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In order to understand the current state of an art it is often necessary to examine its history to see how it evolved. In examining the growth and present state of scientific computing, as contrasted to the other three fields of this session, machine design, software, and business applications, I find that there have been, and are, significant differences-in particular scientific computation has had a much more orderly growth than the others and is probably much more stable now, stable in the sense that the immediate future can be seen reasonably accurately. For example the comparatively ancient text by Whittaker and Robinson can still be used, but a book on coding of five years ago is hopelessly out of date. Two reasons can be given for the more orderly growth of scientific computing. First, for practical purposes scientific computing has had a much longer history of development. It is true that some of our earliest records are clay tablets recording commercial aspects of a civilization, and it is true that in the 1930's and 40's accounting machines of various types were adapted to scientific work, yet it seems fair to say that scientific computing was far more highly developed over most of the last 2000 years than was commercial computing. Furthermore most of the machines of World War II and the early post-war period were designed by and for men in science. Second, behind much of scientific computing stands a highly developed and elaborated body of knowledge known as mathematics. This is very true for the field of numerical methods and