Yes, but what is a non-differentiable curve if you and I don't even have the same definition of a curve? What about a curve which is differentiable in one coordinate system but not so in another?
EDIT: My point is - mathematics is axiomatic in its very basis - the axioms have to be agreed upon by people who agree upon a conclusion derived from those axioms.
EDIT: My point is - mathematics is axiomatic in its very basis - the axioms have to be agreed upon by people who agree upon a conclusion derived from those axioms.