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.