Abstract
The early claims of APL to the attention of the computing world included its closeness to mathematical notation and hence its power both to improve and enhance the understanding of mathematical ideas, and also to smooth the process of realising them on a computer. The new features of APL2, notably nested arrays and operator extensions have brought programming and mathematics even closer together. Mathematical users of APL cannot but delight in the new possibilities, of which just a few are outlined in this paper.