[Paleopsych] CHE: Mathematics and Biology: New Challenges for Both Disciplines
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Mathematics and Biology: New Challenges for Both Disciplines
The Chronicle of Higher Education, 5.3.4
http://chronicle.com/weekly/v51/i26/26b01201.htm
By LYNN ARTHUR STEEN
For most of the 20th century, mathematics was seen as a close and
natural partner of physics and engineering. Secondary and
postsecondary mathematics educators channeled the mainstream of their
programs to nourish the roots of the physical sciences. From
trigonometry through calculus and on into advanced calculus and
differential equations, mathematical study from 10th grade through
sophomore year in college was designed to support the parallel
curriculum in engineering and physics.
Now, however, biology has replaced physics as the crucible of
innovation -- not only in science, but also in mathematics. The
mathematics involved in understanding the folding of proteins, the
causes of heart attacks, and the spread of epidemics is as deep,
elegant, and beautiful as the mathematics of relativity, quantum
mechanics, and subatomic particles. As John H. Ewing, executive
director of the American Mathematical Society, has noted, biology is
"the next big thing in mathematics."
Similarly, some argue that mathematics is the next big thing in
biology. Eric S. Lander, a professor of biology at the Massachusetts
Institute of Technology, speaks of "biology as information," as a vast
library filled with the "laboratory notebooks" of evolution, one for
every species, with chapters for every tissue, each written in a
genetic code that can be deciphered only by means of sophisticated
algorithms. In this new biology, evidence is as often mathematical as
observational, as often quantitative as descriptive.
The relatively sudden emergence of biology as the dominant scientific
partner for mathematics in both research and education has created
major challenges for both disciplines. Biological research -- and with
it the multibillion-dollar biotech industry -- is hampered by the lack
of scientists able to work in teams where both biological and
mathematical skills are employed. Biology professors need to learn
about the new quantitative tools while helping students who may have
assumed that biology was a refuge from mathematics. And mathematics
professors educated in the physics paradigm face the daunting prospect
of learning to teach new cross-disciplinary courses awash in
unfamiliar theories, methodologies, and vocabulary.
BIO 2010: Transforming Undergraduate Education for Future Research
Biologists, a 2003 report from the National Research Council, argued
that as biology becomes more quantitative and as connections between
the life and physical sciences become deeper, biology itself is being
transformed from a disciplinary to an interdisciplinary science. In
contrast, however, "undergraduate biology education has changed
relatively little," being "geared to the biology of the past, rather
than to the biology of the present or future."
Meeting the challenges posed by the new biology will require a
paradigm shift in undergraduate mathematics. The challenges, which are
immense, involve:
Students. Most biology students know too little mathematics, and most
mathematics students know too little biology. Moreover, career options
for both groups are becoming increasingly diverse, with many options
requiring specialized preparation.
Faculty members. Senior faculty members in mathematics and biology
were educated in a monodisciplinary culture. Now they have limited
time, resources, and incentives to learn new areas and develop
cross-disciplinary professional networks.
Curriculum. Few established courses and even fewer curricular programs
focus on the new biology, and biological textbooks and curricula
generally pay too little attention to the role of mathematical tools.
Compounding the problem is a lack of widespread agreement on the kinds
of mathematical knowledge that biologists now need.
Departments. Most departments lack structural mechanisms to sustain
new courses, which are often developed by single professors using
one-time grant support. Too often, departmental reward systems
reinforce disciplinary boundaries and discourage curricular
innovation.
Academic institutions. Administrative structures typically bind
departments to disciplines, and few mechanisms exist for disseminating
successful new programs and courses.
Although many of those challenges represent generic problems facing
higher education, some are unique to the interface of mathematics and
biology. They burden colleges and universities in ways that make it
especially difficult for institutions to confront the urgent challenge
of educating students for the new biology. And it is indeed urgent.
Genomics and proteomics display perhaps the highest profile, based on
their potential for curing genetic diseases. Advances on that frontier
require computer scientists and mathematicians specially trained in
bioinformatics to devise and apply algorithms to solve problems that
have never before been attempted or even contemplated. Even more vital
-- in this era of mass air travel and virulent strains of flu, to say
nothing of bioterrorism -- is the work of mathematical modelers who
invent, explore, and evaluate potential strategies for containing
epidemics. That is the kind of science possible only with mathematical
models: Trial and error is too slow and potentially too lethal.
From visualizing subcellular processes like the misfolding of proteins
that cause mad-cow disease to studying global environmental issues
like the effects of atmospheric warming, mathematics is often the only
tool available for developing hypotheses and anticipating
consequences.
The best way to develop the needed cadre of multidisciplinary experts
is to get mathematics and computer-science students hooked on
mathematically fascinating biological problems early in their college
careers. Fortunately many colleges and universities are beginning to
develop special undergraduate courses, research projects, and joint
majors to do just that. Many are described in a volume I edited, Math
& Bio 2010, and the Web site of the Mathematical Association of
America offers useful links to such efforts (see
http://www.maa.org/mtc). Case studies and examples contained in (or
linked to) those resources suggest strategies that higher-education
administrators may find useful in supporting the new biology on their
own campuses.
The era of biology as a safe haven for math avoiders is over. Whether
they study molecules, cells, or ecosystems, future biologists will
clearly need to understand and use sophisticated quantitative tools.
So too will anyone dealing with the societal impact of biology, like
genetically engineered crops, epidemics, antibiotic-resistant
path-ogens, and bioterrorism.
That includes every college student, not just future life scientists
or health professionals. Citizens who elect legislators, police
officers who deal with terrorist threats, business leaders who make
economic decisions, and school-board members who set educational
policy all need a sound, quantitative understanding of 21st-century
biology.
Lynn Arthur Steen is a professor of mathematics at St. Olaf College.
This essay is adapted from Math & Bio 2010: Linking Undergraduate
Disciplines (Mathematical Association of America, 2005), which he
edited.
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