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					                                                                         Myths in Math
                                                         Charles E. Mannix Jr. and Kenneth A. Ross

There are many myths about mathematics. Some               the current downturn in full-time tenured employment of
people believe that only gifted people can learn           new young mathematicians is not likely to be reversed in
mathematics, that mathematics is only for boys,            the next decade. Even though we are aware of them all in-
etc., but this article is concerned with myths in          dividually, it may be useful to consider them in totality and
mathematics. The December 5, 1994, issue of                to ponder their impact on mathematics. Our purpose is to
Newsweek included an article titled, “No Ph.D.s            state our reasons for our views without claiming to own a
Need Apply”. It discusses The Myth, which took             crystal ball.
hold in the 1980s, that the nation would face a                First, the abrupt end of the cold war eliminated many
shortage of scientists in the 1990s. Notices read-         compelling requirements for advanced R&D along with
ers saw several articles in 1994 and a recent              the organizations and staff supporting weapons develop-
February 1995 editorial on The Myth’s practical            ment. Sizable rollbacks now exist at national labs and high-
impact on today’s young mathematicians seek-               tech aerospace, electronic and design companies which for
ing career employment (for the most recent data,           decades welcomed and employed many mathematicians,
see the Survey article, this issue).                       engineers, and scientists. Displaced, highly qualified, mid-
   A related myth in mathematics, which we                 career individuals are entering the civilian economy on
hear every so often, goes something like this:             both sides of the (former) iron curtain. For thousands of
“Jobs were tight in the early 1970s and then the           them, their option will be to compete with new graduates
market improved. It’s a cyclic business and the            for teaching positions at all educational levels. Overall,
market will get better again soon.” Many of us             this is a healthy development because mathematics has al-
no longer have faith in this myth, for reasons we          ways been a worldwide activity that has largely ignored ar-
will explain, and we believe that mathematics de-          tificial national boundaries, but there is no denying the im-
partments should reconsider their missions. In             pact on the current and future U.S. job market.
particular, they should consider downsizing                    Our world is increasingly international. Worldwide eco-
their graduate programs and should reexamine               nomic competition is forcing downsizing on most high-tech
the education provided in graduate school so that          and even traditional American employers. Much detailed
it more closely fits the reality of what our grad-         design, which creates new openings for U.S. mathematicians
uates will be doing in the future. Some Type I uni-        and engineers, has followed manufacturing offshore. More
versities, such as UC, Berkeley and the Univer-            scientific cooperative efforts, another good thing, also lead
sity of Michigan, have already started this                to fewer technologists in any one country. The fiscal, po-
process.                                                   litical, and scientific pressures to collaborate are rising in
   Many long-term economic, political, acade-              areas from space research to high-energy physics.
mic, historical, and technical issues indicate that            A technological productivity and efficiency revolution
                                                           is affecting routine mathematical and scientific work just
Charles E. Mannix Jr. received the Ph.D. in applied        as the industrial revolution affected manual labor. Many
mathematics in 1993, searched extensively for acade-
                                                           common time-consuming analytical tasks, which gave em-
mic employment last year, and has established an en-
                                                           ployment, especially at the entry level, now are accom-
gineering math modeling/simulation consulting com-
pany with several friends. Kenneth A. Ross started         plished using very powerful and efficient utility software
graduate school before Sputnik, has taught at the Uni-     developed to a mature state. Consider the numerous sym-
versity of Oregon since 1965, and is now president of      bol manipulators, numerical analysis algorithms, statisti-
the MAA. The authors wish to thank the Notices edi-        cal data packages, and graphical products on display at the
tor, Hugo Rossi, for his support and encouragement.        joint San Francisco meeting in January 1995. These greatly

AUGUST 1995                                               NOTICES   OF THE   AMS                                            875
      speed lengthy calculations, yet most do not require their              Other situations in academia translate to
      ordinary user to possess unusual mathematical talent.               problems for mathematics departments. Within
      Note too, fewer mathematicians are needed to write and              static or shrinking outside income sources, uni-
      develop classical applications programs from scratch.               versities and colleges must foster new disci-
      Packaged or easily modified codes now exist in fields rang-         plines: biotechnology, genetic engineering,
      ing from orbit mechanics to finite element modeling. This           telecommunications, to name a few. Increasing
      software maturity results in completion of complex designs          overhead costs (i.e., support staff, pensions, and
      like the Boeing 777 with a smaller but more efficient tech-         insurance) encourage the trend to hire postdocs
      nical workforce. This touches another myth, namely, that            and part-timers. Costs for repairs, materials,
      business and industry can absorb unlimited excess Ph.D.             and labor to maintain the operation and upkeep
      production. While there is much mathematics to be done              of the physical plant at publicly supported in-
      out there, industry traditionally hires people from other           stitutions are accelerating faster than the tax
      disciplines to do this mathematics. Until we educate large          base and state support. A rising percentage of
      numbers of mathematics students appropriately (as sci-              every dollar allocated to colleges goes to worth-
      entists, and not just thinkers) for R&D positions in indus-         while compliance costs for accounting to fund-
      try, those hiring patterns will not change.                         ing agencies, enforcing equal rights laws, en-
         State college systems are largely built according to op-         abling the Americans with Disabilities Act, safety
      timistic expansion plans of the 1960s and 1970s. Thus, few          laws, etc. It is no wonder tuition fees, room and
      or no new sites or major expansions at old campuses can             board, and other student expenses are rising
      be expected. Worse, the equivalent of corporate downsiz-            much faster than inflation, which traditionally
      ing is occurring in academia. Budget cutbacks to state col-         outpaces middle-income family earnings. As
      lege systems have removed fat; ongoing annual reduc-                these attendance costs spiral upward, an in-
      tions are having a serious impact on vital programs. In many        creasingly larger part of our population will be
      places, present faculty and staff positions are more likely         denied access to a traditional four-year college
      to be cut, not replaced, when vacated. Another aspect is a          education, especially if the government cuts
      growing backlog of campuswide deferred projects that                back on student support. The trend will be to-
      will need funding when, and if, budgets ever increase.              wards ever smaller departmental enrollments
      These are all arguments for a long lag before any substantial       and not for substantial numbers of new tenure-
      hiring occurs in mathematics departments.                           track entry-level positions.
         Most tenured faculty today are in midcareer or older,               The unemployment situation facing young
      but not eager to retire. It is unlikely that they will transfer     people in mathematics is far worse than dismal
      elsewhere and leave vacancies which ripple down to cre-             unemployment statistics for any single year’s
      ate tenure-track slots for new Ph.D.s. It has been suggested        class suggest. Consider the invisible “unem-
      that their anticipated retirements will create a wave of            ployed”. There is already the equivalent of sev-
      new positions adequate to eliminate unemployment if only            eral years’ annual Ph.D. production embedded
      we wait. We agree that the projected retirements will have          in the woodwork of U.S. colleges and universi-
      some influence, but it will fall far short of a one-for-one         ties as postdocs, part-time faculty, adjunct fac-
      replacement of a tenured retiree with a tenure-track hire.          ulty, and, of course, the actively unemployed.
      Present and projected numbers of undergraduates annu-               This accumulation vigorously competes with
      ally obtaining mathematics diplomas are substantially               any current year’s graduates for the annual pool
      below the plateaus established two or three decades ago.            of available full-time tenure-track openings. At
      Since large numbers of math majors and first-year gradu-            current hiring levels, it would take some years
      ate students help in justifying math department staffing            to absorb this backlog even if all Ph.D. produc-
      levels, there will be fewer actual tenure-track openings            tion suddenly ceased.
      created than some people expect.                                       Another myth is that the situation could be
         None of this is helped by the shrinking percentage of            dramatically improved if national attitudes and
      the American student body that elects to take upper-divi-           government priorities quickly changed. The feel-
      sion majors in the analytical disciplines. Related to this is       ing that “science helped win World War II” trans-
      the trend to reduce analytical course work requirements             ferred to the public the notion that science would
      in nonmath degree programs. Many academic scientists and            help win the cold war too and help the country
      engineers feel that advanced mathematics is best learned            in other ways. Now, the average citizen no longer
      in the context of their discipline; thus much of what was           ranks pure mathematical research as a top na-
      traditionally provided by mathematics departments has               tional concern. Not only that, a diploma in a
      gravitated to those disciplines. Where other degree pro-            technical field, as we understand the term, is
      grams do need math, more mathematics is being taught                viewed by fewer American families as a com-
      within those programs. Many business schools, engineer-             pelling dream to be pursued and a worthy cause
      ing schools, and other math-utilizing departments now have          on which to sacrifice substantial amounts of
      their own calculus, statistics, quantitative methods, and ap-       money. With truly rare exceptions, such as Al
      plied mathematics courses.                                          Gore, leaders of national prominence do not
                                                                          possess an agenda of technical excellence in the

876                                              NOTICES   OF THE   AMS                              VOLUME 42, NUMBER 8
analytical sciences. In addition, very small num-       a satisfying academic career in a research institution are
bers of new Ph.D.s have entered government at           dim. Their love of mathematics will have to be the main
any level to become future role models and              motivation for pursuing an enriching intellectual experi-
voices at the table when budgets, priorities, and       ence in graduate school. Graduate work in most mathe-
hires are being established.                            matics departments is no longer an apprenticeship program
    Where does this leave us? First, let’s ac-          in which talent and hard work almost surely will lead to a
knowledge the accumulating evidence that the            satisfying career in mathematics. Future graduates from
present traditional program leading to a B.S.,          our programs will need the breadth and flexibility to as-
M.S., or Ph.D. in mathematics does not produce          similate new bodies of knowledge and to attack problems
highly marketable skills central to the “hot”           in a wide range of settings.
growth disciplines in the peacetime global econ-           In short, we need to take professional moral responsi-
omy. We have been training students to under-           bility for the present gap between the 800 or so Ph.D.s that
stand the detailed intricacies in a specific set of     enter academia yearly
problems, but failing to educate them on the po-        and the 500 or so ulti-
tential broad relevance of the contributions our        mately lucky enough to
discipline can offer to the solution of those prob-     obtain permanent po-
lems. The research and development world seeks          sitions, and take the
creative researchers and implementors with the          necessary steps to
flexibility to adapt techniques and ideas to new        close the gap.                 “Jobs were tight in
contexts. The sad irony is that sophisticated              There is likely no
mathematical skills, but not traditional mathe-         one single answer to          the early 1970s and
maticians, are often needed in precisely these dis-     this employment prob-
ciplines.                                               lem. A spectrum of
                                                                                        then the market
    In both education and the industrial high-
tech workplace, people not trained as mathe-
                                                        changes and reforms
                                                        will be needed to im-
                                                                                         improved. It’s a
maticians are doing mathematical work, often            prove the situation. We        cyclic business and
quite successfully. This phenomenon is the              doubt that industry can
legacy of a long and profound failure of math-          absorb the excess Ph.D.        the market will get
ematicians to communicate with other groups.            production, and a long
For example, many mathematicians believe that           time must be allotted          better again soon.”
engineers and scientists are only interested in         for some rooted atti-
the formulas and not the theory of calculus.            tudes to change. Surely,          Many of us no
However, anyone who takes physical chemistry
or thermodynamics needs to understand the
                                                        we must encourage all
                                                        realistic, sensible at-
                                                                                      longer have faith in
chain rule and implicit function theorem at a
much deeper level than is taught in standard cal-
                                                        tempts to increase suit-
                                                        able opportunities in
                                                                                            this myth.
culus of several variables. The net result is that      industry, government,
physicists and chemists are teaching these things       and academia. Re-
more abstractly and thoroughly than most math-          search scientists and
ematics departments. The future of mathemat-            engineers, even invest-
ics may depend on whether the emphasis is on            ment counselors, in-
concepts and insight or on Bourbaki-like for-           creasingly need more and more sophisticated mathemat-
malism and proof. This does not mean that proof         ics. They make do now with self-instruction, but only
is dead, just that insight needs to play a more         mathematics departments can provide an integrated con-
important role. Successful careers in practical life    cept-based instruction which produces versatility in use of
often require conceptualization and abstraction         the knowledge. We must understand that it is insufficient
of the essential problem without the usual list         just to say this. We must structure many of our offerings
of clearly posed questions at the end of the text-      so that nonmathematicians will place sufficient premium
book’s chapter. The majority of our future grad-        on such courses that they routinely become part of their
uates must be professionally adroit and flexible        curriculum.
over a lifelong career which includes many un-             This leads directly to the necessity of re-examining the
certain conditions of excess, insufficient, or con-     size and content of our graduate programs. These of course
flicting theories and data with rarely adequate         are related and are determined by our conception of where
time for contemplation.                                 our students are going. Thus, we badly need to reexamine
    Next, let’s be honest with our students very        our goals and purposes, our definitions and requirements.
early on. Their roles as TA’s and RA’s, faculty im-     Of course, any downsizing and other changes must be
petus, peers, and the present reward system             done most wisely and humanely. The net result ought to
create a mindset that the only quality careers are      be higher-quality students who really want to be mathe-
in academic teaching and research. Graduate             maticians and who have an education that meshes with the
students need to realize that their prospects for       challenges of the next century.

AUGUST 1995                                            NOTICES   OF THE   AMS                                          877

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