For me, the eye opening thing was that any n-dimensional body is a transformation of the n-dimensional standard cube. This brings some mathematical consequences I don't understand, but what's important for me is that equations get much easier for the standard cube transformations because your corners are just ones and zeros.
E. g. I wrote an app that "unbends" a book page from a photo so it looks flat. It can be done with a single but rather large transformation, or with a pair of transformations: to and from the standard cube, and each transformation is then much simpler than their composition. 15 years after I learned that trick and 10 years after I wrote an app, I wrote a book called Geometry for Programmers.
If not for Spivak, I would have drowned in equations, never written the app and would have had nothing to write a book about.