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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