Celebratio Mathematica

Joseph L. Doob

Transcript of the Celebration of the Life of Joseph Leo Doob (held in October 2004)

Department of Mathematics, University of Illinois

One of the im­port­ant ele­ments in Doob’s life was the Sat­urday Hike. An­oth­er im­port­ant ele­ment was mu­sic. So it was fit­ting that the Cel­eb­ra­tion began with mu­sic played by an­oth­er Sat­urday Hiker, Rudolph Haken. Pro­fess­or Haken, a fac­ulty mem­ber of the School of Mu­sic, played three move­ments of the vi­ola ver­sion of J. S. Bach’s Suite III in C-Ma­jor, BMV 1009, ori­gin­ally com­posed for the un­ac­com­pan­ied cello.

The speak­ers fol­lowed. Here their re­marks about Doob are re­vi­sions and ex­pan­sions of their or­al present­a­tions.

Steve Doob (the old­est of Joe and Elsie’s three chil­dren): First, I’d like to say how de­voted my fath­er was to an or­gan­iz­a­tion called “The Hike.” It is made up mostly of uni­versity pro­fess­ors who meet every Sat­urday af­ter­noon at 2 and drive to one of the in­nu­mer­able spots along loc­al rivers where they have been hik­ing for nearly a cen­tury. Some of them make a camp­fire, while the more ad­ven­ture­some build up their ap­pet­ites by hik­ing for an hour or so. And a good ap­pet­ite is what you need for the meal that fol­lows. From the heart healthy “hiker’s de­light” (onions, cheese and hot pep­pers fried in ba­con grease) slathered over rock hard, homemade Ger­man bread, to the steaks, cook­ies and stollen, no one goes home hungry.

I left Urb­ana in 1959 with fond memor­ies of all the unique in­di­vidu­als I met on The Hike while in high school in the fifties and later dur­ing my oc­ca­sion­al vis­its home. Of course, there were many people from the Math De­part­ment, but I also re­mem­ber be­ing im­pressed by rep­res­ent­at­ives of oth­er de­part­ments as well. There were spe­cial­ists in Lit­er­at­ure, Eco­nom­ics, Her­pet­o­logy, Phys­ics, Phys­ic­al Edu­ca­tion and Geo­logy, to name a few. What I hadn’t been ex­posed to be­fore were the adults who dis­cussed and bantered in a light­hearted and ir­rev­er­ent way about the is­sues of the day. What made it all the more in­ter­est­ing was the fre­quent dis­agree­ments, which res­ul­ted in bets of “Pie for the Hikers.” (The loser had to provide a pie the fol­low­ing week.) Con­sider this a plug for The Hike from my fath­er. At his re­quest his ashes were scattered by Hikers at one of his fa­vor­ite spots. Sev­er­al times in his last few months, he ex­pressed the wish that The Hike would out­live him. So far, it has. When I joined it for the Doob Me­mori­al Hike on Oct. 9, there were around 35 people. They were sub­dued and a little too rev­er­ent, however. My fath­er would have been pleased at the large crowd but would have ab­horred the rev­er­ence. From now on, I hope that dis­cus­sions will be live­li­er and that the tra­di­tion of rashly held opin­ions that lead to de­li­cious pies will con­tin­ue. As you might ima­gine, my fath­er did not be­lieve in ghosts, but just in case he has be­come one any­way, I’m sure he would want to be suit­ably en­ter­tained when he joins the Hikers around the camp­fire on Sat­urday nights.

I’d say that one of the keys to my fath­er’s im­press­ive math­em­at­ic­al leg­acy can be found on The Hike, and I sug­gest you try go­ing out on it some­time. For in­form­a­tion, con­tact the cur­rent “Com­mis­sar,” Sam Wag­staff […].

As a child, I didn’t ap­pre­ci­ate my fath­er at all. I had no idea that his tak­ing me fish­ing nearly every week and his tak­ing his fam­ily on sum­mer va­ca­tions to lakes every year were something spe­cial. I know it must have happened, but I can’t re­mem­ber any time that his work in­terfered with my child­hood. What I value now is the in­de­pend­ence that he ex­em­pli­fied and fostered in me. He was not one to fol­low the crowd. He was skep­tic­al of all strongly held opin­ions and be­liefs, and es­pe­cially en­joyed punc­tur­ing any pom­pous­ness he de­tec­ted. When I didn’t agree with him, he rel­ished the ar­gu­ment so much that if I fi­nally gave in he was li­able to change sides just to keep the ar­gu­ment go­ing.

He didn’t pass on any of his math­em­at­ic­al abil­it­ies to me, but he taught me how to fix things that were broken. I learned how to solve elec­tric­al, plumb­ing and car­pentry prob­lems as a child, and this led to my house res­tor­a­tion and auto body ca­reers as an adult. He showed me that you can al­ways find a flaw in your work if you look hard enough; no mat­ter how many you find there is al­ways “one more.” I learned that no mat­ter how many cu­cum­ber beetles you kill in your garden or how many times you pore over your writ­ing, there is al­ways an­oth­er beetle or an­oth­er mis­take that you’ve missed. An­oth­er early les­son I re­mem­ber was that mis­be­hav­ing ma­chinery of­ten re­spon­ded fa­vor­ably to a swift kick. (Could this have led to my 40-year mar­tial art prac­tice?)

I find it amaz­ing that my fath­er, who grew up in New York City, could find life so sat­is­fy­ing in Urb­ana; that he could res­ist the of­fers of po­s­i­tions at more pres­ti­gi­ous in­sti­tu­tions; and that he could do so much in his ca­reer while still do­ing so much with his fam­ily. I know he would have been em­bar­rassed by all the at­ten­tion at this me­mori­al, but at the same time I know he would have been very pleased.

Don Burk­hold­er: Doob’s math­em­at­ic­al work will be dis­cussed in a num­ber of journ­als: the No­tices of the Amer­ic­an Math­em­at­ic­al So­ci­ety, the An­nals of Prob­ab­il­ity, the Illinois Journ­al of Math­em­at­ics, and oth­ers. Our fo­cus here is primar­ily on his life. However, let me men­tion some of the areas of math­em­at­ics to which he made im­port­ant con­tri­bu­tions: com­plex func­tion the­ory, er­god­ic the­ory, mar­tin­gale the­ory, math­em­at­ic­al stat­ist­ics, Markov pro­cesses, the gen­er­al the­ory of stochast­ic pro­cesses, prob­ab­il­ist­ic po­ten­tial the­ory, and ax­io­mat­ic po­ten­tial the­ory which is non­prob­ab­il­ist­ic. For some of these, Doob was the lead­ing pi­on­eer.

In 1987, Paul-An­dré Mey­er, no longer liv­ing now but then a math­em­at­ic­al star in France, es­pe­cially in prob­ab­il­ity and po­ten­tial the­ory, wrote, “Per­son­ally, I think he is one of the really great math­em­aticians of the cen­tury.” In ad­di­tion to his re­search, Doob served the math­em­at­ic­al pro­fes­sion as pres­id­ent of the In­sti­tute of Math­em­at­ic­al Stat­ist­ics in 1950, as pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety dur­ing 1963 and 1964, and in many oth­er ca­pa­cit­ies.

He was elec­ted to the Na­tion­al Academy of Sci­ences in 1957 and to the Amer­ic­an Academy of Arts and Sci­ences in 1965. He was also made a for­eign as­so­ci­ate of the French Academy of Sci­ences in 1975. He was awar­ded the Na­tion­al Medal of Sci­ence at a ce­re­mony in the White House in 1979. Be­ing an in­form­al man, he was not wear­ing a neck­tie. In 1984 he was giv­en the Steele Prize by the Amer­ic­an Math­em­at­ic­al So­ci­ety for his out­stand­ing ca­reer and for his “con­tinu­ing pro­found in­flu­ence.” He re­ceived many oth­er hon­ors, in­clud­ing an hon­or­ary doc­tor­al de­gree from the Uni­versity of Illinois in 1981. He took all of these hon­ors lightly.

Dav­id Black­well (One of Doob’s early stu­dents, Black­well re­ceived four de­grees from the Uni­versity of Illinois the last one be­ing an hon­or­ary de­gree. He is a mem­ber of the Na­tion­al Academy of Sci­ences and has re­ceived much ad­di­tion­al re­cog­ni­tion for his many con­tri­bu­tions to math­em­at­ics, in­clud­ing math­em­at­ic­al stat­ist­ics. He was not able to be present at the Cel­eb­ra­tion but did send the fol­low­ing mes­sage):

“One of the luck­i­est ac­ci­dents of my life was hav­ing Joe Doob as my thes­is ad­viser. It happened like this. Early in my second year as a gradu­ate stu­dent at Illinois, a fel­low gradu­ate stu­dent, Don Kib­bey, asked me who my thes­is ad­viser was. I replied that I didn’t have one and should start look­ing. Then Don said ‘Why don’t you try Joe Doob? He’s my ad­viser, he’s a nice guy, and I’ll bet he’ll take you.’ I’d nev­er met Joe and scarcely knew who he was, but I trus­ted Don and asked Joe, and he AC­CEP­TED. At the time I didn’t even know that he worked in prob­ab­il­ity, just that he was an ana­lyst. At that time prob­ab­il­ity at Illinois was taught by a very nice old pro­fess­or, Ar­thur Crathome.

“For the rest of that year Joe didn’t give me a thes­is top­ic, just meas­ure the­ory and prob­ab­il­ity pa­pers to read, in­clud­ing Kolmogorov’s Grundbe­griffe.1 Later that year Joe gave me his own path-mak­ing pa­per Stochast­ic pro­cesses with an in­teg­ral-val­ued para­met­er to read. That pa­per was my con­stant com­pan­ion for years. It was only after read­ing it that I real­ized that I’d been lucky enough to get one of the founders of mo­dem prob­ab­il­ity as my thes­is ad­viser.

“At the end of that year, Joe gave me two thes­is top­ics, one of which in­volved his re­cent dis­cov­ery that what he called se­quences with prop­erty E con­verge back­ward. Joe knew that these se­quences were im­port­ant, and for sev­er­al years wondered why they didn’t catch on. Fi­nally he re­named them “mar­tin­gales”, and then they did catch on quickly. Nowadays every prob­ab­il­ist any­where knows what a mar­tin­gale is.

“While I was writ­ing my thes­is, Joe and two of his re­cent stu­dents, Paul Hal­mos and War­ren Am­brose, were plan­ning to spend the next year at the In­sti­tute for Ad­vanced Study. Joe de­cided that I needed to spend the next year there also, sug­ges­ted that I ap­ply for a Ju­li­us Ros­en­wald Fel­low­ship, helped me write the ap­plic­a­tion, and of course wrote the let­ter of re­com­mend­a­tion that got the Fel­low­ship for me.

“Joe was a clear lec­turer and took teach­ing ser­i­ously. He was proud of his abil­ity to draw a good circle on the black­board, us­ing his el­bow as cen­ter and his fore­arm as ra­di­us. He would write on the black­board not only for­mu­las, state­ments and pic­tures, but also con­nect­ives and, so that, moreover and even nev­er­the­less.

“I re­garded Joe with a mix­ture of ad­mir­a­tion, af­fec­tion and awe, with a de­sire to im­press him and a de­sire to please him. I think that I im­pressed him once, and pleased him once.

“Once sev­er­al people, in­clud­ing Joe and me, were dis­cuss­ing the first lec­ture in a be­gin­ning prob­ab­il­ity course, ex­plain­ing prob­ab­il­ity as lim­it­ing re­l­at­ive fre­quency. There was gen­er­al agree­ment that this first lec­ture was not much fun, and that it was a pleas­ure to get on to the math­em­at­ics of prob­ab­il­ity. I then said that I nev­er men­tion fre­quency, but spend about two minutes on an ex­plan­a­tion that goes something like this: If there are 5 balls in a box and 2 of them are black, and you draw a ball at ran­dom, i.e., so that each ball has the same chance to be drawn, then the chance of draw­ing a black ball is 2 out of 5 or 2/5 or 40%. In gen­er­al, for any event, we say that its chance or prob­ab­il­ity is 40% if it is just as likely as draw­ing a black ball from that box. On to the math­em­at­ics.

“I think that state­ment im­pressed Joe, one way or the oth­er, be­cause he men­tioned it to me two years later.

“I took a pic­ture of Joe talk­ing with Kolmogorov at the 1954 In­ter­na­tion­al Con­gress in Am­s­ter­dam. It was not a very good pic­ture, but I sent Joe a copy. Per­haps 35 years later, I happened to be in Joe’s study in Urb­ana. There were 3 pic­tures on the wall, and that pic­ture was one of them. Clearly that pic­ture pleased him.”

Wolfgang Haken: When I pre­pared this talk I ex­pec­ted that it would make me sad. But in­stead, hav­ing known Joe Doob for over 40 years is such a de­light­ful ex­per­i­ence that it made me happy. I hope this is ac­cept­able.

An­oth­er prob­lem is, of course, how to con­dense 40 years in­to 5 to 10 minutes, in par­tic­u­lar, if you speak slowly. I have tried to do this by writ­ing my talk up in as few words as I could.

I knew Joe mainly through the Sat­urday Af­ter­noon Hike of which he was the Com­mis­sar for many years. Al­though, over the years, I even learned some Prob­ab­il­ity The­ory — you can’t avoid that.

One of the first things I learned about Joe was that in the 1950s he had been offered a quite dis­tin­guished pro­fess­or­ship at MIT and that he had turned that of­fer down. Many col­leagues were puzzled about that and he was fre­quently asked, “what is so spe­cial about Urb­ana, Illinois, that you prefer that place to MIT at Cam­bridge, Mas­sachu­setts?” Then Joe’s stand­ard reply was, “in Urb­ana there is such a good hard­ware store.” Many years later, Joe con­fided in me that at the time of that of­fer, his wife, Elsie, had just been dia­gnosed with colon can­cer and that it was not clear if she would sur­vive that (which she, for­tu­nately, did by sev­er­al dec­ades); and un­der those cir­cum­stances he did not want to move. He was a very sens­it­ive per­son — los­ing his wife and at the same time mov­ing from the place at which he felt at home would have totally up­rooted him. But for noth­ing in the world would he ever have said something like that.

Also, Joe found it an­noy­ing if and when col­leagues bragged about their math­em­at­ic­al achieve­ments and elab­or­ated on the thought that math­em­at­ics was the greatest thing in hu­man cul­ture and so on and so on. Joe had de­veloped a quite ef­fect­ive, but rather mean, way of bring­ing such talk to an end: He asked the talk­er, very in­no­cently, “how does it come that so many math­em­aticians go to con­certs of clas­sic­al mu­sic?” This was meant to en­cour­age the talk­er to go on even more en­thu­si­ast­ic­ally and to ex­plain that, ob­vi­ously, math­em­at­ics, as the noblest of all sci­ences, is closely re­lated to the noblest of the arts… But then Joe cut him off by say­ing, “Oh no, it is be­cause math­em­at­ics is so bor­ing.” — We all know that Joe was fas­cin­ated with math­em­at­ics, but he did not like this to be the center­piece of the con­ver­sa­tion; that was not his style.

At one of the hikes in the early 1980s, Joe told us that his son, Steve, had presen­ted him with [a] Min­is­ter’s Cer­ti­fic­ate of the Uni­ver­sal Life Church and that this of­fi­cially en­titled him to con­duct fu­ner­als and mar­riages. The ba­sic be­liefs of the Uni­ver­sal Life Church are quite simple (and thus uni­ver­sal) so that it is easy to be­come a min­is­ter there. Es­sen­tially, they be­lieve in that which is true. Secondly, they think that it is not so easy to find out what, in de­tail, is true and that this should be left to the in­di­vidu­al. I thought that this was a won­der­ful fam­ily where, even­tu­ally, the son finds the fit­ting re­li­gion for his fath­er. However, at one of the later hikes, my daugh­ter, Dorothea, took Joe by his word and asked him if he would agree to marry her. Joe’s reply was that, most likely, his wife would ob­ject to that. But then Dorothea ex­plained that she was ask­ing him to con­duct her mar­riage to her fiancé, Steve Blostein, and Joe im­me­di­ately agreed to that. A few weeks later, Joe con­duc­ted an ex­cel­lent wed­ding ce­re­mony at our house and every­body present was highly pleased.

Word about Joe’s new spir­itu­al activ­ity was spread­ing and he con­duc­ted sev­er­al more mar­riages. This went so far that, at one time our (then) De­part­ment Chair­man, Phil­ippe Tondeur, pro­posed to be­stow on Joe the title of Chap­lain of the De­part­ment of Math­em­at­ics.

Moreover, Joe gave to Dorothea and Steve a very unique and per­son­al wed­ding present. This was a small pil­low filled with his own hair. (He was quite skilled in cut­ting his hair him­self and then he col­lec­ted the har­vest and put it to good use.) Steve and Dorothea keep this pil­low as a fam­ily treas­ure. Per­haps, if you rest your head on it for long peri­ods of time, some of Joe’s math­em­at­ic­al brain­power might be trans­ferred to you. Any­way, their son, Mar­tin, is now 12 years old and is de­vel­op­ing an in­terest in math­em­at­ics. — It might really work.

Joe had asked that after he passed away, his ashes should be dis­trib­uted at the next Sat­urday Af­ter­noon Hike at one of those places where he felt that he be­longed. We did that ac­cord­ingly. At that hike, Nadya Shirokova happened to be vis­it­ing and she told us a typ­ic­al story about one of Joe’s vis­its to the Uni­versity of Mo­scow back in the times of the So­viet Uni­on. Joe was be­ing shown around by one of the gradu­ate stu­dents when a se­cur­ity po­lice of­ficer stopped them and asked what Joe was do­ing there and if he had any doc­u­ment on him to identi­fy him­self. Then Joe proudly showed him his Fish­ing Li­cense for Lake Michigan and the some­what puzzled of­ficer let him go on.

Fi­nally, an­oth­er Mo­scow an­ec­dote about Joe which I was told at a con­fer­ence about 25 years ago. It happened in the peri­od of time when the In­ter­na­tion­al Con­gress of Math­em­aticians was tak­ing place in Mo­scow and Joe was, be­sides be­ing Com­mis­sar of the Sat­urday Af­ter­noon Hike, Pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety. After the fest­ive present­a­tion of the pres­ti­gi­ous Fields Medals an ex­cited news­pa­per re­port­er came up to Joe and ex­claimed, “Pro­fess­or Doob, what do you have to say about those new Fields Medal­lists?” And Joe replied, “Oh, I am not wor­ried about that at all — they are as good as every­body else around here.” When I asked Joe about this event, he def­in­itely denied that he ever said any­thing like that. But when he un­der­stood that he re­portedly said this just to a news­pa­per man, he softened up a bit and poin­ted out that he could not pos­sibly re­mem­ber what he might have said to some­body like a news­pa­per re­port­er. So, be­lieve this at your own risk. As a friend of mine com­men­ted, “deni­al is not only a river in Egypt.”

Naresh Jain sent to the reg­u­lar hikers this email:

“I am ex­tremely sorry that I will have to miss this im­port­ant event. I know that you all are go­ing to en­joy re­call­ing so many happy memor­ies of past hikes. There are two an­ec­dotes I liked very much. Here they are:

“(1) One time Joe and Robert Kauf­man were in a heated dis­cus­sion about kids to be re­quired to learn the clas­sics. Robert was all for it and Joe was do­ing everything to pro­voke him. In dis­gust, Robert said: ‘Oh my God’, and Joe calmly replied, ‘Please don’t ex­ag­ger­ate, just call me, Pro­fess­or.’

“(2) One time Joe wanted to get a pie out of me for the hikers. I was sit­ting there with my back to­ward Joe. He told every­body near him that he was go­ing to get me in­to a bet which I surely would lose. He an­nounced loudly, ‘Do you guys know that Gandhi slept with two young girls all na­ked when he was in his late six­ties?’ I didn’t hear him, so he re­peated it again a little louder. Now this was a fact of which I was not aware, so I im­me­di­ately chal­lenged Joe and he asked if I was will­ing to make a bet. I did and lost. The hikers got their pie!

“These and many oth­er memor­ies will al­ways be there in my mind and I am so thank­ful to all the hikers, and to Joe, in par­tic­u­lar, for those won­der­ful mo­ments. Best re­gards, Naresh”

Sam Wag­staff: I first met Joe in Septem­ber, 1971, in the din­ing hall at the IAS in Prin­ceton. He was talk­ing with Deane Mont­gomery and Hassler Whit­ney. All three wel­comed me warmly to the In­sti­tute. When I got a job of­fer from Illinois, I asked Joe about life in Illinois. He told me about the Sat­urday Hike, and I star­ted hik­ing the first Sat­urday I lived in Illinois. I met his wife Elsie in Prin­ceton and, later, many times at their house on High Street. Joe once led a hike in the woods at the IAS and even had a camp fire, with per­mis­sion from the au­thor­it­ies. One nervous of­fi­cial came at the end of the hike and put out the fire with a fire ex­tin­guish­er.

Since I have lived in In­di­ana, I have craved Illinois wa­ter. For many years, every Sat­urday I would drive to Urb­ana and get jugs of drink­ing wa­ter from Joe’s place, first on High Street and then in Clark Lind­sey, and then hike. At first I would take Joe to the hike. After he re­tired from the hike at age 92, I would just vis­it him. He would of­ten give me food, es­pe­cially hot pep­pers, or kind­ling wood for the hike. Joe’s house and apart­ment were al­ways ex­cit­ing places to vis­it. He had many un­usu­al plants, in­clud­ing one grow­ing up­side-down.

Joe’s son Steve made him an “or­dained min­is­ter” of the Uni­ver­sal Life Church. Someone else made Elsie a “saint.” Joe per­formed sev­er­al mar­riages and was some­times called the “Chap­lain” of the Illinois Math De­part­ment.

Joe was Com­mis­sar of the Sat­urday Hike in the 1950s and/or 1960s. He cre­ated hiker’s de­light, a dish still served today at The Hike. Let me share with you sev­er­al hik­ing ex­per­i­ences I had with Joe.

Clar­ence Ber­dahl was an­oth­er hiker who hiked in­to his nineties. One Sat­urday in 1980, Joe, Clar­ence, who was 90, and I hiked at Lodge Park. While Joe, who was only 70, and I walked around the park Clar­ence lit the camp fire next to a monu­ment mark­ing the grave of an In­di­an squaw. While we were eat­ing hiker’s de­light, a park ranger drove up and walked over to us. As he ap­proached, Joe offered him cof­fee. The ranger de­clined and scol­ded us for build­ing a fire so close to a grave stone. We prom­ised nev­er to do it again. He left without mak­ing us put out the fire. After he had gone, Joe told Clar­ence that he should not have made the fire there, and he ad­ded, “And you’re old enough to know bet­ter!”

An­oth­er Sat­urday in the 1980s the hike went to Em­er­ald Pool in Kicka­poo Park. We parked on the road to Em­er­ald Pool and climbed a hill to reach the camp atop a high cliff over­look­ing the Pool. It had a beau­ti­ful view. That night two park rangers raided our camp. The seni­or one walked up the gently slop­ing trail while the ju­ni­or one climbed the steep cliff to pre­vent our es­cape that way. They told us not to have fires there again. Now we have the fire in a rav­ine near Em­er­ald Pool but just out­side the park bound­ary. Joe was dis­ap­poin­ted that we lost this beau­ti­ful camp.

For many years Joe drove a Check­er car, like a taxi, and took it on the Sat­urday Hike. He had sev­er­al Check­ers, one after the oth­er. I re­call one of them get­ting stuck in the snow on the way to Thomas Farm. A friendly farm­er came out in his tract­or and pulled Joe out of the snow drift and we con­tin­ued to The Hike. The Check­ers could hold many pas­sen­gers. The max­im­um num­ber of hikers I ever heard of in Joe’s Check­er was 16. When Joe’s last Check­er was quite old, rear seat pas­sen­gers could see the road go by un­der them through a hole in the floor.

Joe was a kind of fath­er fig­ure to me. After all, he at­ten­ded the Eth­ic­al Cul­ture School in New York City and gradu­ated from its high school. He gave me much good ad­vice on many eth­ic­al sub­jects.

In Spring 2004, when there was no hike for two con­sec­ut­ive weeks, and I saw Joe on the third week, when The Hike re­sumed, Joe told me that, “The Hike has to out­live me.” Also dur­ing Spring, 2004, he asked me sev­er­al times to con­firm that I was the Com­mis­sar of the Sat­urday Hike.

I learned what he meant in June when I was asked to scat­ter his ashes at one of the hik­ing places. I chose Col­lis­on Trestle, one of Joe’s fa­vor­ite places to hike. His ashes are scattered near the tra­di­tion­al camp fire site and along the bank of the Middle Fork River for half a mile where Joe and I of­ten walked. I dumped the re­main­ing ashes off of the old rail­road trestle in­to the river. Ac­cord­ing to geo­lo­gist Paul Pot­ter, it will take from 20 to 2000 years for his ashes that went in­to the Middle Fork to reach the Gulf of Mex­ico. His ashes must have been turn­ing over when I said a pray­er be­fore scat­ter­ing them.

The tiny pond in the rav­ine be­side our camp near the Plank Bridge in Kicka­poo Park has a fam­ous his­tory. This is what happened there on Feb­ru­ary 4, 1995:

“We came even­tu­ally to a very small, shal­low pond covered with ice. Stand­ing on the ice, I said, ‘This ice will hold all of us.’ I urged the oth­ers to join me to test this bet. Joe bet that I was wrong and then re­fused to step onto the ice, claim­ing that he had won the bet be­cause the ice was not hold­ing him.” I felt that I was bet­ting on the strength of the ice rather than on Joe’s will­ing­ness to step onto the ice and that the bet could not be de­cided un­less all five hikers stood on the ice. I even­tu­ally paid that bet with a de­li­cious pie.

Laurie Snell: Joe com­pleted his un­der­gradu­ate work at Har­vard in 1930. In an in­ter­view Doob said:

“When I gradu­ated and it was time to think about a PhD. de­gree, I asked Stone (Mar­shall) to be my ad­viser. He told me he had no prob­lems for me, that I should go to J. L. Walsh, who al­ways had many prob­lems. Walsh ac­cep­ted me and we had a fine re­la­tion­ship: he nev­er bothered me, and con­versely.”

In 1931 Doob re­ceived his Mas­ters de­gree and mar­ried Elsie Field. Doob told me that he sat next to Elsie at the Bo­ston Sym­phony for two years be­fore they spoke to each oth­er. Joe com­pleted his PhD in 1932 and then spent two years on a re­search fel­low­ship at Columbia, spend­ing some time also at Prin­ceton. After that Doob could not get a job be­cause of the de­pres­sion but found sup­port for an­oth­er year at Columbia on a grant of the stat­ist­i­cian Har­old Ho­telling. So the de­pres­sion led Doob to prob­ab­il­ity.

In 1935 Doob star­ted his aca­dem­ic ca­reer at the Uni­versity of Illinois where he soon had three out­stand­ing prob­ab­il­ity stu­dents: Paul Hal­mos, War­ren Am­brose and Dav­id Black­well. All three had been un­der­gradu­ates at Illinois.

In his book I want to be a math­em­atician, Paul Hal­mos de­scribes Doob’s ar­rival at the Uni­versity of Illinois math de­part­ment.

“This boy came in look­ing like a gradu­ate stu­dent, crew cut shirt sleeves and all. He was 25 years old at the time, I later learned, but he looked 19 or 20. A few days after Doob’s ar­rival my di­ary starts hav­ing many entries such as: ‘shoot bull with Doob,’ and ‘Doob’s class good.’ In one of our early squash games I missed a shot and swore in ex­as­per­a­tion. ‘Just call me Joe.’ He said. We talked about math­em­at­ics, not to the ex­clu­sion of polit­ics and mu­sic and pro­fes­sion­al gos­sip and many oth­er hu­man con­cerns, but more than about any­thing else.”

Ac­cord­ing to a story that Naresh Jain sent the hikers, Joe later pro­moted him­self. Naresh writes about an ex­per­i­ence on the hike: One time Joe and Robert Kauf­man were in a heated dis­cus­sion about kids to be re­quired to learn the clas­sics. Robert was all for it and Joe was do­ing everything to pro­voke him. In dis­gust, Robert said: “Oh my God” and Joe calmly replied, “Don’t ex­ag­ger­ate, just call me ‘Pro­fess­or.’ ”

Hal­mos also wrote:

“Doob has an out­go­ing, re­laxed per­son­al­ity; he seems to get along eas­ily with every­one. He seems to take noth­ing ser­i­ously, but he takes every­one equally ser­i­ously.

“As an ex­ample of this, Doob used to tell us that he got his first job based on a wrong the­or­em.

“I once asked Doob what it was like to have such great gradu­ate stu­dents. He said ‘we were all very young and a bit wild.’ ”

Snell con­tin­ues: I must say that in re­view­ing Doob’s pa­pers for this art­icle I found them very hard to read even though I thought I knew much of the ma­ter­i­al. At a Math Col­loqui­um at the U of I in 1997, with Doob in the audi­ence, his friend Kai Lai Chung re­marked that one of­ten hears that Doob’s pa­pers are hard to read. In the writ­ten ac­count of Chung’s talk we read: “Writ­ing this sud­denly put me in mind of my oth­er ex­per­i­ence of read­ing Mar­cel Proust’s in­ter­min­able recher­che of his TIME. Both au­thors are long-win­ded, long-drawn-out, and palp­ably long-suf­fer­ing, and yet both suc­ceed in mak­ing a pro­found and last­ing im­pact, and prove fi­nally re­ward­ing. Doob told me that he had read Proust but found him ‘bor­ing.’ Some read­ers might say the same of Doob. Proust may be read for his style, no mat­ter the con­tent; Doob should be read for his con­tent, no mat­ter the style.”

Am­brose, writ­ing in Hal­mos, Cel­eb­rat­ing 50 years of Math­em­at­ics ex­presses his and Paul’s ap­pre­ci­ation of Doob in a way that most of his stu­dents would ap­pre­ci­ate: “An­oth­er top­ic that I wish to men­tion is the ap­pre­ci­ation that Paul and I both feel to Joe Doob for what he has taught us, mainly in math­em­at­ics but also out­side math­em­at­ics. Of all the people who have in­flu­enced our math­em­at­ic­al and oth­er in­tel­lec­tu­al de­vel­op­ment, Joe stands out. Be­fore Doob, neither of us had ever en­countered such a force­ful thinker. All our pre­vi­ous opin­ions about the world had to be mod­i­fied by the ser­i­ous cri­ti­cism he made of them.”

Snell con­tin­ues: I was one of Doob’s gradu­ate stu­dents dur­ing the years 1948–1951. These were busy times for the Doobs. They had three chil­dren, and Elsie was a phys­i­cian of In­tern­al Medi­cine at the Carle Clin­ic in Urb­ana. The Doobs were gen­er­ous with their hos­pit­al­ity and I was of­ten in­vited to din­ner. At first I could not un­der­stand why Joe and Elsie called each oth­er thee and thou and why Joe of­ten washed the dishes. The thee and thou was ex­plained by the fact that Elsie came from a Quaker fam­ily. As for why Doob washed the dishes, I guess he was just ahead of his time.

At the same time Doob was writ­ing Stochast­ic pro­cesses, Elsie was try­ing to find her broth­ers, Noel and Her­mann Field, who had dis­ap­peared be­hind the Iron Cur­tain. Doob did not be­lieve in us­ing sec­ret­ar­ies. He wrote the first draft of Stochast­ic Pro­cesses us­ing a pen­cil, writ­ing on plain pa­per. He turned these in­to pa­per air­planes that the chil­dren used in air­plane fights. When he typed (pick punch) the fi­nal ver­sion he in­ven­ted a kind of mini­ature TeX which was highly praised by the print­er.

In the pre­face of his Clas­sic­al po­ten­tial and its prob­ab­il­ist­ic coun­ter­part,2 a book with over 840 pages, Doob thanks his typ­ist “usu­ally faith­ful, some­times ac­cur­ate.” He was dis­ap­poin­ted when he found only one per­son who re­cog­nized that Doob was thank­ing him­self.

This book was sup­posed to be a joint book with his friend, the well-known French po­ten­tial the­or­ist Mar­cel Brelot. Brelot was also known for his wild driv­ing and at a po­ten­tial the­ory con­fer­ence in France, Doob in­tro­duced Brelot by say­ing “I nev­er really un­der­stood the con­nec­tion between Browni­an mo­tion and po­ten­tial the­ory un­til I rode with Brelot.”

Joe had many chances to leave Illinois. He was temp­ted by MIT but said he de­cided he would not be able to ride his bike in Cam­bridge. In the in­ter­view he re­marks:

“I was charmed by the small-town at­mo­sphere of Urb­ana as soon as I ar­rived and nev­er wanted to leave, even though the at­mo­sphere changed through the years.”

His fa­vor­ite ex­ample of this was the soup that a neigh­bor brought over when they moved in­to their house.

The Doobs made sev­er­al trips to New Hamp­shire not far from where we lived. In 1959 Elsie was dia­gnosed with can­cer. She was giv­en the choice of two years to live if she had ra­di­ation treat­ment or one year oth­er­wise. She chose the one year and de­cided to spend the sum­mer with Joe in the moun­tains of New Hamp­shire. Joe and Elsie showed us many new places for pic­nics and in­sisted that we sup­port all the small town the­at­ric­al groups in the area. Joe loved to lec­ture the res­taur­ants on how much bet­ter real Ver­mont cheese was than Wis­con­sin cheese they were serving. In­stead of one year Elsie lived some 30 years longer.

I vis­ited Joe a month be­fore he died. He was still driv­ing and I guess I had the same feel­ing Joe had while driv­ing with Brelot. However, he was his old self in every oth­er way — anxious to talk about polit­ics, his chil­dren, the Illinois Hike, his garden, and his latest soft­ware for his be­loved Mac.

In the early time-shar­ing com­puter sys­tem at Dart­mouth you could type in an ex­pres­sion like “Edit ex­plain life” and you got the an­swer “Life is a su­per­martin­gale” (an un­fa­vor­able game). I tried to think what I would put in for “Edit ex­plain Doob”. I think my wife Joan sug­ges­ted the best an­swer: “An ex­traordin­ar­ily straight­for­ward guy.”

This ends the con­tri­bu­tions of Laurie Snell and the oth­er in­vited speak­ers, in­clud­ing those who were not able to at­tend but who did con­trib­ute by oth­er means.

Doob en­joyed play­ing the re­cord­er al­though he claimed he was not so good at it. He would have en­joyed the beau­ti­ful re­cord­er play­ing of Elise Lau­t­er­bur who played sev­er­al se­lec­tions from the many re­cord­er pieces that Jac­ob van Eyck com­posed dur­ing the 17th cen­tury.

This brought to the end the form­al part of the Cel­eb­ra­tion. The in­form­al part came im­me­di­ately after with more than an hour de­voted to con­ver­sa­tion, food, and drink.