**Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University**

*ADDING NUMBERS AND SHUFFLING CARDS*

When numbers are added in the usual way, 'carries' accrue along the way. It is natural to ask 'how do the carries go?' Is there a carry 'about half the time? If there just was a carry is it more (or less) likely that there will be a carry next time? How does it all depend on the base and the number of numbers being added? Strangely, this is closely connected to the question 'how many times should a deck of cards be shuffled to mix it up' I will explain both sides AND the connection. The mathematics connects to all kinds of things, from factoring polynomials to Hochschild homology. I will try to explain it all 'in English' to a general mathematical audience.