Inventing math

My goal when I set out to make this video was to explain divergent series with respect to a p-adic metric, keeping in the back of my mind that someday I may want to build up to an explanation of the series 1+2+3+4+...= -1/12 which does not depend on the relatively opaque operation of analytic continuation.  

The more I worked on it, the more I wanted the explanation to be such that the viewers could imagine that they themselves could have found it, given the appropriate principles.  I've come to think this is probably the hallmark of any good explanation.  Eventually, I shifted the entire theme of the script to center around this idea, leaving the divergent series as a plot device more than anything else.  One benefit here was that I got to work in thoughts I had about the relationship between invention and discovery in math, which felt worth sharing.