"Mathematical foundations" are not always useful to practitioners – or even at all. Algebraic quantum field theory is a good example of the latter, to a large degree [0].
The fact that workers in the field with the presumed "applications" don't seem to care is pretty telling. My guess is that working at a level of generality where subject-specific insights are suppressed automatically limits the usefulness of the work.
The fact that workers in the field with the presumed "applications" don't seem to care is pretty telling. My guess is that working at a level of generality where subject-specific insights are suppressed automatically limits the usefulness of the work.
[0]: http://philsci-archive.pitt.edu/8890/1/critique_sep10.pdf