But it is supposed to be so! At least in physics or mathematics (and the "harder" sciences), if there are multiple descriptions, they better be completely equiv

But it is supposed to be so! At least in physics or mathematics (and the "harder" sciences), if there are multiple descriptions, they better be completely equivalent in the answers they give, otherwise all but one of them are wrong. It is possible that different fundamentally equivalent frameworks might be more suited to different problems (eg: Newtonian mechanics -vs- Lagrangian mechanics)