as the Radon and Fourier transforms, whose theory was initially developed during the nineteenth century. This example illustrates the crucial observation that research in the mathematical sciences has a very long shelf life in the sense that, because of their abstract nature, discoveries in the mathematical sciences do not become obsolete. Hence, a fresh insight about their application may arise several decades (or more) after their publication.

•   When Alice’s doctor prescribes a new medication, she depends on decisions by pharmaceutical companies and the government about the effectiveness and safety of new drugs and chemical and those decisions in turn depend on ever-improving statistical and mathematical methods. Companies use mathematical models to predict how possible new drug molecules are expected to interact with the body or its invaders and combinatorial and statistical methods to explore the range of promising permutations.

•   When Alice and Bob order products online, the processes used for inventory management and control, delivery scheduling, and pricing involve ingredients from the mathematical sciences such as random matrices, scheduling and optimization algorithms, decision theory, statistical regression, and machine learning.

•   If Alice or Bob borrows money for a house, car, education, or to pay off a credit card or invest savings in stocks, bonds, real estate, mutual funds, or their 401(k)s, the mathematical sciences are hard at work in the financial markets and the related micro- and macroeconomics. Mathematical methods, statistical projections, and computer modeling based on data are all necessary to function, prosper, and plan for daily life and retirement in today’s array of global markets. Today, many tools are brought directly to individuals in customized applications for virtually every type of personal computer and personal communication device.

•   When Alice enters an airport or bus station, surveillance cameras are likely to record her movements as well as those of everybody in the area. The enormous task of processing and assessing the images from multiple closed-circuit recordings is sometimes done by mathematical tools that automatically analyze movement patterns to determine which people are likely to be carrying hidden weapons or explosives. Similar techniques are being applied in stores and shopping centers to assess which people are likely to be shoplifters or thieves.

•   Even when Bob stops at the supermarket on the way home, he cannot escape the mathematical sciences, which are used by retailers to place products in the most appealing locations, to give him a set of discount coupons chosen based on his past shopping history, and to price items so that total sales revenue will be maximized.

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