If I were to ask a blacksmith something like "why does quenching and reheating a blade make it stronger" how would he respond? Did blacksmiths develop their methods through pure trial and error, or did they have some form of proto-metallurgy that gave a loose scientific framework?
I asked about the medieval period to give my question some specificity, but an answer about any time period would be welcomed.
No, medieval smithing was not an investigative science. It was learned through an apprentice-master relationship, and techniques were passed down the same way. This is not to say that smiths didn't innovate, but that they didn't do it in a systematic way, and were not overly concerned with anything but the function.