I had never understood how imaginary numbers had any bearing on physics (probably because I'd never been taught). But lately I've thinking about how all mathematics must have some natural physical equivalent or relation. E.g. how does multiplication happen in nature.. what does it mean really to multiply something?...how does this happen in nature? For the most part, we take these things as facts and learn the mechanics, but in physics, it seems to me, you really need to understand how these algebraic interpretations translate into physical realities (also, perhaps sort of obvious for everyone reads HN). For someone who enjoys discovering these perhaps obvious things later in life, it's clear how mathematicians and physicists could clearly come to the same mathematical conclusions from completely opposite vectors.. I guess this probably happens all the time.