The Hippocratic Corpus was the work of many physicians over many generations. Similarly the oath ascribed to Hippocrates, the most famous of the ancient Greek medical texts, is wisdom of the era. An English translation of the Greek oath may seem particularly related to gods and family, but may also hold insight in modern medicine. This oath has been updated many times. Compare the original to the version used at the Penn State College of Medicine. The themes are there, but maybe without the risk to history.

At least the brief, science–centric version for our purposes. Antiquity is before 500 AD. Socrates (born c. 469 BC), Hippocrates (born c. 460 BC), Plato (born c. 427 BC) and Aristotle (born c. 384 BC) are ancients. The middle ages run from 500 to 1400 AD. While we might not have much to say about the scientific story during this time period, there were some really important developments like the founding of the first western university in 1088 AD. From 1400 to 1600 AD it was the renaissance. Book printing started, learning abounded, there was a protestant reformation; a lot happened. The scientific revolution is during this period. The next big phase is the industrial revolution, starting c. 1750 and running 100 years (that is the period of intense change, you live in a industrial society today). This overlaps with the imperial age to secure raw materials. That, more or less, brings us to the twentieth century (I know, ancient history to you) and today.

On the question of mathematics being used in science, see Fawcett TW and Higginson AD (2012) Heavy use of equations impedes communication among biologists Proc Natl Acad Sci 109 11735-9. Here I've linked you to the PubMed Central listing so that not only can you find the paper but also find links to letters in reply to the paper—letters which disagree with the conclusions in the paper. Yes, it is permissible to disagree with conclusions, and, in the literature, some of that disagreement is published. It makes for good reading.

If you'd like to read more about the rediscovery of the lessons of alchemy, consider the introduction to a special issue on alchemy in the journal ISIS, the journal of the History of Science Society. Or, any of the other papers on alchemy in that issue of the journal.