Most of the sciences, at least as we think about them, did not really exist in the medieval world. The problem with all the above replies is that they are coming at science from a modern perspective. For example, talkig about different types of molluscs. Well until Linnaeus (1700s), we did not really have any kind of good classification of animals into real groups and the ideas about things like species were not understood at all well. Science, in the medieval world was so bound up with religion and mysticism as to be indistinguishable from magic.Science in medieval times revolved around concepts that we would find very alien. They searched for things like;
Fluidium vivarum (or life substances) or forces that separate living material from that which was inorganic or had never lived. This was almost a search for God in materials via Alchemy.
Elixir vitae (potion of eternal life), bound up with the discovery of the life substance.
Philosophers stone; a vital principle that would allow transmutation of one material into another. This idea came from experiments with things like Cinnabar (mercury sulphide) which is a rusty brown powder because when you heat this substance it decays into mercury metal. Mercury was thought to be Dragon's semen according to the Chinese estoerics who discovered it and there were whole layers of superstition surrounding this.
Metallurgy was also hedged around with mystical symbolism; how metal was pulled out of ore via smelting. The word Kobold comes from the idea that mischevious underground spirits cursed miners by spoling their ore when in fact the ore actually contained another metal that was spoliing the smelting process; we now call it Cobalt, but you can see where its name came from.
An intrinsic part of medieval sciences was the belief that the past and the future and the nature of things was bound up and linked with their appearance. So we have things like the Doctrine of signatures in herbalism, where plants that look like certain parts of the human body have mystical powers to heal disorders of that organ.
This is also why doctors, even in the 1700s, would chart horoscopes before treating patients because they believed in astrology and the signs and portents that could be gleaned from a study of the stars.
Similarly, medicine was centered around the idea of 4 humours; blood, phlegm, black bile and yellow bile. They believed that an imbalance in the humours could cause disease, as could poisonous miasmas (clouds of toxin or disease). This is why they used to bleed people, to rebalance the humours.
So if I were making up a way of introducing science into D&D, I would try and use this perspective. I do not think any of the sciences were well developed enough to be studied in isolation. Instead, the knowledges should be grouped into the way they were studied at the time during the study for a degree (the examples below are from Oxford);
The Trivium; logic, grammar and rhetoric
The Quadrivium; maths, astrology, music, science.
That way you would need only two skills to understand the nature of the physical world. What you could do with them would be quite limited because most of the theories of the time were only descriptive (they seemed to explain why things were the way they were) not predictive (modern theories allow us to make predictions about the future behaviour of any system at study and hence are useful).
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