Concerned only with the ethereal world of abstraction, mathematicians are free to introduce this notion of a group and to require that anything that is a group satisfy these criteria. These axioms are neither right nor wrong; they are simply the rules that mathematicians have chosen to require of something that they have decided for some reason or other to call a “group.”

The wonder of group theory is that its relevance to the disciplines of both mathematics and natural science far exceeds the self-contained boundaries within which it was first developed.

Bruce A. Schumm (2004). Deep Down Things: The Breathtaking Beauty of Particle Physics.  Johns Hopkins University Press. pp. 143–144. ISBN 0-8018-7971-XOCLC 55229065.