Precisely stating your assumptions happens in a limited way in everyday mathematics, enough so that the project of finding the minimal set of assumptions for ma

Precisely stating your assumptions happens in a limited way in everyday mathematics, enough so that the project of finding the minimal set of assumptions for mathematical theories is a niche project: https://en.wikipedia.org/wiki/Reverse_mathematics https://en.wikipedia.org/wiki/Reverse_mathematics. By everyday mathematics, I mean mathematics outside of set theory/logic/ foundations of mathematics. Rather, what everyday mathematicians do is have a set of axioms that are "safe", and do not need discussion, along with other axioms that require explicit note. They then prove things relative to those axioms, make a limited effort to only use the "unsafe" axioms, and make no effort to restrict their use of safe axioms. Mathematicians will typically describe their philosophy of mathematics as formalist, but it's arguable that everyday mathematicians act much more like Platonists with respect to ZFC.