192:. With respect to the question "what is a variable/indeterminate, really?" I am in the same boat as your professors: I think that, if pressed, I could offer a coherent definition of a single concept, especially as it appears in ring theory/abstract algebra, that might be called "an indeterminate" but might also be called "a variable"; but this definition does not, I think, encompass all uses of those words, and doesn't really distinguish between them. D.Lazard is a person who I generally would trust about such things; but he is not a native English speaker and also often clarifies things by writing what he knows to be true without sourcing it carefully. I probably am not going to involve myself a whole lot more in the discussions, but certainly building up more good sources from as many mathematical perspectives as possible would be the ideal basis for moving forward. --
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