George Lakoff was puzzled by some of what his math professors at MIT taught him.
For example, if the real line is made up of points, how can it be continuous? Either the points touch, in which case, having no dimension, they must be identical, or they don’t touch, in which case there must be empty space between them.
Or again: What is the empty set the set of?
Fortunately, he remained puzzled, and the result is a fascinating theory of mathematics as structural metaphor, embodied in his book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, and in a superb talk he just gave at the Marschak Colloquium.
Only a select few of us got to hear the lecture (if eighty is a select few), but you can read the book.