By Andrew Kingdom. (I'll update the details when I have time.)
The four-colour theory states that any map can be coloured in using a maximum of four colours without using the same colour for neighbouring regions. This has been proven using a computer.
My discovery was a partial-geometric method (collapsing all combinations down to a single set of incomplete-shapes) to prove all combinations on paper, which I believe hadn't been done previously. This can also be done using a divided 2D toroidal (donut) shape series, but I'm not 100% sure it covers all possibilies.