This lecture will be on the old map coloring problem. It was conjectured 150 years ago that four colors suffice to paint the world map where each country is a connected set with finite border. However it was proved only in 1976 using thousands of hours of fast computers of the day. I shall give a proof of the weaker form, i.e. 5 colours suffice for the painting. An exercise in combinatorics and graph theory.