I'd recommend that anyone going on the radio to ad lib a mini-lecture on math for lay listeners first practice in private on non-mathematician friends to see what works, and to develop confidence in their ability to give a successful ad lib mini lecture. --Dan P.S. I also second Joshua's recommendation of "A Certain Ambiguity", which is quite a fascinating book, though somewhat dense (for the lay reader) in some parts. (It also contains the usual quota of (generally non-crucial) mathematical errors, but Princeton University Press has told me that at least the ones I reported would be fixed in the next edition. I would *not* recommend "1,2,3,...Infinity" by George Gamow, as it contains crucial errors in its discussion of infinities. And Dover has refused to fix any of these, despite my reporting them over 10 years ago.