Machinery: Artificer
Architecture: Engineer
Math and physics: Scientist or Sage
There's no one term that works well for the lot of them combined.
Yeah, I am trying to get a sense of where the boundaries are.
For example, which skill is the go-to for mathematics?
I figure it is impossible to do physics without math. So, alchemy gets math? It always had very specific ingredients at precise proportions and processes.
Therefore, the
Nature skill is "natural philosophy", whence mathematics along with the Five Elements being Ether, Fire, Air, Water, and Earth, that refer to the elemental states of matter, being "immaterial force" plus plasma, gas, liquid, and solid. Ultimately even matter itself is made out of immaterial forces. The science of force and matter is mathematical. But it can also be personal, where animism can have a friendship with a particular mountain, sometimes literally an Earth Elemental emerging from the mountain, or an other humanlike manifestation of the mind of that unique mountain. Nature includes knowledgeability about the Elemental Planes, including the Ethereal Plane. Despite the schematic representation cosmology map of the 5e multiverse, I prefer to view the Elemental Planes as aspects of the Material world and somehow pervading and inside matter.
Then the
Engineer skill is a multidisciplinary specialization that focuses on machinery and creating ingenious constructs that coordinate many different kinds of moving parts. This is the clockwork concept, building architecture especially the wonders of the world, and all kind of machines, mechanisms, gadgets, and sometimes even living constructs.
One might want to use the "Nature" skill for the wilderness, plants and animals. But this sense of Nature is elemental, and doesnt. Instead, the
Survival skill is about how "life finds ways to stay alive". It is all the life sciences of botany and zoology, medicine, environmentalism, ecosystems, symbiosis, and expresses well the D&D traditions of Druids and Rangers. Survival can relate to tracking and hunting, to understand animals and develop sustainable sources of food. But Survival is also the life sciences of agriculture, and flourishing farms to feed cities in healthy organic ways. While chemistry is molecular and mainly the elemental Nature skill, organic chemistry regarding building blocks of life, such as DNA and medical research often leans into the Survival skill. As a rule of thumb, if it is about "life" make a Survival check, and if it is about "matter" make a Nature check.