The Evolution of Mathematical Software

Over four decades have passed since the concept of computational modeling and simulation as a new branch of scientific methodology—to be used alongside theory and experimentation—was first introduced. In that time, computational modeling and simulation has embodied the enthusiasm and sense of importance that people in our community feel for the work they are doing. Yet, when we try to assess how much progress we have made and where things stand along the developmental path for this new "third pillar of science," recalling some history about the development of the other pillars can help keep things in perspective. For example, we can trace the systematic use of experiment back to Galileo in the early 17^th century. Yet for all the incredible successes it enjoyed over its first three centuries, the experimental method arguably did not fully mature until the elements of good experimental design and practice were finally analyzed and described in detail in the first half of the 20th century. In that light, it seems clear that while computational science has had many remarkable successes, it is still at a very early stage in its growth.

Many of those who want to hasten that growth believe the most progressive steps in that direction require much more community focus on the vital core of computational science: software and the mathematical models and algorithms it encodes. Of course, the general and widespread obsession with hardware is understandable, especially given exponential increases in processor performance, the constant evolution of processor architectures and supercomputer designs, and the natural fascination that people have for big, fast machines. I am not exactly immune to it. When it comes to championing computational modeling and simulation as a new part of the scientific method, the complex software "ecosystem" that coincides must be forefront.