I was going to edit my old post with this new thought, but then I decided that it really was a different (though related) thought...
So I was wondering exactly why constructive activity (like learning about Maths or anything else) IS useful. You could say that it runs society, but in my opinion its debatable whether our society actually benefits the human race much at all.
My best answer is the constructive activity develops your capacity for daydreaming in a more interesting, and (dare I say it?) constructive way. When I was a baby I doubt my daydreaming went further than wondering when mum would come and give me my next meal. Yet Albert Einstein, who presumably had fairly similar baby-daydreams to me, went on to dream up E=mc2! At some point along the line, development must have taken place.
Was that development the result of constructive activity in some sense? Who knows. But that's my best suggestion...for now.