Abstract: Careful analysis of shuffling can call on tools from many parts of mathematics. It also has applications there. Of course combinatorics, probability and analysis occur, but also lie theory (the shuffle algebra is a close cousin of the Free Lie algebra), Hopf algebras (shuffles give Hodge decompositions of Hochschild homology) and multiple zeta values. Again, I will try to explain all of this 'in English' to a general mathematical audience.