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According to the American Mathematical Society's (AMS's) 2002 Annual Survey of the Mathematical Sciences (Second Report) , the number of U.S. citizens who are awarded a Ph.D. degree in the mathematical sciences continues to drop, although the number of graduate students enrolled in mathematics programs appears to be increasing. This positive lag may or may not figure into the "equation" involving the number of mathematicians of color.

The AMS survey used gender, race, and ethnicity to define groups and included U.S. citizens, permanent residents, and foreign nationals. Additional relevant information included the location and type of employment after graduation. Because the number of professional mathematicians depends on the pool of mathematics students, the AMS report provided part of the rationale behind the establishment of the Mathematical and Theoretical Biology Institute ( MTBI) at Cornell University in 1996 (see box 1). In January 2004 MTBI moved to Arizona State University to expand its efforts in the Southwest. This article examines MTBI's purpose and its success to date.

MTBI's Mission and Program

MTBI focuses on providing research opportunities to undergraduate and graduate students who are interested in working on problems at the interface of the natural and social sciences and mathematics. MTBI offers a summer program that includes sequential research experiences for undergraduates, graduate students, postdoctoral students, and visiting faculty members, typically from teaching colleges (see box 2). The 2003 MTBI's summer institute was held at Los Alamos National Laboratory ( LANL) with the support of the T (Theoretical) Division and its Center for Nonlinear Studies. A large percentage of MTBI students come from undergraduate institutions that offer limited research experiences to undergraduates.

1. The AMS Data

The decrease in the production of Ph.D.s at American universities is alarming. The 2002 AMS report notes, "There were 948 new doctoral recipients reported for 2001-02 by departments responding in time for the 2002 First Report. This is the fourth consecutive drop in the number of new doctoral recipients. The counts for the preceding four years starting in 1997-98 were 1163, 1133, 1119, and 1008."

The number of U.S. citizens who are awarded a Ph.D. degree in the mathematical sciences also continues to drop. In fact, "Only 418 (44%) of the new doctoral recipients for 2001-02 are U.S. citizens, a drop of 76 (15%) from 2000-01 and down 168 (29%) from 586 in 1997-98." Furthermore, the report also notes, "The number of new doctoral recipients from Groups I (Public), I (Private), and II (most selective universities) combined has dropped from 744 in 1997-98 to 521 this year [2002], a decrease of 223 (30%)."

The situation for minorities, particularly for those who are members of underrepresented groups, is tragic. The most recent data (in this report) notes, "Among the 418 U.S. citizen new doctoral recipients, 18 are Asians, 12 are Blacks or African Americans, 8 are Hispanics or Latinos, 370 are Whites, and 10 are other." The mathematics data say that eight Latinos, 12 African Americans, and 0 Native Americans completed a Ph.D. in the mathematical sciences in 2002. The fact that MTBI has sent over 12 Latinos and about 15 underrepresented minorities to graduate school in the mathematical sciences per year is therefore a significant contribution in this context.

2. MTBI Affiliations

The ninth MTBI summer session and the first ASU/LALN joint effort will also be held at LALN with the support of the Department of Mathematics and Statistics and the Office of the Provost at ASU and LANL. MTBI summer programs are carried out with the collaboration of the Santa Fe Institute and the Center for Statistical Genetics and Genome Science Training Program at the University of Michigan. Our active partners include the Departments of Mathematics at the University of Iowa, Howard University, the University of New Mexico, the University of Arizona, New Mexico State University, and Cal Poly, Pomona. MTBI continues to have a strong association with the Center for Applied Mathematics, the Department of Theoretical and Applied Mechanics, and the Department of Biological Statistics and Computational Biology at Cornell University.

Typically, MTBI admits 22 to 24 undergraduates and brings back six to eight MTBI undergraduate alumni. The first group participates in an intensive 4-week collaborative learning experience on dynamical systems (broadly understood to include stochastic processes), modeling, and computational methods. Undergraduate alumni, graduate students, and visitors participate in a collaborative research seminar on advanced dynamical systems, computational methods, and modeling. During the 8-week program, participants typically work 10 to 12 hours per day, 6 days per week.

Other educational events include a 3-day workshop on genomics given by faculty members from the University of Michigan's Center for Statistical Consultation and Research and weekly colloquia with special events. Last summer we had a 2-day international conference on the application of mathematics to homeland security, and this summer we will have a 3-day workshop on complexity at the Santa Fe Institute.

During the final 4 weeks of the research portion of MTBI, students work on projects of their own choosing, that is, students select the area, the research question, and their teammates. Faculty members and graduate students work with each group on their chosen project. Although most of the team members (including faculty members and graduate students) usually have little or no expertise on the selected question or topic, MTBI participants, graduate students, and faculty members become equal research partners, thereby altering the customary research environment. The view that we (the faculty) know everything or that we are smarter than they are quickly dies out.

The last week of the program includes a miniconference in which students present their work to the scientific research community by giving group oral presentations. Students also provide a poster presentation of their work at an "end-of-the program" banquet and submit technical reports in LATEX (word processor for writing mathematical papers) before leaving.

MTBI Student Awards and Publications

Our students have won multiple awards at the joint annual meeting of AMS and the Mathematical Association of America. They have also won several awards at the annual meeting of the Society for the Advancement of Chicanos and Native Americans in the Sciences (SACNAS) and at various regional conferences. In fact, two posters received awards at the 110th meeting of AMS (2004, Phoenix) and a third received an award at the last SACNAS meeting (2003, Albuquerque). Students and alumni have made at least 20 presentations over the past 2 years (2002 and 2003) at four SIAM's special sessions on nonlinear dynamics.

MTBI alumni are prolific writers. Two recent publications by MTBI alumni include "Am I too fat? Bulimia as an epidemic," Journal of Mathematical Psychology 47, 515-526 (2003) and "Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity," Mathematical Biosciences 187, 111-133 (2004). In addition, 78 technical reports have been published in the Technical Report Series in the department of biological statistics and computational biology at Cornell University.

MTBI Results

Over the first eight summers, 123 out of 204 MTBI participants are currently graduate students or have enrolled in graduate programs in quantitative fields (mostly mathematics and statistics). Most MTBI alumni have received multiyear fellowships. For example, 18 of them are attending or have graduated from Cornell University. The numbers of MTBI alumni affiliated with various universities continues to grow, including Princeton (2), Stanford (4), University of Iowa (15), Rice University (4), University of Texas, Austin (3), University of Maryland (2), University of Arizona (4), Oxford (1), Harvard University (2), University of Michigan (2), and Arizona State (4). Our alumni include a Rhodes scholar, a winner of Mexico's 2002 Presidential Youth Award, and winners of national fellowships (e.g., National Science Foundation, Howard Hughes, and Ford)

Two MTBI alumni have completed their Ph.D., at least 11 are Ph.D. candidates (eight at Cornell University), and 30 have completed their master's degree. Furthermore, 52 are currently enrolled in a Ph.D. program, nine in a master's degree program, and eight in professional degree programs (medical and business).

MTBI set out to increase the pool of minority mathematicians by providing research experiences in mathematics. We are proud of what our alumni have been able to achieve and are certain our investment in them will continue to reap benefits for years to come.

Carlos Castillo-Chavez is a Joaquin Bustoz Jr. Professor of Mathematical Biology at Arizona State University and may be reached at chavez@math.asu.edu.