positive integer $n$ with this property.\nColour each edge of the [[complete graph|03WKB2H474]] $K_n$ blue or red, in any way.\nThen there is a blue [[clique|0G52BPNPKG]] with $r$ vertices or a red clique with $s$ vertices.\n\n## Remarks\n\nThe least such $n$ is the [[Ramsey number|01DSVCRF6X]] $R(r, s)$.\nThe proof gives the bound $R(r, s) \\le R(r - 1, s) + R(r, s - 1)$, by induction on $r + s$.\nThe theorem also holds for any finite number of colours.\n\n## History\n\nFrank Ramsey proved the first version of the theorem in a 1930 paper on formal logic.\nThis result started the field now called Ramsey theory.\n\n## Explanations\n\n### L1 human\n\nComplete disorder is impossible in a large enough structure.\nIf you colour the edges of a large complete graph with two colours, a large clique of one colour always appears.\n",
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