> what does Hardy mean when he says there is no permanent place for ugly mathematics? He means the same thing Kelly Johnson did: if something is ugly, it can't be the best solution. There must be a better one, and eventually someone will discover it.

I don't think Hardy's take really stands up today. There is at least one mathematical fact which has been proven through exhaustive computerised tests, and which no-one has (yet) been able to prove without using computers.

Ugly? I suppose so. Is there a 'place for it'? I don't see why not.

https://en.wikipedia.org/wiki/Four_color_theorem#Proof_by_co...