Ultrafilters

One of the challenges in learning mathematics is the vocabulary. Its hard not just because of the sheer number of words. Some words make an old word strangely precise, like "continuous". But many others are naming concepts which have no common equivalent, and each of these requires wholly new paths of thought.

Recently I was reading a book on the positivity of multivariate polynomials, and I had to recall what ultrafilters are. Even having learned that before, its a bit of a struggle to internalize. It did inspire me to make the following "ad":