A Decline In Mathematics Threatens Science—And The U.S.
Earlier this year, an article in the New York Times magazine discussed the work of Yale historian Paul Kennedy, who believes that the United States is in decline. In part, the article said: “Beginning in the 1960’s, Kennedy and his colleagues explain, when Japan and West Germany were busy rebuilding their heavy industries, encouraging private savings and cultivat- ing public education around mathematics and the sciences, America began to experience the chronic ailments of a maturing economy.” These ailments included “deteriorating schools.”
One could argue endlessly about whether—or how seriously—the U.S. is in decline. But there is one trend that is all too visible: Mathematics in the U.S. is paying the price of deteriorating schools—and the American failure to give mathematics education its due.
One sign of the impending crisis in mathematics is the dwindling supply of U.S. citizens among the recipients of doctoral degrees in the mathematical sciences. The steady increase in the percentage of foreign nationals receiving doctorates in mathematics (indeed in all physical sciences and engineering) has been widely reported in the national press and has been the subject of much hand-wringing in professional publications. Yet far more relevant and disconcerting is an actual decline in the number of mathematics Ph.D.s who are U.S. citizens. Fewer than 400 citizens, for example, received doctorates between July 1, 1986, and June 30, 1987. This marked the first time in more than two decades that the number fell below 400, and continued a decline that goes all the way back to the 1970s.
The decline looks even more ominous when one compares mathematics to other scientific disciplines. Since 1975, the ratio of new doctorates in mathematics to new Ph.D.s in chemistry, physics/astronomy, biology, and engineering has dropped steadily (see chart, right). Clearly, these other disciplines are doing a better job of turning out new scientists than is mathematics.
Equally worrisome are drops in both the relative number and quality of mathematics undergraduate majors, slumps that can be traced in part to poorly trained elementary school teachers. If a teacher fails to interest a student in mathematics by the sixth grade, the student has been lost forever.
So why should anyone care? What difference does it make to science in general—or to issues like national security—if the number of mathematicians in the U.S. declines? I would argue that it makes a tremendous difference. Advanced mathematics is becoming increasingly important in almost every field of science, from neurobiology to particle physics. As for national defense, the single largest employer of mathematicians is the National Security Agency. The nation needs mathematicians, and the need probably will grow in the next few decades.
The crucial question, therefore, becomes: Who is going to train the next generation of mathematicians? By the turn of the century, mathematics professors will be retiring in droves. Since the number of new Ph.D.s has been declining for the past two decades, many of these positions will be almost impossible to fill. Some four-year colleges are already having problems recruiting mathematics professors. And as industry reacts to the growing shortage by raising salaries for mathematicians, even top graduate universities may find it hard to attract new professors. At the same time, there are few prospects for improvement in mathematics education at the elementary and secondary school levels.
The result will be a crisis, as the U.S. suddenly loses its ability to train a new generation of mathematicians. We need to do something to reverse the trends. But what?
The first step is understanding why graduate students in mathematics are becoming so rare. The National Science Foundation’s recent survey, Science and Engineering Doctorates: 1960-1986, provides one possible answer. More and more undergraduates who major in mathematics and who go to graduate school decide to get their Ph.D.s in another discipline (see chart). In addition, the number of undergraduate mathematics majors is declining as well.
There is no question in my mind that fields like computer science, biology, and business (in particular, investment banking) are siphoning off students that a generation ago would have pursued serious graduate study in mathematics. Certainly, these fields have their attractions. But I believe that we in mathematics bear some of the blame for this trend. We have not been actively promoting our own field either as a discipline worth studying or as a valuable preparation for serious work in other areas. Indeed, within mathematics itself the specialties of computational mathematics, complexity, population dynamics, genetics, and mathematical economics are flourishing.
Burden Of Responsibility
Yet because of our reluctance to promote our field, we have permitted the perception that mathematics is arcane, irrelevant, and dry, dead, and boring (especially as it is presented to our young). All of us in mathematics must realize that we cannot abdicate our responsibility to both educate the general public on the importance of mathematics in contemporary society and to instruct a few select students in the intricacies of our art.
So what should we do to reverse the trend that threatens our national welfare and strength? First and foremost, professional mathematicians in general, and mathematics professors in particular, must be more willing to work with elementary and secondary schools to interest more of the nation’s young people in mathematics.
Need For Respect
At the same time, government agencies like NSF should cooperate with professional mathematics societies to ensure that every secondary school mathematics teacher has a strong mathematics background. We also need to improve mathematics curricula in elementary schools, where mathematics education is most crucial—and currently most deficient. One possible approach would involve loans and fellowship programs run by state and federal governments. There is already such a model: the National Defense Education Act Fellowships and Loans of the 1960s. The recipients of such awards would be committed to providing a certain number of years of mathematics teaching.
But more than this, mathematicians need to publicize both the variety of opportunities in the mathematical profession—and the value and importance of mathematics in careers as diverse as law, medicine, and business. Finally, we need to re-establish the respect for the teaching profession in general. The reward of knowing that one’s work is respected and valued is intangible yet invaluable. If we in the U.S. can but accomplish this step, we may be able to avoid a serious decline and begin a return to excellence.
Edward A. Connors is a professor of mathematics at the University of Massachusetts, Amherst, and chairman of a joint committee on education for the American Mathematical Society and the Mathematical Association of America.