Imaginary numbers

The names imaginary numbers and real numbers seem a little ironic, given that all maths is imaginary. As an example, consider the number 3. It is not a real thing in the sense that I can't go and observe a three, like I can stone or a tree. It represents the abstraction or concept of threeness, which we have imagined and exists in our minds.

One way to think of maths is as the science of patterns. So we have a huge library of patterns, abstractions, relationships and methods of reasoning about them. When we want to talk about the "real" world, we often draw on this library to give us the vocabulary and tools to do so.

I was thinking about this stuff because I am studying linear algebra at the moment and was reading A Visual, Intuitive Guide to Imaginary Numbers and What is Experimental Mathematics?