There is no precise definition of “the mathematical sciences.” The following definition was used in the 1990 report commonly known as the David II report after the authoring committee’s chair, Edward E. David:
The discipline known as the mathematical sciences encompasses core (or pure) and applied mathematics, plus statistics and operations research, and extends to highly mathematical areas of other fields such as theoretical computer science. The theoretical branches of many other fields—for instance, biology, ecology, engineering, economics—merge seamlessly with the mathematical sciences.1
The 1998 Odom report implicitly used a similar definition, as embodied in Figure 3-1, adapted from that report.
Figure 3-1 captures an important characteristic of the mathematical sciences—namely, that they overlap with many other disciplines of science, engineering, and medicine, and, increasingly, with areas of business such as finance and marketing. Where the small ellipses overlap with the main ellipse (representing the mathematical sciences), one should envision a mutual entwining and meshing, where fields overlap and where research and people might straddle two or more disciplines. Some people who are clearly affiliated with the mathematical sciences may have extensive interactions and deep familiarity with one or more of these overlapping disciplines. And some people in those other disciplines may be completely comfortable in mathematical or statistical settings, as will be discussed further. These interfaces are not clean lines but instead are regions where the disciplines blend. A large and growing fraction of modern science and engineering is “mathematical” to a significant degree, and any dividing line separating the more central and the interfacial realms of the mathematical sciences is sure to be arbitrary. It is easy to point to work in theoretical physics or theoretical computer science that is indistinguishable from research done by mathematicians, and similar overlap occurs with theoretical ecology, mathematical biology, bioinformatics, and an increasing number of fields. This is not a new phenomenon—for example, people with doctorates in mathematics, such as Herbert Hauptman, John Pople, John Nash, and Walter Gilbert, have won Nobel prizes in chemistry or economics—but it is becoming more widespread as more fields become amenable to mathematical representations. This explosion of opportunities means that much of twenty-first century research is going to be built on a mathematical science foundation, and that foundation must continue to evolve and expand.
1 NRC, 1990, Renewing U.S. Mathematics: A Plan for the 1990s. National Academy Press, Washington, D.C.