In neoclassical economics economic growth depends upon savings. The paper discusses problems with this conventional view, and how these have been tackled, from pre-Solowian authors up to the recent New or Endogenous Growth Theory (EGT). These difficulties became particularly clear with the Solow-Swan model of growth in which the savings rate did not affect the rate of growth. In the absence of exogenous circumstances, savings would only depress the marginal productivity of capital forcing the economy towards a stationary state. The paper interprets EGT as an attempt to react to this gloomy theoretical prospect. The paper examines various difficulties with this attempt.