This often arises in the discussion of concepts like "what is somebody's Erdos number", or when one discusses what field a contribution belongs to. When "does it count" or when it is or isn't a contribution in a certain area. It's something that I have thought about when these conversations come up.
Personally, what do you think a mathematical paper is if you were to classify one as "one" or "isn't one"?
For example, I have seen people describe papers as mathematical for simply having experimental data in it that happened to just test against a model. Sure Mathematics is involved, but would you call that a mathematical paper? I mean any reasonable scientific paper could be called mathematical if that were the case.
I'm more of the stance that a mathematical paper contains original mathematical results. For example, it presents a theorem (or more than one) and proves it (pretty traditional). In the empirical sense, maybe the paper presents a new model that could be used empirically, and proves theorems for the model?
Where do you stand on this? What in your opinion is what classifies a paper as a "mathematical paper"? Is it the difference between what a mathematics paper is (in the vaguest sense), or is it even more general than this to encompass non-formal results (e.g., just invokes the use of numbers)?
This is a philosophical question, which probably has many answers. For sure, mathematics is the basis for describing science. David Hilbert (Axiomatic Thought, 1918) claimed that every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics. In that respect your question would trace down to identify the degree of maturity of a scientific paper.
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