 The tools that Cass used to derive his results were from the then-newly developed field of optimal control in mathematics pioneered by Lev Pontryagin.The main results in the paper are a demonstration that under now-standard assumptions on preferences and technology, the optimal accumulation sequence exists and is unique.The other papers in Cass's thesis drew on the major insights of the "Optimum growth..." paper by extending them to show the existence of an optimal growth trajectory in a two-sector model of capital accumulation, and the existence of a so-called turnpike growth path associated with the optimal capital accumulation trajectory in the one-sector model.