The question is “Who are the notable African Americans who have earned Ph.D.s in mathematics?” Would researching the answer be significant? Is it important in the science of mathematics to investigate whether five Ph.D.s awarded to five African Americans between 1925 and 2000 imparts enough impact to the field to fill the gap in the canon of mathematics and history? My intention with this paper is to offer the reader the opportunity to consider the field of mathematics in which five individuals have made and are making contributions, while at the same time suggesting that their path to their achievements were unusual. The first section of this paper is a summary of these five. The second section is concise and provides an overview of how many math Ph.D.s, were awarded to African Americans during that same period. The next two sections examine the contributions and mathematical achievements in general and the barriers and psychology that perhaps has created a dismal increase in underrepresented populations entering the field. The final section highlights the importance and implication of stagnate educational pipelines. In addition, I would like to stretch the mind to consider educational practices, as we know them now and to urge the reader to, bear in mind that in the 21st century, we need the talents, contributions and resources of all citizens in United States.

A Summary of Five Ph.D.s in Math from 1925 to 2000 While there are numerous achievements by minorities the individuals researched are:
1. Elbert F. Cox was the first African-American awarded a Ph.D. in mathematics from Cornell University in 1925. The topic of Cox's dissertation concerned polynomial solutions of difference equations.
2. Euphemia Lofton Haynes was the first African-American women awarded a Ph.D. in mathematics from Catholic University in 1943. Haynes’s thesis was entitled “Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences.”
3. Tasha Inniss thesis title is "Distributed Stochastic Models for the Estimation of Airport Arrival Capacity Distributions.”
4. Sherry Scott-Joseph's thesis is on, "Spectral Analysis of Fractal Noise in Terms of Wiener's Generalized Harmonic Analysis and Wavelet Theory.
5. Kimberly Weems’s thesis is titled, "On Robustness Against Mis-Specified Mixing Distribution and Generalized Linear Mixed Models."
Tasha Inniss, Sherry Scott-Joseph and Kimberly Weems all attended the University of Maryland, the first school to graduate three African American women Ph.D.s in one year (2000). Later in this paper, it will be more apparent as to why it is important to acknowledge the kind of impact higher education has when supporting the educational goals of underrepresented populations in this field. For now, when you consider diversity in the 21st Century, the University of Maryland is considered one of the nation’s leaders in awarding doctoral degrees to minorities in the areas of mathematics, computer and physical sciences and engineering. This distinction and honor, awarded to the University by the Quality Education Minorities (QEM) Network, a non-profit organization based in Washington, DC, which dedicated to improving the education of African Americans, Alaska Natives, American Indians, Mexican Americans, and Puerto Ricans. This organization believes that quality education for minorities improves the quality of education for all.

An Overview To encapsulate seventy-five years of remarkable achievements in mathematics is difficult, however to provide a synopsis of doctorate degrees awarded, Scott Williams, Professor of Mathematics at the University at Buffalo SUNY has created and Index of U.S. Black Mathematicians by year. Beginning in 1925 and ending in 2004, the chart lists 336 African American Math Ph.D.s with 75 of them to African American women. There was almost a twenty-year gap between 1925 (the first African American Ph.D. in Math) and 1943 (the first African American woman Ph.D. in Math).

Contributions and Mathematical Achievements These five individual’s achievements along with all other mathematicians lay the groundwork for a scientific “culture”, which refers to the bottomless composition of knowing, understanding, acting and being in the world. The culture enlightens all human thought and activity; it cannot be put on hold by human beings. Cox’s interest was in pure mathematics, a field concerned with mathematical theory rather than with practice or application. The most significant contribution Cox made dealt with the rigor cultivated in mathematics curriculum.” While the Chair of Mathematics at Howard University, Cox pushed the level of the department and prepared it for the Ph.D. program (He “did not live to see the inauguration of the Ph.D. program at Howard.” ) His prestige as a mathematician gave the department credibility. The education achievements of Martha Euphemia Lofton Haynes were notable, she held a B.A. in Mathematics with a minor in Psychology from Smith College, and an M.A. in Education from the University of Chicago. In addition, she taught for 47 years in the public schools of Washington, D.C. and was the first woman to chair the DC School Board. She was an outspoken and active opponent of the DC school system's structure of segregation. It had a "track system," which placed students in academic or vocational programs depending on ability. The track system, which had structured the city's schools for a number of years and which was said to discriminate against black and poor students, was abolished along with de facto segregation by Judge J. Skelly Wright in June 1967, when Mrs. Haynes was board president. Tracking in the 21st century is disguised in standardized testing. For Tasha Inniss, Kimberly Weems, and Ms. Scott-Joseph “their achievement marks the first time that a university that is not historically black has granted mathematics Ph.D.'s to three black women in one class” The sources researched identified much more with linguistic isolation, the lack of instructional scaffolding and linking effective pedagogical practices rather than how their research has contributed to the mathematical community and the history of mathematics. Barriers and Psychological Implications To understand the implications as it relates to language, instruction and pedagogy, one must also understand underrepresented populations, the course of study and the field.
Linking this information from the ground up, I begin with Charles S. Fisher of Brandeis University who writes, “The expression “problem solving” can have a wide variety of meanings. In the everyday world, it refers to anything from a problem in an arithmetic book to the problem of achieving happiness. What constitutes the problem and its solution in each of these situations differs…When problem solving is mentioned with respect to science, the arithmetic book usually comes to mind…Most routine scientific problems are of this nature: the mathematician finds maxima and minima, and the chemist test acidity.” It is not unusual to have the perception of mathematicians sitting around trying to prove things, and to identify one mathematician’s success as either verified or unproven by another’s scrutiny of the first’s labors. Other social characteristics of mathematicians, is they work virtually in isolation. Their early training is to cultivate a learned feeling of autonomy; they work alone for years with a sense of mathematical correctness. During their course of study, they follow a common education path, sharing knowledge with fellow students and moving into adjacent areas before specializing. Given the framework of social characteristics, the educational pipeline and the science of mathematics, when you embed race and gender within, it is not difficult to unhinge the complexities of both barriers and psychological issues in my view. It is not easy to be a minority student in a majority education system. If, in fact, the mathematical contributions of these individuals were indeed significant to the canon of mathematic history, it has not been written from that perspective. The rate at which African Americans, other minorities and women enter and emerge in the field as contributors is ladened by the degenerative pace of acceptance and acknowledgement. Cross and Slater report, “It is difficult to conceive a world in which blacks achieve social, economic, scientific, and educational parity with whites unless they also achieve a substantial scholarly presence in one of the great intellectual constructs that mankind has devised – the world of theoretical and applied mathematics.” It is a well-known fact that for centuries racism and in this case scientific racism prevailed in the United States. In an article dated 1992 it suggests that even today scholars in mathematics have not entirely conceded to the notion that African Americans are equipped to master the intellectual challenges of the field. An interesting comparison is research reports that minorities do far better in the sciences and mathematics in Europe and other nations that have limited professional bias. An example of how systematic tracking, is still prevalent can be followed by current assessment mechanisms within primary, secondary and the high school system all using standardized tests. The results of these tests determine funding for school districts. To tip the scales toward more funding, various exemptions are used when reporting the results of the schools populations. In addition, these tests are constructed using a socioeconomic standard and language that marginalizes underrepresented populations. How the data is complied is not the issue, using the data to map educational pathways which either includes or excludes a population perpetuates a degenerative result. This passage entitled “A Clear Case of Racial Bias in Mathematics Testing” is an example where: “A group of teachers from an urban middle school discovered that a group of students at their predominantly African-American school responded “strangely” to an assessment item on a district wide mathematics test. The basic structure of the test item was as follows: It costs $1.50 each way to ride the bus between home and work. A weekly pass is $16. Which is the better deal, paying the daily fare or buying the weekly pass? The district’s test designers constructed the problem on the assumption that students who solved the problem correctly would choose to pay the daily fare. Implicit in the design of the test item is the notion that all people work five days a week. It is also assumed, that the employee has only one job. Yet, these assumptions are not consistent with the daily lives and realities of many African-American students. Thus it should not have been shocking that a large percentage of the students in this particular middle school thought that “buy the weekly pass” was the better option. In the families of many African-American students, the financial providers hold several jobs – both on weekdays and weekends. For these students, choosing the weekly pass is economically appropriate and mathematically logical.
- William F. Tate, Assistant Professor of Mathematics February 1994. University of Wisconsin, Madison

I tested this same question, with my daughter and her friends and coincidentally their responses yielded the same result. This was a mixed group of ninth-graders with parents in a variety of backgrounds and each one answered the question with respect to their personal situation. The most important consideration I feel, is they all considered the “week” to mean ‘seven’ days, and not a “five day work week” as assumed.

Implication of a Static Educational Pipeline
Over the span of 70 years systemic tracking, through testing has had a crippling effect on the intellectual health of populations in the United States. The above example, gives credence to linguistic isolation and instructional scaffolding as a mechanism for tracking. Jeannie Oakes, University of California raises these questions and these questions give context to my statement from the beginning of this paper, “we need the talents, contributions and resources of all citizens in United States”: “…How can we have enough highly trained mathematicians, scientists, and engineers in the future? How can we teach the general labor force the knowledge and skills needed for technological work? How can we attain a level of scientific literacy necessary for responsible, democratic decision making about scientific and technological matters? There are no clear-cut answers for these questions. However, many observers suggest that without substantial increases in the achievement and participation of women and minorities, the nation will not meet its scientific and technological needs.” Losing populations because they do not fit in is an unfortunate process. “Systems that fail to diversify are often unstable and vulnerable; the strategy of using diversity to ensure long-term vitality has served well in a variety of natural, social, and economic systems (Wilson, 1992). By broadening the focus of mathematics to include a more diverse range of scholars, the discipline of mathematics would likely be enriched by an expanded range of mathematical thought. What ultimately makes sense is the opportunity for all to achieve enlightened self-interest in the foreground, not the background and for those previously excluded populations to have the right to participate in the enterprise of mathematics and science. I find it extremely interesting that the field of scholarship now surrounds the very reason I decided to pursue my undergraduate degree. No, I do not intend to pursue mathematics or history scholarship. I am already embedded in higher education, but to further position myself in my field, in the United States and as a contributor to the world community as an individual that will continue to empower the pursuit of scholarship, provides a stronger emphasis to my initial goal. This research has given me a much deeper understanding of my purpose.