Have been doing numerical computation ever since I am in the industry but somehow never got to read the following essay. Found it by chance on google.
A must read for anyone interested in Numerical computation
The Need for Numerical Computation
Everyone knows that when scientists and engineers need numerical answers to mathematical problems, they turn to computers. Nevertheless, there is a widespread misconception about this process. The power of numbers has been extraordinary. It is often noted that the scientific revolution was set in motion when Galileo and others made it a principle that everything must be measured. Numerical measurements led to physical laws expressed mathematically, and, in the remarkable cycle whose fruits are all around us, finer measurements led to refined laws, which in turn led to better technology and still finer measurements.
The day has long since passed when an advance in the physical sciences could be achieved, or a significant engineering product developed, without numerical mathematics.
Computers certainly play a part in this story, yet there is a misunderstanding about what their role is. Many people imagine that scientists and mathematicians generate formulas, and then, by inserting numbers into these formulas, computers grind out the necessary results. The reality is nothing like this.
Read more by following this link. http://people.math.umass.edu/~johnston/M552S16/NAessay.pdf