The marriage between mathematics and the sciences (natural and physical) has always fostered strong, deep bonds, but increasingly in today's interdisciplinary world, mathematics may also be associated with other areas such as art, physical education, law, and the social sciences. My hope is that students will not just say, "Math is too hard--I'd be crazy to major in it!" but will seriously consider it as a viable major or minor. This article is the first in a series entitled, "Beyond Numbers and Proofs," which seeks to provide support to students (especially minority students) interested in mathematics as a career.
The role of mathematics as a promoter of change was never clear to me as an undergraduate and graduate student. Because I loved set theory, my goal was to complete a Ph.D. in pure mathematics. I hoped my thesis would involve expansions of the work carried out at the beginning of the 20th century by Polish mathematicians such as Banach, Sierpinski, and Kuratowski.
However, the internal voices that I heard told me that I had to do something useful for my community and that pure mathematics had little to offer. I was wrong. I slightly altered my area of expertise and completed a doctorate in applied mathematics at the University of Wisconsin, Madison, in 1984. (For more information about Dr. Castillo-Chavez's early days, see Adventures of a Mathematical Biologist on MiSciNet.
So the questions are, can my newfound wisdom be transferred to those minority students who feel the way I felt about pure mathematics? How can I show undergraduate and graduate students that applications demand high-power mathematics? How can I show my minority students that the line between pure and applied mathematics is blurred at best? It is not that simple! There is still a culture in the mathematics community that promotes the study of mathematics just for its own sake. Hence, it is not surprising to find limited understanding, within this community, of the philosophical and social issues that drive and impact the career choices of many minorities.
In addition, who will mentor them? The mathematics community at large has just begun to discuss or address these concerns. In fact, I never felt that I could share these views and feelings even with the supportive mentors I had as an undergraduate or graduate student. At the time I felt I had to approach my professional and motivational career decisions exactly the same way my mentors did. This internal conflict pushed me to the verge of quitting every year. Why didn't I quit? Why did I finish my Ph.D.? Frankly, I don't know, but I'm sure luck and my strong desire to become a mathematician played a role.
When I entered the halls of academia, this heart-felt reflection prompted me to create a program that would enlighten students as to the importance of mathematics, so in 1996 I founded the Mathematical and Theoretical Biology Institute (MTBI) at Cornell University (MTBI has recently moved to Arizona State University).
MTBI's philosophy builds on my social concerns, particularly in its summer programs. It begins from the assumption that every student has to find social value in their research. In other words, if the relevance of mathematics to the problems of today's world is the key source of motivation then that should become the impetus of the students' educational program. If social/career concerns, such as becoming a mentor at a community college, grade school, or mentoring mathematics teachers are important to an individual then these concerns must be an integral part of his/her "educational" model.
At MTBI students choose their own summer group projects. These projects also highlight the interdisciplinary nature that is taking hold today in science and technology. Some recent topics include the impact of alcohol on the brain, bipolar disorder treatment for couples, bulimia dynamics, the drug ecstasy, invasion dynamics, gang dynamics, and the role of uncertified teachers on high school dropout rates. MTBI students' research has led to several publications. In fact, MTBI students are the first to ever publish a paper on a model for the population dynamics of bulimia ["Am I too fat? Bulimia as an epidemia," Journal of Mathematical Psychology 47, 515-526 (2003)].
What students learn through their own questions is that mathematics is a powerful tool and that one never knows enough mathematics. My advice for those who want to use mathematics in applications is to learn as much mathematics as they can. The challenge therefore is deeper for those who want to make an identifiable difference using mathematics, otherwise known as "applied" mathematicians. They must become highly proficient in pure and computational mathematics and specialize in a particular area of science.
The continuous advances and paradigm changes in biology, the environment, and social sciences offer a "quick" access into the forefront of scientific research. The growth in fields such as mathematical epidemiology, immunology, physiology, neurobiology, genetics, bioinformatics, conservation biology, and homeland security have begun to change the culture of communication in mathematics departments throughout the country.
Therefore, students who have a strong need to know "why math," can now find a home in many mathematics programs. The National Science Foundation and the National Institutes of Health have found it in their best interest to fund programs such as the Integrative Graduate Education and Research Traineeship National Recruitment Program and institutes that promote interdisciplinary studies.
So why math? Fortunately, there is a growing culture that supports the view that there need not to be a single answer! The importance of such changes in culture and the increased acceptance of a diverse set of views have made several academic programs with a mathematical emphasis receptive to people of color. Minorities are interested in many health issues, but especially diabetes, nutrition, and the socioeconomic impact on their communities. Math can help solve these problems, so the challenges rest with us. We must act by encouraging the development of minority mathematicians, so that the future contributions of some of the country's best minds will not be lost.
Carlos Castillo-Chavez is a Joaquin Bustoz Jr. Professor of Mathematical Biology at Arizona State University and may be reached at firstname.lastname@example.org.