Symmetry doesn't have a "history" - it has always been present as a natural phenomenon. Symmetry is found as a basic property of some natural objects (certain kinds of crystals, for instance - think of snowflakes), various types of interactions (think of musical harmonies) and in many relationships. Symmetry has been used in architecture for thousands of years by cultures around the world.
In adding "math" as a tag to your question, I'm guessing you are working with symmetry in mathematical processes - perhaps looking at graphing symmetrical lines to answer equations. The process of identifying and recognizing such situations varies with each type of problem, so you could trace the history of the person who developed the particular type of math you are considering.