Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by Stephen Stigler

Dav­id Black­well’s re­search work places him in the pan­theon of twen­ti­eth-cen­tury prob­ab­il­ity, game the­ory, and stat­ist­ic­al in­fer­ence, but it is as a teach­er that I best re­call him. To hear Black­well lec­ture was to wit­ness a mas­ter of the art. He was not cha­ris­mat­ic; he spoke slowly and de­lib­er­ately, and, when not writ­ing on the board, used slight hand ges­tures with his palms to­ward the audi­ence, to con­jure up a shape or an en­tire space in our minds. His mas­tery came from the way he was think­ing through the ma­ter­i­al with us at our speed and mak­ing his thoughts our thoughts. With simple ges­tures he could cre­ate an in­fin­ite-di­men­sion­al space in our minds and let us see with start­ling clar­ity how a res­ult could fol­low — or, more ac­cur­ately, how it would be ab­surd that it could fail to fol­low. It was ma­gic­al — but it was last­ing ma­gic, since the know­ledge im­par­ted re­mained with us.

Even in a classroom the work he presen­ted ac­quired a new fla­vor in the pro­cess. When he presen­ted a won­der­ful gen­er­al­iz­a­tion of von Neu­mann’s min­im­ax the­or­em de­signed for stat­ist­ic­al games in func­tion spaces, he named it after the au­thor of an art­icle he cited, but when I con­sul­ted that art­icle later I could see that Black­well had without com­ment re­cast it in a new form; the spark­ling clar­ity of that form was a hall­mark of this ex­traordin­ary math­em­atician’s mind and style.

For a few years in the 1960s Black­well taught an ex­tremely ele­ment­ary Bayesian stat­ist­ics course to a very large audi­ence of un­der­gradu­ates. The book he wrote for that class is al­most un­known today, but in his hands it was a gem. The in­sights he brought to a tired old syl­labus were a won­der­ful re­ward to the stu­dents and teach­ing as­sist­ants alike. At the end of the term he in­vited the large team of TAs to his home at 5 PM and served soft drinks and a large pitch­er of mar­tinis. Many of the for­eign TAs were new to this liba­tion, and some took to it too en­thu­si­ast­ic­ally, but the gra­cious host reined them in, and all felt the warmth of his col­legi­al fel­low­ship.

Black­well was a second-gen­er­a­tion be­ne­fi­ciary of an early 1930s grant from the Carne­gie Cor­por­a­tion to Har­old Ho­telling at Columbia Uni­versity. In 1932 Ho­telling had sup­por­ted Joe Doob, fresh from a Ph.D. in math­em­at­ics at Har­vard and with no good job pro­spects, and in­tro­duced Doob to prob­ab­il­ity and stat­ist­ics. A dec­ade later Doob did the same for Black­well at the Uni­versity of Illinois. No Carne­gie money was ever bet­ter spent.