Four Colour Map Theorem

The theorem states that four colors are enough to color any map such that two adjacent regions will not share the same color.

The conjecture was suggested in 1852 by Frederik Guthrie to his professor, mathematician Augustus De Morgan, who made it public and contributed to its solution.

In a second stage, mathematicians focused on finding techniques to reduce the complicated maps to a set of classifiable cases that could be tested.

Initially, the set was thought to contain nearly 9,000 members, and so the mathematicians appealed to computer techniques to write algorithms that could do the testing for them.

In 1976, Kenneth Appel and Wolfgang Haken reduced the testing problem to a set with 1,936 configurations, and a complete solution to the four-color Conjecture was achieved with the help of the computer.

This theorem is simple enough for school students to try their hand at colouring maps with 3 & 4 colours. That 1,936 different configurations are possible would be a surprise for them.

The theorem was proved within graph theory, with the crucial help of Euler’s formula; however, projective geometry, knot theory, topology, and combinatorics were appealed over time to contribute to the proof.

This was the first time a computer-assisted proof was accepted in math.

It is likely to open the doors for many such proofs.