Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by George G. Roussas

I joined the De­part­ment of Stat­ist­ics at the Uni­versity of Cali­for­nia, Berke­ley (UCB) in the spring semester 1960, after hav­ing gradu­ated with a de­gree in math­em­at­ics from the Uni­versity of Athens, Greece, and hav­ing served my two-year mil­it­ary ser­vice in the Greek army.

Dav­id Black­well was the chair of the de­part­ment at that time, and Lu­cien Le Cam was the gradu­ate ad­visor. Black­well would have a brief in­ter­view with every in­com­ing gradu­ate stu­dent, and it was in this ca­pa­city that I first met him. Right after my in­ter­view with him, a couple of oth­er, also new, gradu­ate stu­dents poin­ted out to me that we had a black man as chair of the de­part­ment. In a way, I was taken by sur­prise, and I re­spon­ded “come to think of it, we cer­tainly do!” Pro­fess­or Black­well’s per­son­al­ity was over­whelm­ingly strong and yet gentle and en­chant­ing, ra­di­at­ing kind­ness around him. These at­trib­utes tran­scen­ded any tri­vi­al­it­ies such as no­ti­cing the col­or of his skin. Be­sides, my cul­tur­al back­ground was ali­en to it.

The UCB cam­pus was an earthly para­dise, and the fac­ulty of the de­part­ment were like Olympi­an fig­ures to me in the stat­ist­ics pan­theon. I had the ut­most re­spect and ad­mir­a­tion for all and each one of them.

Nev­er­the­less, some did stand out, as it were. Thus it was the grand old man Jerzy Ney­man from whom, fool­ishly, I nev­er took a course. He was nice to me, and more than once he re­coun­ted his ex­per­i­ences in Greece as a mem­ber of a cer­tain com­mis­sion soon after World War II. It was Michel Loève from whom I took my first course in prob­ab­il­ity and who in­spired me with rig­or and deep in­terest in the sub­ject mat­ter. Later, I also took his year-long course in prob­ab­il­ity and stochast­ic ana­lys­is. It was the math­em­atician-philo­soph­er Ed­ward Barankin from whom I learned meas­ure-the­or­et­ic prob­ab­il­ity, and I was also in­tro­duced to time series ana­lys­is and suf­fi­ciency. It was Lu­cien Le Cam from whom I man­aged to chip away bits of his vast know­ledge of asymp­tot­ics in stat­ist­ics. They were destined to play a form­at­ive role in my aca­dem­ic ca­reer.

And it was Dav­id Black­well who was destined to be my thes­is ad­visor un­der some pe­cu­li­ar cir­cum­stances.

If I re­mem­ber well, it was in the early 1960s that Lester Du­bins was of­fer­ing a sem­in­ar based on his book (coau­thored with Jim Sav­age) How to Gamble if You Must: In­equal­it­ies in Stochast­ic Pro­cesses. Black­well was at­tend­ing that sem­in­ar, as well as a fair num­ber of stu­dents, in­clud­ing my­self. At the end of each lec­ture, Black­well would sug­gest a num­ber of open ques­tions for pos­sible thes­is top­ics. It was such a ques­tion that he brought to my at­ten­tion and in­sisted that I look in­to. In­deed, I did, and in a couple of months I asked for an ap­point­ment with him to re­port ac­cord­ingly. At that time, he was ad­vising a large num­ber of stu­dents, and his ap­point­ments were lim­ited by ne­ces­sity to a half-hour block of time. Ap­par­ently, he was pleased by what he read, was very en­cour­aging, and also made a num­ber of con­crete sug­ges­tions. After an­oth­er couple of ses­sions like this, he de­cided that the solu­tion that I ar­rived at was what he ex­pec­ted. En­cour­aged by this, I asked wheth­er I could com­bine this piece of work with an­oth­er pa­per on asymp­tot­ics, which was already ac­cep­ted for pub­lic­a­tion in the An­nals of Math­em­at­ic­al Stat­ist­ics, to make up my thes­is. Black­well’s re­sponse was as al­ways brief and clear-cut. “To me, this by it­self is more than enough.”

And that is how I had the priv­ilege and hon­or to be Dav­id Black­well’s stu­dent.

From the courses I took from him (one in game the­ory and the oth­er in cod­ing/in­form­a­tion the­ory) I saw firsthand how a great sci­ent­ist can also be an in­spir­ing and su­perb teach­er. From my in­ter­ac­tion with him, as his ad­visee, I could not help but ad­mire the clar­ity of his thoughts, ar­tic­u­lated in an amaz­ingly brief and simple way. At the same time, his po­lite dis­pos­i­tion and abund­ant kind­ness had ab­so­lutely no match.

Soon after I was con­ferred my Ph.D. de­gree in 1964, I had the op­por­tun­ity to host a din­ner party for Pro­fess­or and Mrs. Black­well in a rather ori­gin­al and up­scale res­taur­ant in the Bay area (I be­lieve it was called the Nero’s Nook), loc­ated in the Los Ga­tos area. It was ap­par­ent that all three of us had a truly en­joy­able time.

After I moved to the Uni­versity of Wis­con­sin–Madis­on (UWM), the first time that I met him was in 1972 dur­ing the Sixth (and last) Berke­ley Sym­posi­um in Stat­ist­ics and Prob­ab­il­ity. The next ten years or so I spent over­seas, at the Uni­versity of Pat­ras, Greece, and I more or less lost con­tact with him ex­cept for a Christ­mas card. In 1984 I dropped by UCB after I re­turned to the West Coast (at the Uni­versity of Cali­for­nia, Dav­is). In Berke­ley, I had the op­por­tun­ity to have lunch with Ed­ward Barankin (in the res­taur­ant of the Dur­ant Hotel), who, un­for­tu­nately, suc­cumbed to can­cer soon there­after. Dav­id Black­well re­ceived me very warmly and in­vited me for lunch at the ca­non­ic­al fish res­taur­ant in Berke­ley (Spenger’s Fresh Fish Grotto). Also, he ex­pressed his sat­is­fac­tion that one of his old stu­dents did fairly well as a seni­or fac­ulty mem­ber now (full pro­fess­or at UWM and chair of ap­plied math­em­at­ics at the Uni­versity of Pat­ras) and also as an aca­dem­ic ad­min­is­trat­or (dean of the School of Phys­ic­al and Math­em­at­ic­al Sci­ences at Pat­ras and also chan­cel­lor of the same uni­versity). However, for me, Dav­id Black­well re­mained “Pro­fess­or Black­well” as an ex­pres­sion of my ut­most re­spect for him and also be­cause of my European early up­bring­ing. But this would not do any­more for Black­well. On the spot he put me in a dif­fi­cult di­lemma; “Either you call me Dav­id or I will nev­er talk to you again!” So, Pro­fess­or Black­well be­came Dav­id for me hence­forth.

Once at UCD, I was giv­en the op­por­tun­ity to drop by UCB, but not as of­ten as I would have liked. From what re­mained of the old guard, Black­well and Le Cam were the people that I would al­ways vis­it.

It was in early June 2010 when we re­ceived an email mes­sage at UCD from Bin Yu, the cur­rent chair of the De­part­ment of Stat­ist­ics at UCB, that Dav­id was not do­ing well. I was about to de­part for the an­nu­al pil­grim­age to Greece (on June 13), but I did make a con­cer­ted ef­fort to ob­tain a brief vis­it with Dav­id be­fore my de­par­ture. That ef­fort was not suc­cess­ful. I re­solved to try again soon after my re­turn (Ju­ly 7). Un­for­tu­nately, that ef­fort nev­er came to be; Dav­id Black­well de­par­ted on Ju­ly 8.

His memory will re­main alive among all those who were for­tu­nate enough to know him and to profit from his wis­dom and his gentle and kind dis­pos­i­tion. For me, Dav­id Black­well was and will re­main the role mod­el of a great math­em­atician, an in­spir­ing teach­er, and a su­perb hu­man be­ing.