How imaginary numbers were invented [video]
The innovation of "imaginary" numbers is that we can concretely reason about multiple dimensions in a unified manner (unlike classical geometry, which relies on geometric primitives). `i` is not some magic, "imaginary" value, it is an invented syntax that means something like "rotate by tau/4 radians" or "orthogonal to the default vector". It turns out that  physical problems are much more accurately modeled in 2 dimensions than in 1 dimension, and even more so in higher dimensions.> Freeman Dyson: “Schrödinger put the square root of minus one into the equation, and suddenly it made sense … the Schrödinger equation describes correctly everything we know about the behavior of atoms. It is the basis of all of chemistry and most of physics. And that square root of minus one means that nature works with complex numbers and not with real numbers.”This quote is emblematic of the mysticism that some mathematicians and academics cannot resist using to advance their careers as public intellectuals. Reality is certainly not based solely in "real numbers" (one dimension), but nor is it based solely in "complex numbers" (two dimensions). The idea that mathematics is "the language of the universe" that can be precisely "discovered" by brilliant minds is a ridiculous notion that only serves the status of the mathematical elite. Mathematics is fundamentally about designing models and abstractions that help us reason about real phenomena with minimal cognitive resources. Everyone does it, and anyone can do it.  Disclaimer: I have a degree in mathematics."All models are wrong, but some are useful" [1][1] - https://en.wikipedia.org/wiki/All_models_are_wrong