Putting to Rest the Damaging Myths About Mathematics

Charles E. Mannix, Jr., and Kenneth A. Ross
Chronicle of Higher Education, August 11, 1995.

One such myth, which took hold in the 1980s, was that the nation would face a shortage of scientists, including mathematicians, in the 1990s. This prediction was based on the number of scientists and engineers then being produced. A related myth still making the rounds is that the demand for mathematicians is cyclical and the market will get better again soon.

It is time we put such myths to rest. They are damaging--to graduate students, mathematics departments, and would-be employers of Ph.D.'s--because they allow departments and universities to avoid changing their operations, despite compelling evidence that drastic reforms are needed.

Today, most mathematics departments view their primary mission as producing research mathematicians. We believe this mission must be reconsidered. Specifically, departments should re-examine and revamp advanced education in mathematics, so that their graduates will be better equipped for the jobs likely to be available in the future. Some major research universities, including the Massachusetts Institute of Technology and the University of Michigan, already have begun this process.

Further, many math departments should consider "downsizing," because a variety of economic, political, academic, and technical developments indicate that the current dearth of tenure-track positions for new, young mathematicians will persist for at least the next decade. We don't claim to own a crystal ball, but we believe that these developments, when considered together, provide ample grounds for cutting back departments and restructuring our offerings. Let's consider some of these factors:

• First, the abrupt end of the Cold War eliminated much of the need for advanced research and development in military weaponry. As a result, our national laboratories, as well as high-tech aerospace, electronics, and design companies, have laid off mathematicians, engineers, and scientists. Thousands of former defense-industry employees--including some from the former Soviet Union and Eastern Europe--now are competing with new graduates for teaching positions at all levels of education. Over all, this is a healthy development, but one cannot deny its impact on the current and future job market in this country.
• In private industry, worldwide economic competition is forcing most high-tech American employers to cut workers. Many design projects, which in the past might have employed U.S. mathematicians and engineers, have followed manufacturing abroad.
• A revolution in technology is affecting routine mathematical and scientific work, just as the industrial revolution affected manual labor. Many commonplace, yet time-consuming, analytical tasks, which once produced jobs, especially at the entry level, now are accomplished using very powerful and efficient computer software. And because much existing software can be easily modified for new applications, fewer mathematicians are needed to write new computer programs.
• Many academic scientists and engineers feel that advanced mathematics is best learned within the context of their discipline or subdiscipline. Thus, much of the material that was traditionally taught in mathematics departments has gravitated to courses in other disciplines. Many business schools, engineering schools, and other departments that require students to learn mathematics now teach their own courses in calculus, statistics, quantitative methods, and applied mathematics.
• Few new colleges and universities will be built in the forseeable future, and widespread budget reductions are forcing institutions to cut positions, rather than hire replacements, when faculty members leave. Most tenured faculty members today are middle-aged or older, but, given the employment picture in math and the nation's economic climate, they are not eager to change jobs or retire. So it will be a long time before any substantial hiring occurs in mathematics departments. Although retirements slowly will open up some jobs, the number of new mathematicians hired will fall far short of a one-for-one replacement of tenured retirees with new tenure-track hires. This is particularly true because the numbers of first-year graduate students are not increasing and thus do not justify new faculty positions.
• New Ph.D.'s in mathematics must compete for the few available academic jobs with people who received their degrees a few years ago. Many of those earlier Ph.D.'s either could not find any academic position or have been hanging on at universities as postdoctoral students or part-time faculty members, in the hope that a tenure-track job would open up. At current hiring levels, it would take some years to absorb this backlog, even if all production of math Ph.D.'s suddenly ceased.

First, let's be honest with our students. Graduate students must be warned that their prospects for a satisfying academic career at a research university are dim. Graduate work in most mathematics departments is no longer an apprenticeship program in which talent and hard work almost surely will lead to a job in academe. Future graduates of our programs must look outside academe for work and thus will need the kind of broad training that will give them the flexibility to assimilate new bodies of knowledge and attack problems in a wide range of settings in business and industry.

In short, we need to take professional and moral responsibility for the present gap between the approximately 800 Ph.D.'s who find temporary jobs in academe yearly and the 500 or so who ultimately will be lucky enough to obtain a permanent position. To do that, we must re-examine the size of our graduate programs and be prepared to reduce enrollment.

Next, we must acknowledge the accumulating evidence that the traditional programs leading to a bachelor's, master's, or doctoral degree in mathematics do not produce the highly marketable skills needed to enter the 'hot' growth fields in the peacetime economy--biotechnology, genetic engineering, and telecommunications, to name a few. While much work involving mathematics is done outside academe, industry traditionally hires people from other disciplines to do it. The sad irony is that sophisticated mathematical skills, but not traditional mathematicians, are often needed in today's new fields. The research-and-development world seeks creative researchers and people with the flexibility to adapt techniques and ideas to new situations. Unfortunately, many mathematics Ph.D.'s are not adept at solving problems that arise in the real world. Until we prepare our students appropriately for research-and-development positions in industry, the hiring patterns won't change."

In academe, as well as in high-tech industries, people not trained as mathematicians are doing mathematical work, often quite successfully. This phenomenon is the legacy of a long and profound failure of mathematicians to communicate with other groups. For example, many mathematicians believe that engineers and scientists are interested only in the formulas and not the theory of calculus. However, anyone who takes physical chemistry or thermodynamics needs to understand "the chain rule" and the "implicit-function theorem" at a much deeper level than is taught in standard mathematics courses. The net result is that physicists and chemists are teaching that information more abstractly and thoroughly than are most mathematics departments.

The future of mathematics departments may depend on whether we emphasize concepts and insight or formalism and proof. Since most of our future graduates will be employed in non-academic settings, they must be professionally adroit and adaptable enough to handle problems that present them with too much or too little information and afford them too little time for finding ideal solutions.

Research scientists and engineers, even investment counselors, increasingly need to employ sophisticated mathematics. They make do now with self-instruction, but mathematics departments, if they chose to, could provide integrated, concept-based courses that would teach students how to use information in a variety of contexts. We must structure more of our offerings so that non-mathematicians, as well as graduate students in mathematics, find them valuable.

Recent experience has taught us that a business-as-usual approach no longer works in our changing economic and political environment. If we act now to re-examine both the content and size of our graduate programs, we can begin producing mathematicians better trained to meet the challenges of the next century.

Charles E. Mannix, Jr., a 1993 recipient of a Ph.D. in applied mathematics who was unable to find academic employment, is one of the founders of Aero-Geo-Astro, Ltd., an engineering consulting company. Kenneth A. Ross is a professor of mathematics at the University of Oregon and president of the Mathematical Association of America.

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