Do mathematical truths subsist independently of human consciousness? Take the axioms of group theory as a lab example. There are many groups which vary in a number of ways, but they all share these properties: A group is a set G with a function p from its cartesian product GXG to G satisfying 1. p(a,p(b,c)) = p(p(a,b),c)) 2. there is an element e of G for which p(a,e) = p(e,a) = a for all elements of G. e is called the identity of the group G. 3, For every element a of G, there is an element a' satisfying p(a,a') = p(a',a) = e. a' is called the inverse of a. Groups were discovered in the nineteenth century, largely by Galois. My question, did the properties of a group exist before Galois? Did all the many theorems of group theory derives from those proerties exist then? Were they TRUE then?