A clarification on the existence and the specifics of some medicinal and scientific skills.

Esoteric medicine:
This is a catch all for a number of different techniques. The main one is church taught medical chanting. These are low power chants, used to reinforce normal first aid procedures. It’s not strictly magical, anyone can learn it with a proper teacher, and it functions as well as the physician skill (so it can do long term care, restart stopped hearts, ect). Other esoteric medicines exist, many religiously based. I invite you to invent your own if you want, they’re all only as effective as first aid.

Alchemy:
Alchemy is the skill of making elixirs with “magic potion” style effects, although side effects are common. In comparison to Herb Lore, it allows for faster preparation of potions, salves, tonics, and oils, and enables more immediate effects, but ingredients are more expensive.

Herb Lore:
Herb lore generally requires inexpensive ingredients, or free ingredients that require time to gather, and takes more man-hours to prepare than alchemy. Herb lore is also limited to slow effects, generally improving existing traits instead of granting new powers. For example, a healing salve vs a healing potion. The salve would cost less than the potion, but takes much longer to have an effect and would take more time to gather and prepare ingredients.

Pharmacy(Herbal):
Would be the knowledge of why the things that Herb Lore does and the ability to apply them skillfully, but doesn’t give you the ability to manufacture anything. You can assemble stuff, if you have the raw ingredients (dried rosemary, a pinch of salt from a still cove, moss scraped off a tree this morning), but don’t have any ability to go and get it yourself. Pharmacy(Herbal) would be the skill for healers who have supplies delivered, or assistants to someone with Herb Lore.

Now for the sciences:
There are probably people who study how the world works experimentally (ie. have ranks in math, physics, biology, chem, ect). Unfortunately such people are few and far between, and no formal institute of knowledge exists to teach those skills. More common is the expert skill Natural Philosophy (IQ/hard), which is arguing about how the world works without experiments, just guesses. It covers all of the sciences, but doesn’t have experimental evidence to support it. Think Aristotle, arguing that there are indivisible atoms, or that everything in the world must be made up of the 4 classical elements in different proportions. Thaumatology is perhaps the only true science skill that is commonly taught.
I guess the ability to throw fireballs draws good funding :P