[pnathan]

It's actually the case that even in straight up "theorem/proof" math, it's instructive, useful, and informative to have multiple ways to prove a given theorem. This is how you link multiple subfields of mathematics together and create cross-pollination of understanding between areas as advances in one feed into the other via the multiple correspondences (and, yes, that's a very handwavy and not terminology-correct way to put it).