The Four Colour Theorem

Any map of contiguous regions can be coloured with only four colours so that no two adjacent regions share the same colour. This was conjectured in 1852 but only proved in 1976 by Kenneth Appel and Wolfgang Haken – the first major theorem proved with extensive computer assistance. They reduced the problem to 1,936 unavoidable configurations, each checked by a program. Critics complained, but today computer‑assisted proofs are standard. The theorem is a landmark in combinatorics and computational mathematics.