Celebratio Mathematica

David H. Blackwell

A Tribute to David Blackwell

by W. Sudderth

My first en­counter with Dav­id Black­well was as a stu­dent in his course on dy­nam­ic pro­gram­ming at Berke­ley in the fall of 1965. There were, as I re­call, about forty or so stu­dents from vari­ous ap­plied areas, to­geth­er with a few math types like me. The class met once a week in the even­ing for about two hours. Dav­id al­ways ar­rived right on time, nat­tily dressed and sport­ing a bow tie. He would take a small piece of pa­per from his shirt pock­et, glance at it briefly, and then, with no ad­di­tion­al notes, lec­ture for about an hour. There was then a short break, after which Dav­id would look at the oth­er side of the piece of pa­per be­fore lec­tur­ing for the second hour.

The lec­tures were so clear that the ap­plied stu­dents could un­der­stand and we math types could eas­ily see that the ar­gu­ments were air­tight. Dav­id would of­ten give an in­tu­it­ive ex­plan­a­tion for why a res­ult should be true and then fol­low it with a rig­or­ous proof. I still have my notes from the course and con­sult them al­most every year to re­mind my­self of an ar­gu­ment or a key ex­ample.

Dav­id held of­fice hours at 8 AM. Since few stu­dents showed up at this early hour, I was able to see him a num­ber of times with ques­tions about dy­nam­ic pro­gram­ming and later on about my thes­is prob­lem and oth­er mat­ters. These meet­ings were al­ways fruit­ful for me. Dav­id could al­ways see quickly to the heart of a prob­lem. Some­times he knew the solu­tion and, if he did not, he al­ways had a good idea about where to look.

My thes­is ad­viser Lester Du­bins was a good friend of Dav­id’s. Lester liked to work with fi­nitely ad­dit­ive prob­ab­il­ity meas­ures, and, fol­low­ing his lead, I worked with them, too. Dav­id was quite du­bi­ous of this be­cause of the non­con­struct­ive nature of purely fi­nitely ad­dit­ive meas­ures. He once re­marked that he was im­pressed by all the in­ter­est­ing res­ults we were able to prove about these meas­ures that do not ex­ist.

On an­oth­er oc­ca­sion, when Ro­ger Purves and I had been work­ing a long time on an ob­scure meas­ur­ab­il­ity prob­lem, we asked Dav­id wheth­er he thought our en­deavor was worth­while. He said that when a prob­lem arises nat­ur­ally in a the­ory and is dif­fi­cult to solve, its solu­tion may well re­quire new math­em­at­ic­al tools that will be use­ful for oth­er pur­poses as well. In­deed, when, with the aid of Lester Du­bins and Ashok Maitra, we fi­nally found the an­swer to our prob­lem, it did re­quire new tech­niques that we were able to ap­ply else­where.

Dav­id made sem­in­al con­tri­bu­tions to math­em­at­ic­al stat­ist­ics, prob­ab­il­ity the­ory, meas­ure the­ory, and game the­ory. He also found deep con­nec­tions between game the­ory and de­script­ive set the­ory. As already sug­ges­ted, he was a great teach­er. His only fail­ing, which I ob­served while serving on search com­mit­tees at the Uni­versity of Min­nesota, was that he was too kind to ever write any­thing but a good let­ter of re­com­mend­a­tion for a job can­did­ate.