Why has the combination of mathematical analysis methods and computers been so important?
The combination of mathematical analysis and computers has been a strong alliance, especially with regard to engineering, technology, and the sciences. In the past few decades, researchers have used this combination to help predict the weather, describe in great detail nuclear fusion in the Sun, understand the movement of space bodies around the solar system (orbital mechanics), and the flow of water in underground aquifers (fluid dynamics). There are also the studies of chaos—the unpredictable behavior of nonlinear systems—and quantum mechanics, or the physics of very small particles, both of which entail the use of applied mathematics and computers.
In addition, in engineering (and almost all technology) the mathematical analysis-computer combination has helped create structures that surround us every day. This includes familiar modes of transportation and communication: from plans for airplanes and bridge construction to designing fiber optic cables and cell phone towers. It also includes how engineers design control systems, which are used in such diverse areas as robotics, aerospace engineering, and biomedical research.
Computers and mathematical analysis have also been a boon to such interdisciplinary fields at operations research (also called decision or management science). In this case, the mathematical science focuses on the effective use of the technology of an organization, such as forecasting, financial engineering, logistics, and industrial engineering. Applications may include, for example, scheduling airplanes and crews; signal processing, such as the transmission of radio signals or traffic light control signals; or managing the flow of water from a reservoir or dam site.