As someone who does lots of constructive math, intuitionistic math can't reproduce a large number of results on the reals and this is a kind of well-known thing

As someone who does lots of constructive math, intuitionistic math can't reproduce a large number of results on the reals and this is a kind of well-known thing. Even basic notions of continuity can't be reproduced in the same way and as a result there are multiple competing formalisms. It is possible that there are alternative ways to reproduce results of interest to physics but that's far from obvious.