In mathematics, is an AXIOM assumed as an act of faith? Why or why not?

Any mathematics above arithmetic is abstraction, it is given that it is an artificial model of reality, not reality itself, so an axiom is a convention that while not entirely arbitrary, it is understood that other axia may be used in different forms of the same branch of math (e.g there are two major forms of non-Euclidian geometry that substitute different axioms for Euclid's forth axiom).