cal engineering”b: it is focused on the creation of new mathematical objects under constraints, such as low time and space complexity for discrete algorithms, good numerical convergence for numerical algorithms, or good precision and recall for classifiers; the difference between mathematics and “mathematical engineering” is precisely the emphasis on such constraints.

As technology progresses, new constraints need to be considered. For example, time complexity is increasingly irrelevant when communication (to memory, disk, and network) replaces computation as the main performance bottleneck, and when energy consumption becomes the critical constraint. New technologies that will take us “ Beyond Moore’s Law” (quantum computing, molecular computing) will require new mathematical abstractions.

Part of C&I, namely computer engineering, has always been concerned with the interplay between the mathematical abstractions and their physical embodiment. In addition to mathematics, physics is foundational for this specialty, and will continue to be so. Physics is also important for cyber-physical systems that directly interact with their physical environment.

b Mathematical engineering was apparently
used as a synonym for “computer science” in
Holland, in the early days of the discipline. It
is now used by some schools as a synonym for
“scientific computing.”
I believe, however, that physical
constraints are a small fraction of the
constraints relevant to the design of C&I
systems. For example, software engi-
neering research has strived for de-
cades to define code metrics that rep-
resent how complex a code is (hence,
what effort is required to program or
debug it)—with limited success. Such
a code metric would measure how dif-
ficult it is for a programmer to com-
prehend a code. But this is a cognitive
issue: It is highly unlikely that one can
develop successful theories on this
subject without using empirically vali-
dated cognitive models that are based
on our best understanding of human
cognition. Unfortunately, traditional
software engineering research has not
been rooted in cognitive sciences.

figure 3. c&i—an inclusive view.

use-inspired
basic research
Applied
research
Prototypes

Mathematics,
statistics,
social sciences,
physical
sciences…
Products
Foundations

Science,
engineering,
arts, humanities,
business,
medicine
Systems, applications,
data repositories
Application areas

and the technical: One may well argue that the essential insight that enabled efficient Web search and led to the creation of companies such as Google is that the structure of the Web carries information about the usefulness of Web pages—a socio-technical insight. Progress in graphics and animation increasingly requires an understanding of human vision: otherwise, one makes progress in quality metrics that have low correlation to the subjective quality of an image; examples can be easily multiplied.

Another important aspect of the evolution of our field is the increasing importance of applications. Precisely because software is so malleable and universal, one can develop very specialized systems to handle the needs of various disciplines: computer-aided design, medical imaging, DNA matching, Web auctions—these are but a few examples of application areas that have motivated significant specialized C&I research. Such research cannot be successful without a good understanding of the application area.

This suggests a new view for the organization of C&I that is described in Figure 3: Mathematics is no longer the only foundation. For those working close to hardware or working on cyber-physical systems, a good foundation in physics continues to be important. An increasing number of C&I research areas (such as human-computer interaction, social computing, graphics and visualization, and information retrieval) require insights from the social sciences (cognitive psychology, sociology, anthropology, economics, law, and so forth); human subject experiments become increasingly important for such research. At a more fundamental level, the development of artificial cognitive systems provides a better understanding of natural cognitive systems—of the brain and its function; and paradigms borrowed from C&I become foundational in biology. Insights from neuroscience provide a better way of building artificial intelligent systems and biology may become the source of future computing devices. Finally, research in C&I is strongly affected by the multiple application areas where information technology is used (such as science, humanities, art, and business), and profoundly affects these areas.