Is random close packing of spheres well defined?

Despite its long history, there are many fundamental issues concerning rand om packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP can not be made mathematically precise and support this conclusion via a molecu lar dynamics study of hard spheres using the Lubachevsky-Stillinger compres sion algorithm. We suggest that this impasse can be broken by introducing t he new concept of a maximally random jammed state, which can be made precis e.