The concept of random close packing (RCP) of spheres remains ill-defined, as evidenced by discrepancies in experimental and computational results. The RCP is traditionally considered the maximum density achievable by a random packing of spheres, but this definition is ambiguous and protocol-dependent. For example, different methods yield varying packing fractions, ranging from 0.60 to 0.649. This ambiguity is attributed to the competing effects of disorder and order in sphere packings. The authors propose a new concept: the maximally random jammed (MRJ) state, which is a precisely defined state where the packing is jammed (no further compression is possible) and has the highest possible randomness. The MRJ state is defined as the jammed state that minimizes an order parameter, which quantifies the degree of order in the system. The order parameter is derived from statistical measures of translational and orientational order. The authors performed molecular dynamics simulations using 500 hard spheres, finding that the MRJ state occurs at a packing fraction of approximately 0.64, close to the RCP value reported by Scott and Kilgour. The results show that the MRJ state is a special subset of jammed structures, with the lowest possible order. The study highlights the need for a precise mathematical definition of RCP and introduces the MRJ state as a more rigorous alternative. The MRJ state is defined in terms of an order parameter, which allows for a quantitative analysis of randomness in sphere packings. The authors emphasize that further research is needed to develop new protocols for generating jammed states and to systematically investigate better order parameters. The results demonstrate that the notion of RCP as the highest possible density for a random packing is ill-defined, as one can achieve packings with arbitrarily small increases in volume fraction at the expense of small increases in order.The concept of random close packing (RCP) of spheres remains ill-defined, as evidenced by discrepancies in experimental and computational results. The RCP is traditionally considered the maximum density achievable by a random packing of spheres, but this definition is ambiguous and protocol-dependent. For example, different methods yield varying packing fractions, ranging from 0.60 to 0.649. This ambiguity is attributed to the competing effects of disorder and order in sphere packings. The authors propose a new concept: the maximally random jammed (MRJ) state, which is a precisely defined state where the packing is jammed (no further compression is possible) and has the highest possible randomness. The MRJ state is defined as the jammed state that minimizes an order parameter, which quantifies the degree of order in the system. The order parameter is derived from statistical measures of translational and orientational order. The authors performed molecular dynamics simulations using 500 hard spheres, finding that the MRJ state occurs at a packing fraction of approximately 0.64, close to the RCP value reported by Scott and Kilgour. The results show that the MRJ state is a special subset of jammed structures, with the lowest possible order. The study highlights the need for a precise mathematical definition of RCP and introduces the MRJ state as a more rigorous alternative. The MRJ state is defined in terms of an order parameter, which allows for a quantitative analysis of randomness in sphere packings. The authors emphasize that further research is needed to develop new protocols for generating jammed states and to systematically investigate better order parameters. The results demonstrate that the notion of RCP as the highest possible density for a random packing is ill-defined, as one can achieve packings with arbitrarily small increases in volume fraction at the expense of small increases in order.