Moore's law states that both the speed and memory of computer hardware are approximately doubled every 18 months. While such progress can not be sustained indefinitely, it has continued for more than 30 years, and has been one of the principal reasons for the so-called information
revolution; it is showing no signs of slowing down. In scientific and engineering computations, Moore's law has been having a profound effect on the interactions between computers and humans, between hardware and software, between different types of algorithms, and between different types of humans involved in the process.
In this talk, I will examine the consequences of Moore's law in the scientific computing environment, especially from the point of view of a designer of numerical algorithms. As an illustration, I will discuss in some detail the design of Fast Multipole Methods for the numerical solution of scattering problems; the effectiveness of the approach will be demonstrated via several numerical examples.