I think, oversimplifying their attitudes, that many mathematicians see computation as inferior to proving theorems, many computer scientists focus their attention on linguistic issues or information technologies, and computational scientists from other disciplines believe that Moore's law will solve their remaining problems. We seem to overlook the continuing contributions that mathematics makes to improvements in computing. When we bundle existing algorithms into libraries and wrap them into packages to facilitate easy use, we create de facto standards that make it easy to ignore numerical analysis. This is needed, but we also need to maintain our investment in continuing research on algorithms themselves. I maintain that the relative neglect of mathematical aspects of computation weakens the foundations of our growing computational enterprise, foundations that desperately need to be strengthened to support computation at the interface between computers and the physical world.
Computers are far more than passive devices for information storage and retrieval.
Our success in these endeavors is dependent upon efficient and accurate computations. Algorithmic problems arise repeatedly as we attempt new applications. There are frequently common features in these computational problems, and research directed at finding general solutions to classes of questions has been a critical part of the increased use of digital technologies. A description of some of the current issues related to simulation, an area in which I have a personal interest, can make this point more concretely. We seek to implement ambitious simulations of global climate change, entire automobiles, electric power networks, military battles, stock markets, and the human brain.