## Celebrating Black History Month

## African-American Statisticians Serve as Models for Helping Others

The month-long tradition of celebrating the achievements of blacks/African Americans in February began with Carter G. Woodson and the Association for the Study of Negro Life and History (ASNLH) in 1926. Carter and the ASNLH were dedicated to researching and promoting the achievements of black Americans when they began organizing Negro History Week, taking place during the second week of February and coinciding with the birthdays of Abraham Lincoln and Frederick Douglass.

In celebration of Black History Month, we recognize the famous professor David Blackwell along with 16 individuals from the black/African-American collective who have made tremendous contributions to the field of statistics.

Blackwell was a trailblazer with an expansive career that traversed more than 50 years. In celebration of his career and 100th birthday, Jackie Hughes-Oliver tells us about his impact on diversity and statistics, along with his personal interactions and accounts of events in his life. Hear his voice in these accounts, which provide life lessons on how we can positively affect the careers and lives of others.

Blackwell’s 62nd PhD student, Richard Lockhart, further recognizes Blackwell’s achievement by highlighting the impact of his research and career contributions.

The 16 featured individuals have made significant successes as researchers, professors, deans, and entrepreneurs. They inspire professionals on the rise and their peers by being role models, organizing workshops, mentoring, and advocating for increased representation in the field of statistics. Their bios exemplify the life lessons offered by Hughes-Oliver from the life of Blackwell. Read them to learn more about how they entered the field of statistics, what they’ve accomplished, and the role of mentoring in building their professional careers.

~

Dionne Swift

2019 Chair, Committee on Minorities in Statistics

### Lessons from the Life of David Harold Blackwell

By Jacqueline M. Hughes-Oliver

David Harold Blackwell was a once-in-a-lifetime, brilliant, off-the-charts, amazing genius in probability, game theory, information theory, and Bayesian inference. And he was black.

Many interviews and articles have been recorded and written that speak to the many sides of Blackwell. The most extensive source I have discovered is the 157-page transcript of interviews conducted by Nadine Wilmot in 2002 and 2003 (*David Blackwell: An Oral History with David Blackwell*) in which the voice of Blackwell is loud and clear. While these interviews touched on Blackwell’s research, they were mostly focused on his life experiences, and that is also the focus of this article.

Blackwell was quick to acknowledge that while he worked hard for his accomplishments, his success was also facilitated by others. I have identified five running themes in his life, and I believe these themes offer guidance on how each of us can work toward diversifying and strengthening the discipline of statistics. The themes are stability, support, expectation, advocacy, and opportunity.

David Harold Blackwell was born on April 24, 1919, in Centralia, Illinois, and died on July 8, 2010, in Berkeley, California. His father, Grover Blackwell, was born in Tennessee and moved to Centralia in 1912 to work as a strike breaker for the Illinois Central Railroad. **Grover Blackwell** had a fourth-grade education but maintained employment with the railroad during the Great Depression.

Blackwell’s mother, **Mabel (Johnson) Blackwell**, was born in Missouri and completed two years of high school. Mabel was a housewife and independent woman who owned and managed a couple of rental properties.

Blackwell’s maternal grandfather was **David S. Johnson**. Born and well-educated in Ohio, Johnson was a school teacher in Weakley County, Tennessee, before becoming a successful storekeeper in Centralia.

Blackwell was the eldest of four children and spoke of growing up in a community where all parents expected their children would be well educated, even though the parents may not have been. His brother Johnson Wesley became a railroad worker; another brother, Joe, became a lawyer; and his sister, Elizabeth Louella, became a school teacher.

Blackwell’s formative years were heavily influenced by family. When asked who encouraged his abilities in math, he said the following:

Acknowledging the disconnect between his grandfather being well educated and his uncle not going to school, Blackwell pointed to his grandfather attending school in a more accepting location, according to Donald Albers in *Mathematical People: Profiles and Interviews.*

There were several high-school teachers who were pivotal in Blackwell’s life. These teachers expected him to succeed, served as advocates for his abilities, and created opportunities for him. In *David Blackwell: An Oral History with David Blackwell*, Wilmot captured Blackwell saying the following:

**Caroline Luther** was his geometry teacher. “She invited me to come and visit her a couple times after I was in college,” said Blackwell. “I had always been pretty good at math and somewhat interested in it, but geometry really excited me.”

**Raymond Huck** was the math club teacher. “There was a mathematics magazine that was partly for high school mathematics students, and it had a problems section,” said Blackwell. “Mr. Huck encouraged us to try to solve the problems there, and sometimes we did. I solved a couple of them, and Mr. Huck wrote up my solution and mailed it into the mathematics magazine,” continued Blackwell. “And a couple of times, my name appeared in the magazine and once even my solution—really Mr. Huck’s write-up of my solution—appeared in the magazine. I was very pleased with that.”

**Grace Seiler** secured a scholarship for Blackwell to attend college. “There was an English teacher, Grace Seiler, who encouraged me to go to college,” said Blackwell. “In fact, she wanted me to go to her alma mater, which was DePauw University.”

Speaking more generally of his teachers, Blackwell said, “They had a general interest in the students, not just me particularly. They kept up with students after they left.”

The Great Depression (1929–1939) was in full swing by the time Blackwell graduated high school. But, in those days, every high-school graduate from Illinois was eligible for admission to the University of Illinois. Blackwell said to Wilmot, “There was never any doubt in my mind, I wanted to go to the University of Illinois, and I intended to go there.” There was a statewide exam in which the top scorer in each county received a four-year scholarship to attend the University of Illinois. Blackwell earned the top score in Marion County and enrolled at the University of Illinois in 1935, at the age of 16.

Blackwell had no connections in Champaign-Urbana, home of the University of Illinois, and arrived on campus with no place to stay. He traveled there alone, walked 1.5 miles from the train station to campus, and began heading to the administrative building to inquire about housing. His good fortune was that the black fraternities on campus (Alpha Phi Alpha and Kappa Alpha Psi) had a system in place to support their fellow students. Members would regularly watch for new black students arriving on campus and offer them housing. Blackwell was invited to stay at the **Alpha Phi Alpha** house, and he lived there during his entire six years at the University of Illinois.

Blackwell recalled his fellow students providing critical support in other areas, as well. Although he won a four-year scholarship to pay his tuition ($35 per semester), the scholarship did not cover living expenses or books. His father took loans to handle these expenses the first year, but Blackwell refused to allow his father to go into debt beyond that.

Another custom within the black Greek campus community was that some students earned money by washing dishes and serving as wait staff at various locations on campus. As one such student graduated, they sought a replacement from among their group to guarantee their junior colleagues continued to benefit. In this way, Blackwell earned money by working at the Pi Beta Phi sorority. His fellow students assisted in other important ways, too, according to Wilmot.

Some college professors were also instrumental to Blackwell’s success. **Arthur Crathorne** hired Blackwell for odd jobs, including as a bookkeeper to support Crathorne’s position as a church treasurer and to check answers in Crathorne’s new algebra book. Crathorne taught calculus and probability, and Blackwell came to realize these employment opportunities were likely designed to provide funding, rather than to truly fulfill a need. “I didn’t appreciate it at the time. It was only when I look back on it that I realize how [Crathorne] helped me,” Blackwell told Wilmot.

It was also Crathorne who invited **Jerzy Neyman** to the University of Illinois in 1937 and made sure Blackwell was introduced. Of course, this first encounter is important, given the role eventually played by Neyman in Blackwell’s career.

Upon completing his bachelor’s degree in mathematics in 1938 at the age of 19, the United States was still experiencing the Great Depression. With an extra year of scholarship remaining, Blackwell decided to continue his studies, completing a master’s degree in mathematics in 1939. While studying for his master’s degree, Blackwell applied for funding to complete a doctoral degree in mathematics, also at the University of Illinois. Blackwell recalled to Wilmot the following:

Blackwell’s doctoral adviser was **Joseph Doob**. Doob was relatively young, having earned his PhD in 1932 from Harvard University in analytic functions, and he was laying the foundations as a self-taught expert in probability theory.

Blackwell defended his dissertation, titled “Properties of Markov Chains,” in 1941 at the age of 22. And, of course, there is an interesting backstory that highlights the impact of personal relationships. Doob was planning to spend the 1941–1942 academic year at the Institute for Advanced Study in Princeton. Paul Halmos and Warren Ambrose were fellow doctoral advisees of Doob, but they had finished and were going with Doob to the institute. So it was important to Doob that Blackwell also finish. According to Wilmot, Blackwell said the following:

A historical digression is important to fully appreciate the preceding paragraph. After the Great Depression ended within the United States, the country immediately became embroiled in World War II (1939–1945). Opportunities were limited. The Rosenwald Fund was created by Julius Rosenwald, former president of Sears, Roebuck, & Company, and its goal was the equalization of opportunities among Americans, according to Jayne Beilke in her 1997 *Journal of Negro Education* paper, “The Changing Emphasis of the Rosenwald Fellowship Program.” From 1928 to 1948, the fellowship program awarded grants to black scholars, writers, educators, and artists. Without this funding, Blackwell would not have been able to spend time at the institute.

While at the institute for the 1941–1942 academic year, Blackwell became interested in game theory and met John von Neumann. (Many years later, in 1979, Blackwell became the first African American to win the von Neumann Theory Prize.) It was also during the year at the institute that Blackwell became “mildly interested in statistics” as he attended lectures by Sam Wilks, according to Wilmot. Once again, Blackwell gained immensely from his contemporaries. He recalled, “Again, as in my graduate days, I learned more from my contemporaries than I did from the higher-ups, so to speak.” Jimmie Savage was a particularly influential contemporary, but more on that later.

But that year at the institute almost did not happen. In those days, visiting members of the institute became honorary faculty at Princeton. **Frank Aydelotte** was director at the institute and staunch supporter of Blackwell. Unfortunately, the president of Princeton objected to Blackwell entirely on the basis of race. Several professors in the institute (including **Oswald Veblen**) threatened to disconnect the institute from Princeton, so the president acquiesced and Blackwell was allowed to visit. Blackwell said to Wilmot, “And I was just welcomed cordially along with everybody else. It was only much later that I found out that there had been all of this to-do.”

Blackwell expected his best employment opportunities would come from a black college, so he only applied to black colleges—all 105 of them. He also embarked on a driving tour to present himself to about 30 colleges on the East Coast, starting at Morgan College (now Morgan State University), then Howard University, and then moving south.

Blackwell accepted the first offer he received, and that came from Southern University in Baton Rouge, Louisiana. For the 1942–1943 academic year, he taught only elementary undergraduate courses.

His 1943 move to Clark College (now merged with Atlanta University and known as Clark Atlanta University) was motivated by the regional strength offered by the Atlanta colleges for black education, namely Morehouse College, Morris Brown College, and Atlanta University. These schools had a joint seminar series, and Blackwell would have the opportunity to teach at the graduate level. It was while he was working at Clark College that Blackwell met his wife-to-be, Ann Madison.

Although interviewed by the head of the math department at Howard University during his 1941–1942 driving tour of black colleges, Blackwell did not get an offer. But another man was listening to the interview from his desk and asked some questions afterward. Two years later, this man—**Dudley Woodard**—became head of the math department and made an offer to Blackwell to join the faculty at Howard.

Woodard was only the second African American to earn a PhD in math (1928, University of Pennsylvania), which he was so committed to earning that he resigned as dean of the Howard College of Letters and Sciences so he could pursue the PhD. Woodard was committed to math excellence at Howard and started both a math library and a math seminar.

Blackwell was the seventh African American to earn a PhD in math, and he joined Howard University in 1944—the same year he married Madison. He was promoted to professor and department head in 1947. With many veterans returning from World War II and wanting training through the G.I. Bill, the math department saw a large increase in enrollment. Blackwell talked fondly about hiring William Claytor, the third African American to earn a PhD in math (1933, University of Pennsylvania). Once again, the black community provided stability, support, and opportunities for Blackwell, with the expectation he would excel.

The Howard University years also allowed professional development. Blackwell said to Wilmot, “My interests were basically formed at that time, while I was at Howard.”

Howard’s proximity to Washington, DC, provided many opportunities. He became a consultant at the Operations Research Office in DC, where he found motivation for his work in game theory and optimization theory. He met (Meyer Abraham) Abe Girshick at a Washington, DC, chapter meeting of the American Statistical Association. Girshick was a major influence on Blackwell’s work in statistics; he provided an introduction to Wald’s sequential analysis and, when he became a full-time employee at RAND Corporation in California, Blackwell became a consultant.

Girshick joined the newly formed Stanford University Department of Statistics in 1948, and Blackwell spent the 1950–1951 year in residence there. Blackwell and Girshick wrote the early authoritative book on games and statistical decisions, *Theory of Games and Statistical Decisions*.

It was also at RAND where (Leonard) **Jimmie Savage** influenced Blackwell to embrace the Bayesian paradigm. Blackwell’s 1969 book, *Basic Statistics*, is regarded by some as one of the first books covering Bayesian inference.

Blackwell discovered the Rao-Blackwell Theorem, written about in his 1947 *Annals of Mathematical Statistics* article, while employed at Howard University. (On a personal note, this theorem is special to me because it is how I first learned that someone who looked like me had fundamentally contributed to the field of statistics.) The backstory of this discovery is both inspiring and poignant, best relayed in Blackwell’s own words to Wilmot:

*many*results in his thesis. So, because in his thesis, the result was buried among several other results, people hadn’t paid much attention to it, and I didn’t know anything about it. But, when I rediscovered it, and used the rediscovery to explain the Girshick-Mosteller-Savage estimate, people paid attention to it.”

Asked about his interactions with Rao, Blackwell said to Wilmot, “I don’t remember what our first meeting was like. I do know, though, that he’s not especially happy that my name is attached to the theorem. And he shouldn’t be, because he has the priority by two years. It’s just that somehow when I did it, it got publicity. … There were maybe twenty citations in the first couple of years. … I may never have cited that paper after that.”

Blackwell transitioned to the University of California at Berkeley in 1954 as a visiting professor. As it turns out, he almost had the chance to join the department 12 years earlier, in 1942. Neyman, who had been introduced to Blackwell in 1937 by Crathorne, interviewed Blackwell in 1942, and the math department at UC Berkeley agreed to hire him. Unfortunately, the department head’s wife, who frequently hosted gatherings for the department, said she “was not going to have that darky in her house,” according to Wilmot.

By 1954, the department of statistics was forming at UC Berkeley and, in 1955, Blackwell became professor of statistics. He served as chair of the department of statistics from 1957 to 1961 and was assistant dean of the UC Berkeley College of Letters and Sciences between 1964 and 1968. Blackwell was the first African American tenured at UC Berkeley. To recognize his distinguished service and accomplishments, UC Berkeley opened a new dorm named David Blackwell Hall in 2018.

Blackwell has indeed been acknowledged with numerous honors. In 2014, President Barack Obama posthumously awarded him a National Medal of Science. In 2002, the Blackwell-Tapia Prize was created in honor of Blackwell and Richard Tapia to recognize research excellence in the mathematical sciences by an individual who has also worked to increase diversity and broaden representation. In 1994, the MAA-NAM Blackwell Lecture was created to exemplify the spirit of Blackwell for promoting understanding, where the target audience consists of undergraduate students with a strong interest in conducting research in mathematics. And Blackwell holds at least 13 honorary Doctor of Science degrees.

Blackwell also holds many records as either the first or one of the first African Americans to achieve various titles. For example, he was the seventh African American to earn a PhD in math; the first African-American fellow of the Institute of Mathematical Statistics (IMS); the first African-American president of the IMS, 1955; the first African-American fellow of the ASA, 1962; the first African-American elected member of the National Academy of Sciences, 1965; elected to the American Academy of Arts and Sciences, 1968; the first African-American winner of the von Neumann Theory Prize, 1979; vice president of the American Mathematical Society (AMS), 1968–1971; vice president of the International Statistical Institute, 1975–1977; and vice president of the ASA, 1978.

Blackwell’s excellence can be denied by no one. It is clear he was exceptional. His brilliance and fortitude allowed him to achieve under circumstances in which many other prodigies would have failed. Period.

Nevertheless, I am encouraged because Blackwell’s exceptional life provides many clues for how we can positively influence the lives of others. Indeed, anyone can play a critical role, as evidenced by the many names appearing in boldface throughout this article. Blackwell provided a model for how to take time to honor those who help us along the way, and he provided a guide for how we can help others. His network offered him the stability and support he needed to make the most of his opportunities. His advocates, even in the face of pressure, showed commitment and surrounded him with an air of expectation that allowed him to blossom. Diversity in the profession can be achieved if each of us earnestly commits to these same actions.

### David Blackwell: Impact

##### By Richard Lockhart

David Blackwell was a singular mathematician who put understanding first, isolated the crucial features of a problem, and then wrote with precision and clarity, making things as simple as possible for his audience—whoever that was. I hesitate to use the label “mathematician”; his contributions to statistics, probability, game theory, operations research, information theory, and many other areas are so varied that it is impossible, even improper, to place him in one box—even one as big as mathematics.

The scope of Blackwell’s work prevents one writer from appreciating properly the impact of his many contributions to many communities. Here, I start where I met him, sample a few areas of his work and outstanding features of his style, look at other indicators of his impact, and touch on his impact on me.

I am privileged to be one of 65 PhD students Blackwell supervised between 1955 and 1981. I asked Blackwell to be my supervisor after hearing him give a talk at Stanford in the Berkeley-Stanford colloquium series. He discussed his idea of “Borel programmable” sets, even using transfinite induction, in what remains the clearest talk I have ever attended. Clarity of exposition was a constant hallmark of Blackwell’s work, even with the most difficult ideas.

That clarity was paired with brevity. Blackwell wrote 84 papers and two books. Only eight papers were more than 10 pages long; all these ‘long’ papers had co-authors (who I credit with the ‘wordiness’). In fact, 23 of Blackwell’s papers have three or fewer pages. This is strikingly different from the modern pattern. I believe the brevity helped Blackwell have profound influence. Modern papers drone on, discussing several similar ideas, providing applications to a welter of closely related problems, and giving extensive simulation studies; key ideas are often buried in the process. Blackwell would isolate and highlight these ideas, state one or two succinct and meaningful theorems, and provide utterly clear and explanatory proofs.

Readers can see this brevity in action in two 1973 papers in The *Annals of Statistics* on Dirichlet process priors. Each is three pages long. The first, with JB MacQueen, constructs Dirichlet process measures as limits of Polya urn schemes; the second, by Blackwell alone, reproves Ferguson’s key result that Dirichlet process measures are almost surely discrete. Nothing is repeated, no words wasted, and—as always for Blackwell—arguments are completely tight. These well-cited papers are undoubtedly Blackwell’s most influential direct contribution to Bayesian statistics. (He was a Bayesian.) The Polya urn paper, in particular, is one of Blackwell’s most heavily cited—still getting more than 60 citations per year some 47 years later.

Blackwell has many influential publications that continue to be well cited. His most-cited work is his 1954 book with Abe Girshick, *Theory of Games and Statistical Decisions*. In 2019, this book had citations in sources as diverse as the *Journal of Machine Learning*, *Annual Review of Economics,* and the *Journal of Quantitative Analysis in Sports*. This is extraordinary longevity and dispersal of what are obviously important ideas.

One way David had impact was by writing papers that carefully explore the fundamentals of an area. Two highly influential papers on dynamic programming do this in the *Annals of Mathematical Statistics* in 1962 and 1965. These rather long papers (eight and 10 pages) lay out the structure of optimal solutions to undiscounted and discounted rewards problems. Both were well cited in 2019.

I would be remiss if I failed to mention Blackwell’s work on comparison of experiments, his work on renewal theory (Google the Blackwell renewal theorem.), his work on information theory with Leo Breiman and Aram Thomasian, and his many contributions to the theory of Markov Chains. And, of course, generations of statisticians have learned the Rao-Blackwell theorem (but Blackwell acknowledged Rao’s priority in this).

The ideas themselves have the biggest impact, but there are other indicators and forms of impact. For mathematicians, articles in the *Annals of Mathematics* are seen as career making; Blackwell has three, including his first (1941) publication. He has 31 papers in the *Annals of Mathematical Statistics*, another four in the *Annals of Statistics*, and six in the *Annals of Probability*. Add to that many more in leading journals of the American Mathematical Society (AMS) and you see Blackwell’s work routinely reached the highest venues for theoretical statistics and probability. He served as president of the Institute of Mathematical Statistics, president of the Bernoulli Society, vice president of the International Statistical Institute, vice president of the AMS, and vice president of the ASA—all positions of international influence and impact. And his impact and genius were widely recognized: He was the Wald Lecturer, won the Fisher Award, and received a dozen honorary degrees.

Blackwell’s career may sound straightforward, but there were many barriers for a black man—no matter how brilliant—along the way. His first long-term appointment was at Howard, the leading historically black college, in 1944. Just three years later, he was professor and head of the mathematics department there. Jerzy Neyman finally succeeded in hiring Blackwell in 1955 at the birth of the University of California, Berkeley Statistics Department; just two years later, Blackwell was chair.

I became Blackwell’s student in the middle of 1977. For the next 18 months, we met roughly weekly for a half hour; Blackwell would give me just enough insight for me to find my way. I grew to admire profoundly his oft-cited quote (from an interview with Donald Albers in his and Gerald Alexanderson’s 1985 book, *Mathematical People: Profiles and Interviews*), “Basically, I am not interested in doing research. I am interested in understanding, which is quite a different thing.”

The contrast between that quote and the modern academic climate is striking. Papers are long, turning problems over every which way. Assumptions in theorems become matters of convenience, chosen to make proofs easy or like other writers’ proofs. From Blackwell, I learned to admire natural assumptions and proofs that use natural structure. I learned to admire short, clear writing. I lack Blackwell’s talent for brevity, so I am struck constantly by the fact that it is—or at least was—possible to have so much impact in so few words.

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