Engineering, finance, science, and many areas of mathematics itself make use of quantities that are too complicated, too difficult, and even too abstract to work with directly. A major goal of approximation theory is to discover and analyze simple, easy to work with, concrete quantities that can do a good, efficient job in their place - for example, splines to fit messy curves, wavelets to analyze noisy signals and to compress large images, and radial basis functions to fit scattered data and serve as the approximation engine'' of neural networks.