While Greece was in its Golden Age, the Etruscans (the precursors of the Romans) were burying their dead with appliances that were used to maintain space and prevent collapse of the dentition during life. Then in a Roman tomb in Egypt, a researcher found a number of teeth bound with a gold wire -- the first documented ligature wire! At the time of Christ, Aurelius Cornelius Celsus first recorded the treatment of teeth by finger pressure. Despite all this evidence and experimentation, no significant events in orthodontics really occurred until the much later, in around the 1700s.
Braces continued to wrap around the teeth until the mid 1970s, when direct bonding became a reality. Why did it take so long for dentists to invent the modern bonded bracket? The adhesive! The bonded bracket was actually invented earlier, but the formulation for the adhesive wasn't perfected until almost a decade later.