[andrewcchen]

I'd love to know what makes this theorem so useful, but I doubt I will understand much considering this is in an area of math I know almost nothing about.

I imagine it must be very hard to explain the theorem while making it accessible and interesting to the general public.

[AstralStorm]

Among other things, completeness of simplex, trust-region like optimization, problem space search algorithms.

[tezka]

how is it related to any of these? do you have links to articles?

[p1esk]

He said it takes him “hours” to explain the theorem to phds in other subfields of math.

[8bitsrule]

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.)