Ancient Greece is a fascinating period as this is the start of the rational and scientific study of the world and many scientific principles were laid down. The Greek philosophers where in particular the first to think seriously about the role of institutions, markets and the functioning of government. In terms of health and medicine, we have all learned about the first attempts to explore and rationalize the human body, using a secular and scientific approach that was unparalleled until much later in history.
Carl Hampus Lyttkens points out that there was also a counter-movement where health care was leaning much more on religion. He also remarks that this is not unlike what we experience now with alternative medicine that has many followers and is even part of state sponsored health care in some countries. Calling these health cults, Hampus Lyttkens claims they arise because people are afraid of the uncertainties of life and cling to anything to reassure themselves. Just think about how many people believe in life after death while there is no scientific evidence for it. And healing cults are often, now and then, the realm of those who cannot afford the services of the scientific healers.