Celebratio Mathematica

In Dav­id Black­well, we have that ex­traordin­ary com­bin­a­tion of ex­cep­tion­al schol­ar­ship and su­perb teach­ing that all aca­dem­i­cians as­pire to but rarely achieve. The teach­ing as­pect was mani­fest at all levels, ran­ging from a ba­sic in­tro­duct­ory course to cut­ting-edge re­search. Any­one who has been at Berke­ley for any length of time is fa­mil­i­ar with the fact that his sec­tion of “Stat-2” class routinely had more stu­dents than the com­bined en­roll­ment of all oth­er sec­tions of the same course, which were typ­ic­ally taught by oth­ers. My own in­tro­duc­tion to his teach­ing style was also through an un­der­gradu­ate course in dy­nam­ic pro­gram­ming that I took in my second or third semester as a gradu­ate stu­dent. His en­ga­ging style of ex­plain­ing a prob­lem and bring­ing it to life in this class I be­lieve, on re­flec­tion, was a de­cis­ive in­flu­ence on my choos­ing stochast­ic dy­nam­ic pro­gram­ming and its ap­plic­a­tions to prob­ab­il­ity as the primary area for my dis­ser­ta­tion re­search. One of my fond memor­ies of how he brought a prob­lem to life in class con­cerns a story of how, over a peri­od of time, he and Samuel Karlin wrestled with the prob­lem of prov­ing the op­tim­al­ity of the so-called “bold play” strategy in a sub­fair “red-and-black” game that is an ideal­ized ver­sion of roul­ette.

The New York Times ob­it­u­ary of Ju­ly 17, 2010, de­scribes him as “a free-ran­ging prob­lem solv­er”, which of course he truly was. His was a mind con­stantly in search of new chal­lenges, break­ing new ground in dif­fer­ent areas every few years with astound­ing reg­u­lar­ity. As Thomas Fer­guson told UC Berke­ley News in an in­ter­view re­cently, Black­well “went from one area to an­oth­er, and he’d write a fun­da­ment­al pa­per in each.” His sem­in­al con­tri­bu­tions to the areas of stat­ist­ic­al in­fer­ence, games and de­cisions, in­form­a­tion the­ory, and stochast­ic dy­nam­ic pro­gram­ming are well known and widely ac­know­ledged. He laid the ab­stract found­a­tions of a the­ory of stochast­ic dy­nam­ic pro­gram­ming that, among oth­er things, led Ral­ph Strauch, in his 1965 doc­tor­al dis­ser­ta­tion un­der Black­well’s guid­ance, to provide the first proof of Richard Bell­man’s prin­ciple of op­tim­al­ity, which had re­mained un­til then a paradigm and just a prin­ciple without a proof!

Each of us who have been for­tu­nate enough to count ourselves to be among his stu­dents will no doubt have our per­son­al re­col­lec­tions of him that we will fondly cher­ish. A re­cur­ring theme among such re­col­lec­tions and the last­ing im­pres­sions they have left on us in­di­vidu­ally, I be­lieve, would be his ment­or­ing philo­sophy and style. He en­cour­aged his stu­dents to be in­de­pend­ent and did not at all mind even if you did not see him for ex­ten­ded peri­ods as a doc­tor­al stu­dent un­der his charge. He trus­ted that you were try­ing your level best to work things out your­self and waited un­til you were ready to ask for his coun­sel and opin­ion. A con­sequence of this, ex­cep­tions not­with­stand­ing, was per­haps that his stu­dents took a little longer than av­er­age to com­plete their dis­ser­ta­tions (al­though I have no hard data on this), but it made them more likely to learn how to think for them­selves.