Comment by normalhuman

> Why are you so bitter?

I don't know, it's just how I am.

> I doubt PhD+ people do that type of research "just for fun"

Well you'd be surprised. All the professional mathematicians I know do math for its own sake. Some amateurs also do it "just for fun", as you say.

> Someone answered elaborately, and I'm glad they did. Thanks anyway.

A bigger person than me, especially considering the tone of your question.