Good mathematicians see analogies between theorems;
great mathematicians see analogies between analogies.
The Minds call it Infinite Fun Space.
The space of all possible mathematical worlds, free to explore and to play in.
It is infinitely more expressive than the boring base reality and much more varied: base reality is after all just a special case.
From time to time the Minds have to go back to it to fix some local mess, but their hearts are in Infinite Fun Space.