1238 NOTICES OF THE AMS VOLUME 47, NUMBER 10 H ow should 24-dimensional toy merchants most efficiently store their marbles? This is one rather fanciful statement of the “sphere packing problem” in R24. This problem is not just a plaything of high-dimensional Euclidean geometry: it relates to a surprising range of mathematical disciplines, pure as well as applied, including number theory, finite groups, orthogonal polynomials, and signal transmission. The same is true of the closely related… CONTINUE READING