When numbers are added in the usual way, 'carries' accrue along the way. How do the carries go? if there was just a carry, is it more or less likely to have a carry in the next place? It turns out that carries form a Markov chain with an 'Amazing' transition matrix (really? are any matrices amazing?). This same matrix occurs in the analysis of the usual method of shuffling cards. I'll use it to prove 'the seven shuffles theorem' and show how it comes up in understanding the Veronese embedding of a projective variety. And then, carries are cocycles and much goes over to general groups. I'll try to do all of this 'in English' for a general mathematical audience.
