> on the other what can happen is that philosophical differences can cause schisms and result in n-fold duplicated work
It would indeed be nice to have a principled answer to the issue of differing foundations, including e.g. working in ZF(C) vs. type theory. (The dirty little secret there - and what makes mathlib more popular than it might be otherwise - is that while most practicing mathematicians appeal to ZF(C) as their default foundation they don't actually work with it in a formal sense, and the way they do reason about math is a lot easier to account for in type theory. See also https://math.andrej.com/2023/02/13/formalizing-invisible-mat... ) I guess the closest thing we have to that is logical frameworks, which are designed to accommodate even very weak/general foundations at the outset and "bridge" theorem statements and proofs across when needed.
It would indeed be nice to have a principled answer to the issue of differing foundations, including e.g. working in ZF(C) vs. type theory. (The dirty little secret there - and what makes mathlib more popular than it might be otherwise - is that while most practicing mathematicians appeal to ZF(C) as their default foundation they don't actually work with it in a formal sense, and the way they do reason about math is a lot easier to account for in type theory. See also https://math.andrej.com/2023/02/13/formalizing-invisible-mat... ) I guess the closest thing we have to that is logical frameworks, which are designed to accommodate even very weak/general foundations at the outset and "bridge" theorem statements and proofs across when needed.