A computer was used to forecast, on an operational (as opposed to experimental) basis, the wind currents and pressure in the upper atmosphere fifty years ago today. From this modest beginning, modern meteorology has become, by far, the most successful predictive science. We make consistently good three day forecasts, often good five day forecasts (especially in the cooler half of the year) and, at times, have some skill out to ten days.
I began my forecasting career just two years after, so still learned many of the successful rules-of-thumb, analogs and other techniques that were used prior to computers. So, I've often felt I've had the best of both worlds.