{"id":"four-colour-theorem","domain":"discrete","type":"Theorem","title":"Four Colour Theorem","slug":"four-colour-theorem","url":"/mathematics/discrete/four-colour-theorem/","statement":"Any planar map can be coloured with 4 colours such that no two adjacent regions share a colour.","conjectured":"1852, Francis Guthrie","proved":"1976, Kenneth Appel and Wolfgang Haken","summary":"First major theorem proved using essential computer assistance (1,936 cases checked). Formally verified in Coq by Gonthier, 2005.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Appel, K. and Haken, W. (1977). Every planar map is four colorable. Illinois Journal of Mathematics, 21, 429-567."},{"tier":1,"citation":"Robertson, N., Sanders, D., Seymour, P. and Thomas, R. (1997). The four-colour theorem. Journal of Combinatorial Theory, Series B, 70(1), 2-44."},{"tier":2,"citation":"Gonthier, G. (2008). Formal proof—the four-color theorem. Notices of the AMS, 55(11), 1382-1393."},{"tier":3,"citation":"Wilson, R. (2002). Four Colors Suffice. Princeton University Press."}],"relationships":[{"type":"uses","target":"graph-theory","label":"Graph Theory — planar graphs"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.5"}