Scientific computation has a long history, dating back to the astronomical tables of the Babylonians, the geometrical achievements of the Egyptians, the calendars of the Mayans, and the number theory of the ancient Chinese. The success of these activities led in many parts of the world to the development of mathematical theories trying to explain the surprising applicability of pure thought to physical phenomena. Probably the most important such development took place in ancient Greece, where mathematics, as we know it today, was created.
Just as practical advances in scientific computation have stimulated the development of theory, so also newtheoretical breakthroughs have led to whole neww ays of mathematizing science. A prominent example is the development of calculus by Newton and Leibnitz and its application in all areas of science. Mathematical theory, however, became more and more abstract and removed from possible applications.
The twentieth century witnessed the advent of computing devices in the modern sense. Right from the beginning these machines were used for facilitating scientific computations. The early achievements of space exploration in the 1950s and 1960s would have been impossible without computers and scientific computation.
Despite this success, it also became clear that different branches of scientific computation were taking shape and developing apart from each other. Numerical computation sawitself mainly as a computational offspring of calculus, with approximations, convergence, and error analysis forming its core. On the other hand, computer algebra or symbolic computation derived its inspiration from algebra, with its emphasis on solving equations in closed form, i.e., with exactsolution formulae. Both of these branches were very successful in their own right, but barely interacted with each other.