Mathematical methods have long played an important role in management and economics but have become increasingly important in the last few decades. ``Business mathematics,'' such as the computation of compound interest, appeared in ancient Mesopotamia but became prevalent in the mercantile economy of the Renaissance. Mathematics later contributed to the engineering advances that made the Industrial Revolution possible. Mathematics crept into economics during the 18th and 19th centuries and became firmly established in the 20th.

It is only in the last few decades that management per se has received the sort of rigorous study that permits the application of mathematics. In the early part of this century ``scientific management,'' called ``Taylorism'' after its founder F. Taylor, was fashionable. This movement made some worthwhile contributions, such as time-and-motion studies, but it was coupled with dreadful labor relations practices. The symbol of the movement was the efficiency expert policing the shop floor with stopwatch and clipboard.

After Taylorism waned, interest shifted more to making efficient use of labor and other factors than making employees work harder. Shortly before the Second World War a team of scientists solved the operational problems of coordinating Britain's radar stations and thereby created ``operational research,'' called ``operations research'' in the U.S. During the war this practice of putting scientists and mathematicians to work on operational problems was surprisingly successful in both the British and American military, partly because members of the professional class who had not previously ``dirtied their hands'' had their first opportunity to apply their training to operational problems. Their success attracted attention, and operations research spread to industry during the fifties.

After the war, G. Dantzig and others developed linear programming at about the same time that computers became available to solve linear programming models. Linear programming proved a remarkably useful tool for the efficient allocation of resources, and this gave a great boost to operations research. In the early postwar years J. von Neumann and O. Morgenstern invented game theory (closely related to linear programming), and H. W. Kuhn and A. W. Tucker broke ground in nonlinear programming. W. E. Deming and others developed statistical techniques for quality control, and the statistical methods first designed for psychometrics in the early 20th century became the mathematical basis for econometrics. Meanwhile business schools began teaching many of these techniques along with microeconomics and other quantitative fields. As a result of all this, mathematical modeling has played an increasingly important role in management and economics.

In fact one can make a case that overreliance on a mathematical approach has sometimes led to neglect of other approaches. After its first few years, operations research focused almost exclusively on mathematical modeling. The reigning orthodoxy in much of economics is the ``neoclassical'' paradigm, which is heavily mathematical. There is little communication between people in quantitative fields and those in such ``soft'' fields as organizational science and general management.

In fact both approaches appear to be in a crisis. Economics and operations research have achieved much, but neither can adequately understand phenomena that involve human beings. The soft sciences take on the difficult, ill-structured, human-oriented problems, but it is unclear even what counts as a satisfactory theory in these areas.

One can hope that this double crisis will lead in the coming years to a ``paradigm shift'' that will supplant the ``hard'' and ``soft'' approaches with an integrated science with the rigor of one and the breadth of the other. There are faint signs of such a shift, but they are not sufficiently crystallized to show up in a business school curriculum.

Despite the limitations of the quantitative methods discussed in this course, in many specific areas they are quite useful. In fact the potential of most mathematical techniques, particularly those of operations research, is only beginning to be realized in practice. Affordable personal computers and user-friendly software are motivating managers to learn about mathematical models and use them. Also the line between managerial and technical staff is blurring, so that managers now run models on their notebook computers that systems analysts once ran on mainframes. This again leads to more widespread use.

Mon Aug 24 12:46:36 EDT 1998