Craig J. Benham is a professor in the Department of Biomathematical Sciences at the Mount Sinai School of Medicine in New York, where is currently Acting Chair of one of the only institutions in the world where students can earn a Ph.D. degree in the rapidly emerging field of mathematical and computational biology. The Biomathematical Sciences Department is one of twelve basic science departments in the medical school.. Since the department has no undergraduate degree, he splits his time between teaching graduate level courses, administration, and research.
"The mathematical sciences, broadly defined, are rapidly becoming increasingly important in biology and medicine," says Craig. "They have traditionally played major roles in epidemiology, physiology, imaging, genetics, pattern formation and many other fields within the biological sciences. But the recent revolution in molecular biology has caused profound changes in the paradigms and methodology of biology that are vastly increasing the importance and usefulness of mathematical and computational methods."
Craig has an AB degree in mathematics from Swarthmore College and a Ph.D. in mathematics from Princeton University, where he worked in complex manifold theory. As an assistant professor at the University of Notre Dame he encountered Dr. John Kozak, a theoretical chemist working on protein structure problems. He became interested in the field because many of the important problems had significant mathematical components. "To get additional training in the area of molecular structure," he recalls, "I spent a year as a postdoc with Dr. Max Delbrueck in the Biology Division at the California Institute of Technology. There I switched my interests to DNA, primarily because the mathematical problems relating to DNA structure involved an intricate interplay among topology, geometry and mechanics. I have been working in this field ever since."
Craig believes there are many biologically important problems that need the work of someone who has sufficient knowledge of the biological problem, and the ability to develop and use the appropriate mathematical or computational tools. To work in this field one needs to have a strong interdisciplinary perspective. "To be successful in this interdisciplinary enterprise one must acknowledge that one is working in biology, albeit with mathematical tools," says Craig. "This means one must choose problems primarily for their biological importance and their susceptibility to mathematical or computational attack. Thus, one must develop a biologist's sense of what makes a problem important, and what constitutes a useful contribution to its resolution. One cannot overemphasize the importance (and difficulty) of developing this truly interdisciplinary, indeed multicultural, perspective."
Craig admits that the mathematical knowledge required to work in the field of biomathematics will vary with the biological problem being considered. Among the areas that find important uses in a range of fields within biology are group theory, linear algebra, topology, differential equations (ODEs, PDEs, and in some cases delay and/or stochastic DEs), differential geometry, including the calculus of variations, integral geometry, and the many subdisciplines of applied mathematics. "In addition to a strong background in mathematics," adds Craig, "any mathematician or computer scientist interested in developing the biological outlook necessary for success in this emerging area would be well advised to work in a biology lab for a time."
