Comment by srean

I agree and not all mathematicians care about or are motivated by how well a set of axioms model the real world. To a mathematician the richness of the consequences of a set of axioms is its own reward.

In this sense mathematicians are board-game designers. It matters less how well the game describes nature's reality than how fun it is to play the game that results.

Now if you were a physicist, the game has already been design by some other mechanism and you have to probe to understand the rules and discover its consequences.