I agree with that distinction. Another notable class of mathematical "hypotheses" are those, like the continuum hypothesis [0], whose truth is formally undecide

I agree with that distinction. Another notable class of mathematical "hypotheses" are those, like the continuum hypothesis [0], whose truth is formally undecideable but that many mathematicians nevertheless believe to be true in some sense. If this class of statements has any analogue in the empirical sciences, I guess it must be "unscientific" (untestable) hypotheses, about which philosophers (or theoretical physicists) might still find interesting things to say. Mathematicians also use the word "hypothesis" to refer to a whole implication in the phrase "inductive hypothesis". But it most often simply means the left side of an implication: the phrase "A is true by hypothesis" means that A was assumed to be true—that is, it was the starting point of a proof. 0. https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis