I once told a colleague that I sometimes feel like I’m living somebody else’s dream. Sure, I’ll admit to the standard “grow up, get married, have kids, and live in a nice home” dream, but I also wanted a career. As a young girl growing up in Portsmouth, Va., in the 1960s and 70s, that meant emulating my superb elementary and junior high school teachers. Some might find that surprising, since my schools were essentially segregated and all-black: black students and black teachers. However, teaching was considered a prestigious and lucrative career to which most African Americans could aspire, and it attracted some of the best and brightest minds.
I was born shortly after the landmark Brown vs. Board of Education Supreme Court decision, which declared laws specifying a separate but equal education for blacks and whites unconstitutional. But school integration was more theory than application during the first decade or so after the ruling. In the early 60s, Portsmouth implemented “Freedom of Choice,” a policy that allowed students to attend any public school in the city. This typically meant that a few black students attended white schools, but no white students attended black schools. Like most black students, I continued to attend black schools. But by the early 70s, the threat of court cases pressured many school systems—including Portsmouth—to abandon their failed integration policy and implement forced busing.
Being bused across town to Cradock High School was socially devastating, separating me from my closest friends. Still, I was fortunate. Black kids in my neighborhood were assigned to the same high school all four years, while most of my junior high friends were bused to multiple high schools as battles raged over what to do with the black high school. My friends excelled despite the turmoil, but one brilliant student suffered a mental breakdown a few years later. Today I’m still haunted by the possibility that her experience during those years caused or hastened her distress.
I began my first year at Cradock with some apprehension about the transition to an integrated environment. My academic fears, at least, dissipated once I received my first report card with 5 As and a B (in chorus). By the next report card even that lonely B had become an A, and at the end of four years I graduated as valedictorian.
I applied to a small number of colleges, both black and white, and eventually chose the College of William and Mary (W&M). From earlier visits, I knew that black enrollment at W&M was small, but the sparsity of African American students still surprised me when I arrived for orientation — only 23 blacks in a freshman class of around 1,000 students.
W&M had only two black professors in the 70s, but almost all of the housekeeping staff, bus drivers, and food service workers were black. On many days, just a wave, smile, or kind word from one of them was a big comfort. On one occasion a friend and I, busy talking as we walked back to our dorm after class, barely noticed the campus bus roll by. At the very next meeting of the Black Student Organization, the president suggested that some of us were becoming a little “uppity” because bus drivers were complaining that we weren’t waving back at them!
I majored in mathematics, intent on becoming a high school math teacher. For the most part, my professors seemed knowledgeable and fair, but recent conversations with other black alumni suggest that my STEM major offered me some protection against subjectivity and bias. Still, I heard the occasional “off-color joke” from a professor who apparently “forgot” that his class included black students, and watched a troubling behavioral science film concerning human-imprinting in monkeys that never should have seen the light of day.
One of the worst college incidents that I recall happened my junior year. Upon returning from a holiday break, I found my roommate, a young black woman, staring blankly into space. She and a white friend had planned to ride back to school together, but the joint trip was scrapped after her friend’s mother told her daughter that it wasn’t socially acceptable to be friends with blacks.
Fortunately, my recent visits to campus indicate that much has changed since then. Minority enrollment has increased significantly, and the university is currently celebrating the 50th anniversary of the first three African Americans to live on campus. Two new dorms were also recently named in honor of blacks, one of which—Lemon Hall—is named after an 18th-century slave owned by the university. Like many U.S. universities, W&M is making an effort to atone for its ownership and exploitation of slaves.
After graduation, I pondered an offer to teach in the Portsmouth public school system and an acceptance letter from the graduate Department of Mathematics at the University of Virginia (UVA). The lure of tackling challenging mathematics at UVA eventually won out.
I enjoyed theoretical mathematics at UVA, but harbored a fascination—inspired by earlier classes at W&M and a high school summer program at Old Dominion University (ODU)—with writing computer codes to solve practical mathematical problems. Once I blurted out to my classmates, “What’s this stuff good for?” A fellow student laughed and said, “Bonita, you’re not supposed to ask that question!” These concerns, and a professor’s insight on job opportunities in numerical analysis and applied science, convinced me to wait before pursuing a Ph.D. After graduating with a master’s thesis in commutative algebra, I accepted a teaching offer from Norfolk State University.
However, an ad for a new master’s program in computational and applied mathematics at ODU drew me back to school. I enrolled part time to pursue a second master’s degree while continuing to teach at Norfolk State, and later Hampton University. When ODU’s math department was approved for a doctoral program, I received a letter congratulating me on my admittance. Upon questioning my acceptance into a program to which I hadn’t even applied, the director said with a sneaky smile, “Oh, we put all of our promising students into the Ph.D. program!” I decided to stay.
It was a great decision. Philip Smith, my dissertation advisor, helped me obtain an internship with an aerospace engineer at NASA’s Langley Research Center. This eventually led to a graduate student research fellowship at NASA that paid more than my teaching position at Hampton.
Figure 1. A two-dimensional grid around an airfoil, or wing cross section. The area near the wing looks dark because of the large concentration of grid points needed to solve the equations close to the wing’s boundary. Farther away from the wing, the airflow is less affected and fewer grid points are needed. Figure credit: Bonita Saunders.
My research involved boundary-fitted grid, or mesh, generation. Such grids are used in fields where equations are solved over an oddly-shaped domain, such as aerodynamics (aircraft, automobile design), hydrodynamics (ship design), electromagnetics, and materials science. Figure 1 shows a grid constructed via variational methods and tensor product B-splines that may be used to assess the effectiveness of wing design by solving the equations of motion around an airfoil. Both a grid’s shape and the interior points’ distribution can severely affect the accuracy of numerical simulation.
Budget issues limited the number of new positions at NASA, so after earning my Ph.D. I moved to the Washington, D.C. area and spent four years as a programmer analyst with a defense contractor. The work was spotty and somewhat boring, but provided an excellent opportunity to enhance my computer skills. Still, I was ecstatic when contacts suggested by Smith, my dissertation advisor, led to a job in the Applied and Computational Mathematics Division (ACMD) at the National Institute of Standards and Technology (NIST).
NIST’s broad mission to conduct theoretical and applied research to advance measurement science and promote U.S. innovation offers project flexibility. ACMD allows scientists to design or join projects that align with their research interests within NIST goals.
Such was the case when I joined NIST’s Digital Library of Mathematical Functions (DLMF) Project, created to replace the classic National Bureau of Standards’ Handbook of Mathematical Functions  with a new, expanded online resource and print companion . Like the original handbook, the DLMF contains definitions and formulas for all types of high-level mathematical functions that solve problems in the mathematical and physical sciences, but also enhances ease of use through the power of the web.
I focused on informative graphs and visualizations for the DLMF Project, realizing that grid generation techniques could facilitate the plotting of function surfaces containing branch cuts, zeros, poles, and other areas of interest (see Figure 2). I created a sub-project supported by a dedicated team of both NIST computer scientists and mathematicians, and college students employed under NIST’s Summer Undergraduate Research Fellowship internship program. We created more than 600 graphs and visualizations of complex functions while also advancing research in interactive three-dimensional web graphics. Over a decade of work has led to numerous technical publications and presentations at international conferences. The DLMF Project team has received several awards and honors, including a U.S. Department of Commerce Gold Medal (2011); a cover article in Notices of the American Mathematical Society (August 2011); and recently, an invited article in Physics Today, the flagship publication of the American Institute of Physics .
Figure 2. A Digital Library of Mathematical Functions (DLMF) webpage with an embedded visualization of the Riemann zeta function, an important function that arises in the field of number theory (left). Computing the function value at each point on the grid (right) provided the surface data, and computing values along the boundary and around the hole produces a nice clipping—or cutoff—of the function surface and a smooth color map. Figure credit: Bonita Saunders.
I serve on the DLMF editorial board and also lead one of several spinoff efforts, the NIST Standard Reference Tables on Demand Project. The project is a collaboration between NIST’s ACMD and the University of Antwerp’s Computational Mathematics Research Group to build an online testing service where users can generate high-precision tables of special function values with certified error bounds for comparison with their own uploaded function data.
So why do I feel like I’m living somebody else’s dream? Well, my career bears little resemblance to the dream I initially described. But fortunately, I’ve had some time to reflect on a hasty comment made during a pensive mood.
What was I thinking? Of course I’m living somebody else’s dream! I’m living the dream of Hidden Figures’ Mary Jackson, who reluctantly gave up her engineering career to accept a position as an equal employment opportunity manager to advance the careers of other women and minorities; the dream of my excellent first-grade teacher, who longed for the chance to be excellent in another career; the dreams of my parents, who graciously viewed my accomplishments as a fulfillment of their own dreams; the dreams of civil rights legends like Congressman John Lewis, who have lived to see the heirs to their dreams. And may I never forget: the dreams of countless slaves, whose only freedom was their dreams.
 Abramowitz, M., & Stegun, I.A. (Eds.). (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York, NY: U.S. Government Printing Office.
 Olver, F.W.J., Lozier, D.W., Boisvert, R.F., & Clark, C.W. (Eds.). (2010). NIST Handbook of Mathematical Functions. New York, NY: Cambridge University Press.
 Schneider, B.I., Miller, B.R., & Saunders, B.V. (2018). NIST’s Digital Library of Mathematical Functions. Physics Today, 71(2), 48-53.
| Bonita Saunders is a research mathematician in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology. She is the secretary for the SIAM Activity Group (SIAG) on Geometric Design, and webmaster and mailing list moderator for the SIAG on Orthogonal Polynomials and Special Functions.