David Blackwell and me

9 October 2018

This post is part of black mathematician month.

When I first came across the great Black mathematician and statistician, David Blackwell (1919-2010), circa 1975, I was actually informed that he was white. He was also then Irish. Or, so I was told by a triumphal fellow MSc economics and econometrics student at Southampton University, himself Irish, and now also a professor of economics.

The occasion of this initial meeting with Blackwell was our econometrics class’s introduction to the eponymous Rao-Blackwell theorem—a fundamental result in the theory of optimal statistical estimators. In simple terms, this theorem shows how to improve upon a rudimentary unbiased estimator of a statistical parameter, and indeed, get the best unbiased estimator of that parameter, when certain technical conditions are satisfied. I remember being struck by the beauty of this result. Perhaps it was my excitement about it that led my Irish colleague to try to deflate me by claiming his own racial and national part-ownership for the theorem by telling me that Blackwell was a white Irishman—Rao’s Indian extraction being self-evident. Maybe, more charitably, he was just engaging in supposedly characteristic Irish blarney, without malice. Regardless, I never bothered to check his claim—and, why should I have doubted a fellow student’s word about something as inconsequential as someone’s nationality, as I thought then?

So, for almost a decade afterwards, I happily persisted in the belief that Blackwell was indeed Irish and blithely assured others of this. I must have given much wry amusement to those who knew otherwise. It was not until the academic year 1984-85, which I spent as a joint fellow at CORE (Centre for Operations Research and Econometrics) and IRES (Institut de Recherches Économiques et Sociales) at Université Catholique de Louvain-la-Neuve, that I was finally disabused of my misinformation by another researcher.

Encounters with Blackwell

The Rao-Blackwell theorem is named for Blackwell and Indian mathematician CR Rao, who both derived the result independently. Image: Prateek Karandikar, CC BY-SA 4.0

My next encounter with David Blackwell was also at CORE during that fellowship year. This time I met him in the CORE Library, in the pages of Neyman: from life, Constance Reid’s 1982 biography of Jerzy Neyman, one of the founding fathers of modern theoretical statistics. I was captivated by the story of how Neyman, recognising young Blackwell’s immense talents, had wanted him appointed to a faculty position at the University of California, Berkeley, in 1942, but had been initially thwarted in this ambition by naked racism. From Reid’s account, Blackwell was blocked by one of the “faculty wives” (according to Madan L Puri in the A Tribute to David Blackwell actually the wife of the then chair of Berkeley’s maths department) who let it be known that she would have difficulties if she had to be in a room with “a darkie”. Blackwell would have been accustomed to such slights already because, although granted a Rosenwald scholarship at the Institute of Advanced Study in Princeton in 1941-42, he was not allowed, as customary, to attend lectures or do research at Princeton University itself. The memorial essay by David Brillinger and John W Addison Jr that Berkeley published on Blackwell’s death noted that he was one of only two mathematicians at the Institute of Advanced Study not allowed into the Princeton University mathematics building at that time because of military work going on there. The other was Hans Samelson, who was of German origins and classified as an enemy alien. It said volumes about the treatment of Black people in the USA that Blackwell, born and bred in the USA, as were his parents before him, was nevertheless categorised alongside an enemy alien. Yet, despite this climate, Neyman did not abandon his efforts to attract Blackwell to Berkeley. He finally succeeded in 1954 when the statistics group split from the mathematics department at Berkeley and Neyman became chair of the newly-formed statistics department. Blackwell became a full professor of statistics at Berkeley in 1955 and also a professor in the mathematics department in 1973.

Blackwell in 1967, when he was chair of UC Berkeley’s statistics department. Image: Konrad Jacobs, CC BY-SA 2.0.

My third and final substantive encounter with David Blackwell was in 1990 at the University of Warwick. I was then a lecturer (assistant professor) in economics. One of my administrative duties in that role was to serve as the economics representative on the mathematics, operations research, statistics and economics (MORSE) Board for Warwick’s then unique undergraduate degree. It was in that capacity that I suggested that Blackwell be awarded an honorary degree—a suggestion that Jeff Harrison, himself a noted Bayesian forecaster and founding professor in Warwick’s statistics department, which was in overall charge of the MORSE degree, picked up enthusiastically. Blackwell was awarded the honorary DSc by Warwick in 1990. This was one of twelve honorary degrees that he received during his illustrious career, but one of only two received from outside the USA, the other being from Lesotho. Importantly for me, I was able to meet the great man in person during his visit to receive the award. He confirmed, without bitterness or rancour, the veracity of the accounts of his treatment in the 1940s and early 50s that I had read. He also mentioned that, by perhaps one of the most ironical of ironies, he had been the 1986 RA Fisher Lecturer. This lecture series is named after the 20th century’s most eminent statistician, who also happened to have been a eugenicist. Had Fisher had his way, maybe Blackwell, as a member of an allegedly inferior race, would have been euthanized or selectively-bred out of existence. Blackwell’s willingness to give a lecture named for someone who was, by definition, a scientific racialist throws an interesting light on one of today’s controversies: how Black people should engage, if at all, with notable historical figures like Galton, Colston and Rhodes, who were racialists. In his 2002-03 oral history interviews with Nadine Wilmot, Blackwell discussed his adroitness in avoiding being drawn into arguments about race by Nobel prize-winning physicist William Shockley Jr, with whom he maintained a civil relationship although Shockley Jr was much more rabid in promoting his eugenics ideas than Fisher ever was.

Blackwell’s story can be read as one of the triumph of genius over racism. Not only was he a great researcher (something that he himself disputed), he was also a renowned teacher at all levels. He had 64 PhD students, but he also delighted in teaching undergraduates. Many contributors to the collection A tribute to David Blackwell, some of them his former students, described him as the best teacher they ever encountered.

A modern perspective

In Black History Month, as in every other month, we would be remiss to not ask if the academic landscape has changed much since Blackwell’s early career. It is undeniable that there are many more Black people in academic positions, albeit predominantly in the lowest grades, on both sides of the Atlantic. It is also true that equality and diversity considerations mean that no-one’s appointment would be vetoed now in the blatantly racist terms that his was initially at Berkeley. Nevertheless, one still wonders how Blackwell would have fared, as a Black professor, under today’s student evaluation of teaching (SET) and RateMyProfessor. Extensive published research shows that these instruments are disfigured by gender and racial bias. The evidence shows that the competence of Black academics is often either questioned or resented by many white students who appear to believe, with some justification, that if they complain enough about them, such academics will be sacked. Yet, institutions knowingly persist with such mechanisms while professing a commitment to equal treatment for their staff. Blackwell did not work with real data. However, one empirical regularity that would almost surely have impressed him is the data showing that Black academics always come last in SET rankings. As Blackwell was a pioneer of the statistics of informativeness (which provides methods for ranking information structures), one wonders as well what he would have deduced from the fact that the variance of the SET scores for Black academics always seems to exceed that for white academics.

Blackwell as an outlier

My encounters with Blackwell also prompt me to wonder about the role of role models. Blackwell unquestionably now fulfills that role pre-eminently for Black mathematicians in a way that he would not do had he, say, really been a white Irishman. It is not obvious that he himself had any academic role models in his formative years. Perhaps, as his formidable talents were recognised very early on in his life, he did not really need them and his illustrious life is testament to the belief that genius will prevail. He had moved on from his initial ambition of being just a school maths teacher by the time he graduated as a scholarship student from Illinois University with a PhD in mathematics in 1941. Yet, interestingly, after his Rosenwald scholarship experience at Princeton and his initial rebuff at Berkeley in 1942, he did not immediately see an academic career for himself beyond the 105 historically Black colleges. Rather than head-butt further the concrete ceiling that is a fact of life for Black people, he initially decided instead to settle into what might now be described as an academic “safe space” by taking appointments at Southern University, Clark College, and then Howard University. It is interesting in this respect to compare and contrast his experiences and career with those of the other great contemporary Black mathematician, J Ernest Wilkins Jr (1923-2011).

J Ernst Wilkins Jr was as gifted as Blackwell, but did not pursue an academic career. Image: Dan Dry CC BY 3.0.

Wilkins was even more precocious than Blackwell. He entered University of Chicago to study mathematics aged 13 and graduated with a PhD in mathematics aged 19 in 1942. He was awarded a Rosenwald scholarship at the Institute of Advanced Study that same year, the year after Blackwell, and was the first teenager so honoured. Nevertheless, like Blackwell initially, he found it impossible to get an academic appointment at a major research university. Unlike Blackwell, Wilkins does not appear to have tried to do so again after an initial rebuff in 1943. Instead, apart from 1944-45, when he did notable work on the mathematics of neutron absorption for the Manhattan project with future physics Nobel laureate Eugene Wigner, Wilkins worked mainly in industry, with conspicuous success. Among other things, he was the 1974-75 president of the American Nuclear Society and the second Black American elected to the US National Academy of Engineering. His career suggested that it was easier for an academically brilliant Black person to gain access to and succeed in business than in academia, which might still be true today. Perhaps a major difference between Blackwell and Wilkins in this respect is that, from very early in his career, Blackwell published with other outstanding statisticians, mathematicians and mathematical economists, including Meyer Girshick, Richard Bellman and economics Nobel laureate Kenneth Arrow. Conversely, Wilkins mostly published mathematics as a sole author. Although he had numerous publications in top journals from the outset of his career, it is possible that he received less attention than Blackwell simply by virtue of the latter’s co-authors.

David Blackwell was no “hidden figure”. His brilliance quickly projected him into the academic limelight, even while working at Howard University (primarily a teaching rather than research university) from 1944 to 1954. He is indubitably the doyen of Black mathematicians, a status he retains even in death. Ultimately, for all his great and enduring accomplishments and prizes, perhaps the features that honour him most are the facts that he neither allowed racism to define him nor, unlike many successful Black academics, did he deny the existence of racism. While many successful Black people in academia and elsewhere have sought to put distance between themselves and their roots by claiming either that racism does not exist, or they have never knowingly witnessed or experienced it, Blackwell never pretended that it had not impacted significantly in his life. Yet, he succeeded handsomely in spite of it.