the four colour theorem

How many colours does it take to colour a map? The title probably gives you a hint.

When I was a kid (no, I don’t know how old exactly… around 10), my dad set me and my brothers a challenge. Could we create a map which required more than four colours to colour it in? Here are the rules:

– no two adjacent “countries” can have the same colour,
– if two “countries” meet only in a point then they are not adjacent, and
– each “country” must be completely connected (Alaska, for instance, couldn’t count as part of the USA)

At the time I had no idea that this was a world famous mathematical concept, I just thought it was a frustrating problem. We didn’t find a map requiring 5 colours and, indeed, we couldn’t have. It was proved in 1976 that 4 is the maximum number of colours needed and, importantly, it was proved by using a computer.

In 1976 this was revolutionary, groundbreaking and contentious. Lots of mathematicians refused to accept the proof because it couldn’t be checked by hand. It has since been proven by a computer program we know to be reliable but it was a point of argument among mathematicians for many years.

 

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