> And -let me get this right- you want society to keep paying you, so you can play with your imagination?

No, pure mathematics is almost never completely recreational. No serious paper gets published in a decent journal without having some motivation and connection to the rest of mathematics.

It is of course valid to ask why we should fund research in pure mathematics, which is not directly related to any "real" applications.

Same question applies to things like niche art, literary studies, history, etc. One answer is that these things are relatively cheap, and our culture would be poor without these things.

With pure maths the advantage is also that it is cheap, and the payoff in applications (if and when they happen) is high.