Videos: Why 8 and 9 are cool

These partly came out of a conversation I had with my son, and my realizing that I didn’t know of any other examples (besides 0,1 and 8,9) of consecutive perfect powers. I assumed that there was some very old result about such things, but last year (2012), when there was a flurry of news about the abc conjecture, I learned from a paper by Barry Mazur that that question was only very recently resolved, and gives a very natural intro to abc. So these lectures explicate a little bit of Mazur’s paper.