Colonialism and the Four-Colour Theorem

The Four-Colour Theorem about planar graphs implies that you only need four colours to properly draw a map, making sure that neighbouring countries are coloured differently. But this application comes with a caveat: the theorem is only guaranteed to work if the countries are all connected. This is essentially true of modern countries, so current political maps of the Earth only need four colours. But it wasn’t always this way; things were a lot more complicated back in the age of empires.

If we look back to the late 19th century, most of the planet was ruled by only a few countries, each having many satellite colonies scattered across the globe. Each colony was a new opportunity for empires to violate the hypotheses of the Four-Colour Theorem (as well as the basic principles of human decency). In sub-Saharan Africa, for example, the British, French, German, Portugese, and Belgian empires bordered each other — a configuration requiring five colours on a map.


What historical map requires the most colours?