Do you find some mathematical activities useless?

[Jim Horn]

I used to claim that the universe runs on differential equations. One of my college professors disagreed and pointed out that it runs on convolutions. He had a point!

With the way matrix math can describe multibody motion as state spaces, convolution describes all sorts of responses using (nonexistent) unit pulse inputs and other such features of Mathematics, I can see why there's belief in "The Book". Algebra, geometry, calculus and more were drudgery in school - but discovering how they represent and resolve real things (and can drastically simplify more elementary approaches) was always a terrific revelation and delight.

I *do* recommend http://www.3blue1brown.com/ for some well done introductions and demonstrations of some truly elegant aspects of math that aren't very well known.