In the 'Numberphile' video mentioned above (about 3 minutes in), it says the initial problem about illumination was asked in the 1950s. This leads me to suspect

In the 'Numberphile' video mentioned above (about 3 minutes in), it says the initial problem about illumination was asked in the 1950s. This leads me to suspect that it has something to do with building weapons. (Brit physicist Roger Penrose found a solution where some spots were dark.)